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# Hydraulic Machines-Turbines

Hydraulic Machines-Turbines

Contents

Classify Turbine and Pump 3

Explain the Hydroelectric Power 4

Explain the general layout of Hydroelectric Power Plant 5

Define the Efficiency of Turbine 7

Explain the different types of Efficiency of a Turbine 8

Classify the Hydraulic Turbines 9

Explain the working of the Pelton Wheel 10

Describe the Velocity Triangles and Work done for a Pelton Wheel 11

Explain the Maximum Efficiency of the Pelton Wheel 12

Describe the procedure for Designing of Pelton Wheel 12

Explain the Reaction Turbines and its Components 13

Explain the Function of the Draft Tube 14

List various types of Draft Tube 15

Describe the Efficiency of the Draft Tube 16

Explain the working of the Francis Turbine 17

Describe the Velocity Triangles and Work done for a Francis Turbine 18

Explain the Efficiency of the Francis Turbine 19

Describe Working Proportion of Francis Turbine 20

Explain the Analysis of the Francis Turbine 21

Explain Axial-Flow Turbines (Kaplan and Propeller Turbine) 22

Describe working Proportions of Kaplan Turbine 23

Explain the Specific Speed of a Turbine 23

Explain the Non-dimensional Specific speed (Shape number) of a Turbine 25

List and explain the different types of Unit Quantities 26

Explain Model Testing of the Turbines 27

Explain the Cavitation in Turbine 27

Define Thomas Cavitation Factor 28

# Define Hydraulic Machines, Turbines, and Pumps

In fluid mechanics, hydraulic machines are devices that use the energy of a fluid flow to perform work. There are two main types of hydraulic machines: turbines and pumps.

1. Turbines: Turbines are hydraulic machines that convert the kinetic energy of a fluid flow into mechanical energy. This is achieved by the fluid flowing over a set of blades, which rotates a shaft. There are several types of turbines, including water turbines, steam turbines, and gas turbines. The most common application of turbines is in the generation of electricity in hydroelectric power plants.
2. Pumps: Pumps are hydraulic machines that convert mechanical energy into the pressure energy of a fluid. This is achieved by compressing the fluid and increasing its pressure. Pumps are used in a variety of applications, including water supply, irrigation, and industrial processes. There are several types of pumps, including centrifugal pumps, reciprocating pumps, and positive displacement pumps.

Both turbines and pumps are important components in fluid systems, as they are used to control the flow and pressure of fluids. The design and optimization of hydraulic machines is an important area of study in fluid mechanics, as the efficiency and performance of these machines can greatly impact the overall efficiency and cost-effectiveness of fluid systems.

# Classify Turbine and Pump

Turbines and pumps can be classified based on several criteria, including the type of fluid flow, the design of the blades, the direction of fluid flow, and the type of energy conversion that takes place.

Classification of Turbines:

1. Based on fluid flow: Turbines can be classified based on the type of fluid flow, including radial flow turbines, axial flow turbines, and mixed flow turbines. Radial flow turbines have blades that are perpendicular to the axis of rotation, while axial flow turbines have blades that are parallel to the axis of rotation. Mixed flow turbines have blades that are positioned at an angle between radial and axial.
2. Based on blade design: Turbines can be classified based on the design of the blades, including impulse turbines and reaction turbines. Impulse turbines have blades that are struck by the fluid flow, while reaction turbines have blades that generate lift in the fluid flow.
3. Based on direction of fluid flow: Turbines can be classified based on the direction of fluid flow, including inward flow turbines and outward flow turbines. Inward flow turbines have fluid entering the center of the turbine, while outward flow turbines have fluid flowing outwards from the center of the turbine.
4. Based on energy conversion: Turbines can be classified based on the type of energy conversion that takes place, including kinetic energy turbines and potential energy turbines. Kinetic energy turbines convert the kinetic energy of the fluid into mechanical energy, while potential energy turbines convert the potential energy of the fluid into mechanical energy.

Classification of Pumps:

1. Based on fluid flow: Pumps can be classified based on the type of fluid flow, including positive displacement pumps and dynamic pumps. Positive displacement pumps trap a fixed volume of fluid and compress it, while dynamic pumps increase the velocity of the fluid to increase its pressure.
2. Based on design: Pumps can be classified based on their design, including centrifugal pumps, reciprocating pumps, and gear pumps. Centrifugal pumps use a rotating impeller to increase the pressure of the fluid, while reciprocating pumps use a piston to compress the fluid. Gear pumps use intermeshing gears to move the fluid.
3. Based on application: Pumps can be classified based on their application, including water pumps, oil pumps, and gas pumps.

Classifying turbines and pumps based on these criteria can help engineers and scientists to better understand their behavior and select the most appropriate type for a given application.

# Explain the Hydroelectric Power

Hydroelectric power is a form of renewable energy that uses the kinetic energy of falling water to generate electricity. It is one of the most widely used forms of renewable energy, and is considered a clean and sustainable source of power.

The basic principle behind hydroelectric power is to convert the kinetic energy of falling water into mechanical energy, which can then be used to generate electricity. This is typically achieved by constructing a dam across a river, which creates a reservoir of water. The water is allowed to fall from a height, creating kinetic energy. This kinetic energy is then used to turn a turbine, which rotates a generator to produce electricity.

There are several factors that can impact the efficiency and effectiveness of a hydroelectric power plant, including the height of the dam, the volume of water available, the flow rate of the water, and the design of the turbine.

Hydroelectric power has several advantages over other forms of energy. It is a clean and renewable source of energy, and does not produce any emissions or contribute to air pollution. It is also relatively low cost and requires minimal maintenance, which makes it a reliable source of power.

However, there are also some challenges associated with hydroelectric power, including the need for large dams, which can impact the environment and displace local communities. Additionally, the availability of water can be impacted by changes in the weather, which can affect the output of the hydroelectric power plant.

Despite these challenges, hydroelectric power remains an important and widely used source of renewable energy, and continues to be an important area of study and research in the field of fluid mechanics.

# Explain the general layout of Hydroelectric Power Plant

The general layout of a hydroelectric power plant typically includes the following components:

1. Dam: A dam is typically constructed across a river to create a reservoir of water. The dam serves as the foundation for the power plant and provides a means to store and regulate the flow of water.
2. Reservoir: The reservoir serves as a storage facility for the water that will be used to generate electricity. It allows the water to be regulated, so that the flow rate can be controlled to optimize the generation of electricity.
3. Penstock: The penstock is a pipe or channel that carries water from the reservoir to the turbine. It is designed to minimize the loss of energy in the water as it flows from the reservoir to the turbine.
4. Turbine: The turbine is the main component of a hydroelectric power plant, and is responsible for converting the kinetic energy of the water into mechanical energy. The turbine is typically located at the base of the dam and is connected to a generator by a shaft.
5. Generator: The generator converts the mechanical energy from the turbine into electricity. It typically consists of a rotor and a stator, with the rotor being driven by the shaft from the turbine, and the stator containing the electrical coils that generate the electricity.
6. Control and Monitoring System: A control and monitoring system is used to regulate the flow of water and control the operation of the turbine and generator. The system may include sensors, controllers, and other components that help to ensure the safe and efficient operation of the power plant.
7. Transmission Lines: The electricity generated by the generator is typically transmitted from the power plant to the electrical grid via high-voltage transmission lines. These lines are designed to carry the electricity over long distances, so that it can be distributed to homes, businesses, and other consumers.

This general layout of a hydroelectric power plant provides a basic overview of the components and systems involved in the generation of electricity from falling water. The specific design and configuration of a hydroelectric power plant will depend on a variety of factors, including the location, the volume and flow rate of the water, and the desired output of the power plant.

In fluid mechanics, “head” refers to the height difference between two points in a fluid system. This height difference can be used to determine the potential energy and kinetic energy of the fluid.

1. Gross Head: Gross head refers to the total height difference between the inlet and outlet points of a fluid system, including the dam or reservoir. It is the total energy available to the system and is expressed in units of length, such as meters.
2. Net Head: Net head refers to the actual height difference that is available for the conversion of potential energy into kinetic energy. It is calculated by subtracting the losses in the system, such as friction and turbulence, from the gross head. The net head is an important parameter in determining the efficiency of a fluid system, such as a hydroelectric power plant.

In a hydroelectric power plant, the gross head is the height difference between the surface of the water in the reservoir and the outlet of the penstock. The net head is the actual height difference that is available for the conversion of potential energy into kinetic energy, after taking into account the losses in the system. The net head is used to calculate the flow rate, velocity, and power output of the system.

It is important to understand the difference between gross head and net head in order to accurately design and operate a fluid system, such as a hydroelectric power plant. The gross head provides information about the total energy available in the system, while the net head provides information about the actual energy that can be used for the generation of electricity.

# Define the Efficiency of Turbine

The efficiency of a turbine refers to the percentage of the energy input that is converted into useful output. In the case of hydraulic turbines, the energy input is the potential and kinetic energy of the water, while the useful output is the mechanical energy that is transferred to a generator to produce electricity.

Turbine efficiency is an important performance parameter because it directly affects the amount of electricity that can be generated for a given flow rate and head. A higher efficiency means that more of the energy in the water is converted into electricity, which results in a higher power output.

The efficiency of a turbine can be calculated by dividing the output power by the input power. The input power is the sum of the potential and kinetic energy of the water, while the output power is the mechanical energy that is transferred to the generator. The efficiency of a turbine is usually expressed as a percentage and can range from 60% to 90% depending on the type of turbine and the operating conditions.

Turbine efficiency is influenced by various factors, such as the design of the turbine, the flow rate and head, the operating speed, and the presence of losses due to turbulence and friction. The efficiency of a turbine can be improved by optimising the design, reducing losses, and operating the turbine at the optimal speed and flow rate.

In conclusion, the efficiency of a turbine is a key performance parameter that determines the amount of electricity that can be generated for a given flow rate and head. A higher efficiency means that more of the energy in the water is converted into useful output, which results in a higher power output.

# Explain the different types of Efficiency of a Turbine

There are several types of efficiencies associated with a turbine, which are used to evaluate the performance of the turbine under different conditions. The most common types of efficiencies are:

1. Hydraulic Efficiency: Hydraulic efficiency refers to the proportion of the energy input that is converted into useful output. It is calculated by dividing the output power by the input power, which is the sum of the potential and kinetic energy of the water. Hydraulic efficiency is usually expressed as a percentage and ranges from 60% to 90% depending on the type of turbine and the operating conditions.
2. Mechanical Efficiency: Mechanical efficiency refers to the proportion of the output power that is transferred to the generator. It is calculated by dividing the mechanical power delivered to the generator by the output power. Mechanical efficiency is usually expressed as a percentage and ranges from 90% to 99% depending on the type of generator and the operating conditions.
3. Overall Efficiency: Overall efficiency is the product of hydraulic efficiency and mechanical efficiency. It represents the proportion of the energy input that is converted into useful output in the form of electrical power. Overall efficiency is usually expressed as a percentage and ranges from 50% to 90% depending on the type of turbine, the operating conditions, and the presence of losses.
4. Energy Conversion Efficiency: Energy conversion efficiency is the proportion of the energy input that is converted into useful output in the form of electrical power. It is calculated by dividing the electrical power output by the input power, which is the sum of the potential and kinetic energy of the water. Energy conversion efficiency is usually expressed as a percentage and ranges from 50% to 90% depending on the type of turbine, the operating conditions, and the presence of losses.
5. Turbine-Generator Efficiency: Turbine-generator efficiency refers to the proportion of the output power that is transferred to the generator and converted into electrical power. It is calculated by dividing the electrical power output by the output power. Turbine-generator efficiency is usually expressed as a percentage and ranges from 90% to 99% depending on the type of generator and the operating conditions.

In conclusion, there are several types of efficiencies associated with a turbine, each of which provides different information about the performance of the turbine under different conditions. The most common types of efficiencies are hydraulic efficiency, mechanical efficiency, overall efficiency, energy conversion efficiency, and turbine-generator efficiency. Understanding these efficiencies is important for optimising the performance of a turbine and maximising the energy conversion efficiency.

# Classify the Hydraulic Turbines

Hydraulic turbines are classified into several categories based on the type of fluid flow and the way in which the fluid imparts its energy to the turbine blades. The most common types of hydraulic turbines are:

1. Impulse Turbines: Impulse turbines, also known as Pelton turbines, are designed to work with high-head, low-flow applications. The fluid flow is directed onto the blades of the turbine with high velocity, which generates a high-pressure drop and a high-velocity jet. The high-velocity jet is then redirected onto the blades of the runner, causing it to rotate and generate mechanical power.
2. Reaction Turbines: Reaction turbines are designed to work with low-head, high-flow applications. The fluid flow is directed onto the blades of the runner, which creates both lift and drag forces. The lift forces cause the runner to rotate and generate mechanical power, while the drag forces reduce the fluid velocity and convert it into pressure.
3. Mixed Flow Turbines: Mixed flow turbines are a combination of impulse and reaction turbines. They are designed to work with intermediate-head, intermediate-flow applications. The fluid flow enters the turbine axially and exits radially, causing both lift and drag forces on the runner blades. The lift and drag forces combine to generate mechanical power.
4. Radial Flow Turbines: Radial flow turbines are designed to work with high-head, high-flow applications. The fluid flow enters the turbine radially and exits axially, causing both lift and drag forces on the runner blades. The lift and drag forces combine to generate mechanical power.
5. Axial Flow Turbines: Axial flow turbines are designed to work with low-head, low-flow applications. The fluid flow enters the turbine axially and exits axially, causing only drag forces on the runner blades. The drag forces cause the runner to rotate and generate mechanical power.

In conclusion, hydraulic turbines are classified into several categories based on the type of fluid flow and the way in which the fluid imparts its energy to the turbine blades. The most common types of hydraulic turbines are impulse turbines, reaction turbines, mixed flow turbines, radial flow turbines, and axial flow turbines. Understanding these classifications is important for selecting the appropriate type of turbine for a given application and optimising its performance.

# Explain the working of the Pelton Wheel

The Pelton wheel is a type of impulse turbine that is used to convert the kinetic energy of high-head, high-velocity water into mechanical energy. The Pelton wheel operates on the principle of a high-velocity jet of water striking and splitting into two parts on the buckets of the runner.

The following is the step-by-step working of a Pelton wheel:

1. High-pressure water from a reservoir or a pipeline is directed through a nozzle onto the runner of the Pelton wheel.
2. The nozzle converts the pressure energy of the water into kinetic energy, resulting in a high-velocity jet of water.
3. The high-velocity jet of water strikes the buckets of the runner, splitting into two parts. The first part of the jet continues to flow over the bucket and the second part flows along the bucket.
4. The split jet of water exerts a force on the buckets, causing the runner to rotate. The force generated is proportional to the square of the velocity of the water.
5. As the runner rotates, the buckets move out of the way of the incoming water, allowing the water to escape and continue its flow through the turbine.
6. The mechanical energy generated by the Pelton wheel is transferred to a shaft that connects to a generator. The generator converts the mechanical energy into electrical energy, which can be used for various applications.

In conclusion, the Pelton wheel is a type of impulse turbine that converts the kinetic energy of high-head, high-velocity water into mechanical energy. The high-velocity jet of water splits into two parts on the buckets of the runner, generating a force that causes the runner to rotate. The mechanical energy generated is then transferred to a generator, which converts it into electrical energy.

# Describe the Velocity Triangles and Work done for a Pelton Wheel

The velocity triangles and work done in a Pelton wheel can be described as follows:

1. Velocity Triangles: Velocity triangles are graphical representations of the velocity vectors of fluid particles at different points in a hydraulic turbine. In a Pelton wheel, the velocity triangles can be used to calculate the work done by the water jet on the buckets.
2. Incoming Velocity Triangle: The incoming velocity triangle represents the velocity of the water jet just before it enters the bucket. It is represented by a vector, which is the sum of the velocity of the jet in the axial direction and the velocity of the jet in the radial direction.
3. Outgoing Velocity Triangle: The outgoing velocity triangle represents the velocity of the water jet just after it leaves the bucket. It is represented by a vector, which is the sum of the velocity of the jet in the axial direction and the velocity of the jet in the radial direction.
4. Work done: The work done by the water jet on the buckets can be calculated using the velocity triangles. The work done is equal to the product of the force exerted by the jet and the distance travelled by the bucket. The force exerted by the jet can be calculated using the velocity triangles.
5. The difference between the incoming and outgoing velocities of the water jet represents the velocity change of the water, which is proportional to the work done. The work done is proportional to the square of the velocity of the water.

In conclusion, the velocity triangles and work done in a Pelton wheel are essential concepts in the understanding of the operation of this type of hydraulic turbine. The velocity triangles represent the velocity vectors of fluid particles at different points in the turbine and are used to calculate the work done by the water jet on the buckets. The work done is proportional to the square of the velocity of the water and is an important factor in the efficiency of the Pelton wheel.

# Explain the Maximum Efficiency of the Pelton Wheel

Explain the Maximum Efficiency of the Pelton Wheel is an educational objective that focuses on the understanding of the highest level of energy conversion that can be achieved in a Pelton wheel, a type of hydraulic turbine used for the generation of hydroelectric power.

A Pelton wheel is a type of impulse turbine that works by shooting a high-velocity jet of water against spoon-shaped buckets attached to a wheel. The impact of the water on the buckets produces a torque that rotates the wheel and generates mechanical energy. The efficiency of the Pelton wheel is a measure of how much of the energy of the water is converted into mechanical energy and how much is lost as friction, turbulence, and other forms of energy dissipation.

The maximum efficiency of the Pelton wheel occurs when all the energy of the water is converted into mechanical energy, and no energy is lost as friction or turbulence. This condition can be achieved by designing the Pelton wheel with the appropriate geometry, flow rate, and operating conditions. The key factors that affect the maximum efficiency of the Pelton wheel include the size and shape of the buckets, the speed and flow rate of the water, and the pressure drop across the turbine.

To achieve the maximum efficiency, the Pelton wheel must be designed with the right size and shape of the buckets to minimize the losses due to friction and turbulence. The speed of the water must also be optimised to ensure that the impact of the water on the buckets is as forceful as possible, while still avoiding overloading the wheel. Additionally, the flow rate of the water must be adjusted to match the capacity of the turbine and avoid excessive losses due to turbulence and pressure drop.

In summary, the maximum efficiency of the Pelton wheel is achieved by optimising the design of the turbine, the speed and flow rate of the water, and the pressure drop across the turbine. By doing so, it is possible to maximise the conversion of the energy of the water into mechanical energy and minimize the losses due to friction and turbulence.

# Describe the procedure for Designing of Pelton Wheel

Describe the Procedure for Designing of Pelton Wheel refers to the process of creating the specifications and plans for the construction of a Pelton wheel, a type of hydraulic turbine used for the generation of hydroelectric power.

The design of a Pelton wheel involves several steps, including:

1. Determining the flow rate and head of the water: The first step in designing a Pelton wheel is to determine the flow rate and head of the water that will be used to drive the turbine. This information is necessary to determine the size and speed of the turbine and the size and shape of the buckets.
2. Selecting the number of buckets: The number of buckets on the Pelton wheel affects the efficiency and power output of the turbine. The designer must choose the appropriate number of buckets to ensure optimal performance.
3. Designing the bucket shape: The shape of the bucket is a critical factor in the performance of the Pelton wheel. The designer must choose the appropriate bucket shape to ensure maximum efficiency and to minimize losses due to friction and turbulence.
4. Determining the speed and torque: The designer must determine the speed and torque of the turbine based on the flow rate, head, and bucket design. This information is necessary to ensure that the turbine operates within safe and efficient limits.
5. Selecting the material: The designer must choose the appropriate material for the construction of the Pelton wheel. This includes the selection of materials for the shaft, bearings, and other components of the turbine.
6. Finalising the design: The final step in the design process is to refine the specifications and plans for the construction of the Pelton wheel. This may involve further calculations, simulations, and testing to ensure that the turbine meets the desired performance and efficiency requirements.

In summary, the procedure for designing a Pelton wheel involves determining the flow rate and head of the water, selecting the number of buckets, designing the bucket shape, determining the speed and torque, selecting the material, and finalising the design. The designer must consider various factors such as efficiency, power output, and safety in order to create a Pelton wheel that meets the desired performance and efficiency requirements.

# Explain the Reaction Turbines and its Components

Explain the Reaction Turbines and its Components refers to the study of reaction turbines, a type of hydraulic turbine that converts the energy of flowing water into mechanical energy.

Reaction turbines are hydraulic turbines that operate on the principle of fluid reaction. In reaction turbines, water enters the turbine through a nozzle or an inlet and flows through the runner blades, creating a pressure drop that drives the turbine. The runner blades are shaped in such a way that they cause the fluid to change direction, producing a force that rotates the runner and generates mechanical energy.

The main components of a reaction turbine are:

1. Inlet: The inlet is the point where the water enters the turbine. The inlet can be a nozzle or an opening that guides the water into the turbine.
2. Runner: The runner is the rotating part of the turbine that converts the energy of the water into mechanical energy. The runner is typically made up of a disc with blades or buckets attached to it.
3. Guide vanes: The guide vanes are stationary blades that control the flow of water into the runner. The guide vanes are designed to direct the water onto the runner blades in an efficient manner, minimising losses due to friction and turbulence.
4. Draft tube: The draft tube is a cone-shaped tube that surrounds the runner and collects the water after it has passed through the runner. The draft tube helps to slow down the flow of the water, reducing the turbulence and pressure losses in the system.
5. Casing: The casing is the outer shell of the turbine that houses the runner, guide vanes, and draft tube. The casing is designed to protect the turbine from external damage and to minimize losses due to friction and turbulence.

In summary, reaction turbines are hydraulic turbines that convert the energy of flowing water into mechanical energy by utilising the principle of fluid reaction. The main components of a reaction turbine include the inlet, runner, guide vanes, draft tube, and casing, each of which plays a crucial role in the performance and efficiency of the turbine.

# Explain the Function of the Draft Tube

Explain the Function of the Draft Tube refers to the study of the purpose and role of the draft tube in hydraulic turbines, particularly reaction turbines.

A draft tube is a cone-shaped tube that surrounds the runner of a reaction turbine and collects the water after it has passed through the runner. The draft tube plays a crucial role in the performance and efficiency of the turbine.

The main function of the draft tube is to slow down the flow of the water after it has passed through the runner. The reduction in velocity of the water helps to reduce the turbulence and pressure losses in the system, improving the overall efficiency of the turbine.

Additionally, the draft tube also helps to convert the pressure energy of the water into kinetic energy. This allows the water to be discharged from the turbine at a lower velocity, reducing the losses due to friction and turbulence.

The design of the draft tube is critical to the performance and efficiency of the turbine. The shape, size, and curvature of the draft tube must be carefully selected to ensure that the flow of water is optimised and the losses are minimised.

In summary, the draft tube is a cone-shaped tube that surrounds the runner of a reaction turbine and collects the water after it has passed through the runner. The main function of the draft tube is to slow down the flow of the water, reduce the turbulence and pressure losses in the system, and convert the pressure energy of the water into kinetic energy. The design of the draft tube is critical to the performance and efficiency of the reaction turbine.

# List various types of Draft Tube

List various types of Draft Tube refers to the study of the different types of draft tubes used in hydraulic turbines, particularly reaction turbines.

Draft tubes are cone-shaped tubes that surround the runner of a reaction turbine and collect the water after it has passed through the runner. The draft tube plays a crucial role in the performance and efficiency of the turbine.

There are several types of draft tubes used in hydraulic turbines, including:

1. Straight draft tube: The straight draft tube is the simplest and most basic type of draft tube. It consists of a straight, cone-shaped tube that is attached directly to the runner.
2. Bell-shaped draft tube: The bell-shaped draft tube is a more complex and efficient type of draft tube. It consists of a bell-shaped tube that is attached to the runner and has a larger diameter at the outlet than at the inlet.
3. Diffuser draft tube: The diffuser draft tube is a type of draft tube that has a gradually increasing diameter from the inlet to the outlet. This design allows the water to decelerate gradually, reducing the turbulence and pressure losses in the system.
4. Vortex draft tube: The vortex draft tube is a type of draft tube that is designed to create a vortex in the flow of water. The vortex helps to reduce the turbulence and pressure losses in the system, improving the overall efficiency of the turbine.
5. Coanda draft tube: The Coanda draft tube is a type of draft tube that is designed to follow the principle of the Coanda effect. The Coanda effect states that a fluid will tend to follow a curved surface if it is in close proximity to it. This type of draft tube takes advantage of the Coanda effect to reduce the turbulence and pressure losses in the system.

In summary, there are several types of draft tubes used in hydraulic turbines, including the straight draft tube, bell-shaped draft tube, diffuser draft tube, vortex draft tube, and Coanda draft tube. Each type of draft tube has its own unique design and function, and the choice of draft tube depends on the specific requirements of the turbine and the desired level of efficiency.

# Describe the Efficiency of the Draft Tube

Describe the Efficiency of the Draft Tube refers to the study of the impact of the draft tube on the performance and efficiency of hydraulic turbines, particularly reaction turbines.

The draft tube is a cone-shaped tube that surrounds the runner of a reaction turbine and collects the water after it has passed through the runner. The design and performance of the draft tube have a significant impact on the overall efficiency of the turbine.

The main function of the draft tube is to slow down the flow of the water after it has passed through the runner. The reduction in velocity of the water helps to reduce the turbulence and pressure losses in the system, improving the overall efficiency of the turbine.

The efficiency of the draft tube depends on several factors, including its design, the flow rate of the water, and the operating conditions of the turbine. A well-designed draft tube can increase the efficiency of the turbine by reducing the losses due to turbulence and pressure drops.

Additionally, the choice of the type of draft tube is also critical to the efficiency of the turbine. Different types of draft tubes, such as the straight draft tube, bell-shaped draft tube, diffuser draft tube, vortex draft tube, and Coanda draft tube, have different designs and functions, and the choice of draft tube depends on the specific requirements of the turbine and the desired level of efficiency.

In summary, the draft tube is a crucial component of a reaction turbine that has a significant impact on its efficiency. The efficiency of the draft tube depends on its design, the flow rate of the water, and the operating conditions of the turbine, as well as the choice of the type of draft tube. A well-designed draft tube can increase the efficiency of the turbine by reducing the losses due to turbulence and pressure drops.

# Explain the working of the Francis Turbine

Explain the working of the Francis Turbine refers to the study of the functioning and operation of the Francis turbine, a type of hydraulic turbine used to convert the energy of falling water into mechanical energy.

The Francis turbine is a reaction turbine that is designed to work with high-head and medium-flow applications. It consists of a runner with radial vanes, a volute casing, and an inlet pipe.

The operation of the Francis turbine can be described as follows:

1. Water from a high-head source enters the inlet pipe and flows into the turbine. The inlet pipe guides the water to the runner, and the radial vanes direct the flow of water onto the blades of the runner.
2. As the water flows over the blades of the runner, it creates a reaction force that rotates the runner and the attached shaft. The speed of the runner is proportional to the flow rate of the water, and the direction of the runner rotation is determined by the direction of the flow of the water.
3. The water then exits the runner and flows into the volute casing, which is shaped like a spiral. The volute casing guides the flow of water and helps to convert the velocity energy of the water into pressure energy.
4. The water then exits the volute casing and is returned to the river or other water source. The mechanical energy generated by the turbine is transferred to a generator, which converts the mechanical energy into electrical energy.

In summary, the Francis turbine is a reaction turbine that converts the energy of falling water into mechanical energy. It consists of a runner with radial vanes, a volute casing, and an inlet pipe. The operation of the Francis turbine involves directing the flow of water onto the blades of the runner, which creates a reaction force that rotates the runner. The volute casing guides the flow of water and helps to convert the velocity energy of the water into pressure energy, and the mechanical energy generated by the turbine is transferred to a generator to convert it into electrical energy.

# Describe the Velocity Triangles and Work done for a Francis Turbine

Describe the Velocity Triangles and Work done for a Francis Turbine refers to the study of the flow of water through a Francis turbine and the calculation of the work done by the turbine.

The velocity triangles for a Francis turbine are graphical representations of the velocity of the water at different points in the turbine. These triangles are used to calculate the work done by the turbine by considering the change in velocity and direction of the water as it passes through the turbine.

The velocity triangles are created by considering three points in the turbine: the inlet, the outlet, and the blade. The velocity vectors of the water at each of these points are drawn and the angles between them are measured. The velocity triangles can then be used to calculate the work done by the turbine by considering the change in velocity and direction of the water as it passes through the runner.

The work done by a Francis turbine can be calculated using the equation for work done by a system, which is W = m * Δv, where m is the mass flow rate of the water and Δv is the change in velocity of the water as it passes through the turbine. The work done by the turbine can be expressed in terms of hydraulic power, which is the product of the flow rate and the head, or the difference in height between the inlet and the outlet of the turbine.

In summary, the velocity triangles and work done for a Francis turbine are used to calculate the flow of water through the turbine and the work done by the turbine. The velocity triangles are graphical representations of the velocity of the water at different points in the turbine, and the work done by the turbine is calculated using the equation for work done by a system, which considers the change in velocity and direction of the water as it passes through the runner.

# Explain the Efficiency of the Francis Turbine

Explain the Efficiency of the Francis Turbine refers to the study of the performance of a Francis turbine and how to calculate its efficiency.

The efficiency of a Francis turbine is defined as the ratio of the hydraulic power output to the mechanical power input. The hydraulic power output is the product of the flow rate and the head, or the difference in height between the inlet and the outlet of the turbine. The mechanical power input is the power generated by the turbine’s runner, which is driven by the flow of water.

The efficiency of a Francis turbine can be expressed in terms of the hydraulic efficiency, which is the ratio of the hydraulic power output to the theoretical hydraulic power, and the mechanical efficiency, which is the ratio of the mechanical power output to the mechanical power input.

The hydraulic efficiency of a Francis turbine can be influenced by several factors, such as the head, the flow rate, the diameter of the runner, and the design of the runner blades. To improve the hydraulic efficiency of a Francis turbine, it is important to optimize the design of the runner blades and the shape of the runner, and to minimize losses due to friction and turbulence.

The mechanical efficiency of a Francis turbine can be influenced by factors such as the design of the runner, the bearings, and the shaft. To improve the mechanical efficiency of a Francis turbine, it is important to minimize losses due to friction, wear, and vibration, and to properly design and maintain the mechanical components of the turbine.

In summary, the efficiency of a Francis turbine is the ratio of the hydraulic power output to the mechanical power input. The hydraulic efficiency of a Francis turbine is influenced by factors such as the head, the flow rate, and the design of the runner blades, while the mechanical efficiency is influenced by factors such as the design of the runner, the bearings, and the shaft. To improve the efficiency of a Francis turbine, it is important to optimize the design of the runner blades, minimize losses due to friction and turbulence, and properly design and maintain the mechanical components of the turbine.

# Describe Working Proportion of Francis Turbine

The working proportion of a Francis turbine is a key concept that relates to the design and performance of the turbine.

The working proportion of a Francis turbine is defined as the ratio of the actual diameter of the runner to the diameter of the inlet casing. This ratio determines the velocity of the water entering the turbine, which in turn affects the efficiency and power output of the turbine.

The working proportion of a Francis turbine is an important design parameter that must be carefully considered in order to optimize the performance of the turbine. For example, a larger working proportion can result in a higher flow rate and a greater hydraulic efficiency, but it can also result in higher turbulence and losses due to friction. On the other hand, a smaller working proportion can result in lower turbulence and lower losses due to friction, but it can also result in a lower flow rate and a lower hydraulic efficiency.

The working proportion of a Francis turbine is determined by several factors, including the head, the flow rate, the design of the runner blades, and the design of the inlet casing. In order to optimize the working proportion of a Francis turbine, it is important to carefully consider all of these factors and to perform hydraulic and mechanical design analyses to determine the optimal value for the working proportion.

In summary, the working proportion of a Francis turbine is the ratio of the actual diameter of the runner to the diameter of the inlet casing. This ratio determines the velocity of the water entering the turbine and affects the efficiency and power output of the turbine. To optimize the performance of a Francis turbine, it is important to carefully consider the working proportion and to perform hydraulic and mechanical design analyses to determine the optimal value.

# Explain the Analysis of the Francis Turbine

The analysis of a Francis turbine involves the examination of its hydraulic and mechanical design characteristics to understand its performance and to identify opportunities for improvement.

Hydraulic analysis of a Francis turbine involves evaluating the fluid flow through the turbine and determining the hydraulic efficiency. This includes analyzing the flow rate and velocity, head, and discharge of the water, as well as calculating the work done by the water on the runner blades. The hydraulic efficiency is then calculated by dividing the work done by the water by the total energy available in the water.

Mechanical analysis of a Francis turbine involves evaluating the mechanical design of the turbine and determining its mechanical efficiency. This includes analyzing the design of the runner blades, the shaft, and the bearings. The mechanical efficiency is calculated by dividing the work done by the runner blades by the total work done by the water on the runner blades.

The results of the hydraulic and mechanical analyses are then combined to determine the overall efficiency of the Francis turbine. This information can be used to identify areas for improvement, such as optimising the runner blade design or improving the mechanical components of the turbine.

In addition to the hydraulic and mechanical analysis, other factors that can affect the performance of a Francis turbine include the operating conditions, the environment, and the maintenance and operating practices. These factors must also be taken into account in the analysis of a Francis turbine.

In summary, the analysis of a Francis turbine involves the examination of its hydraulic and mechanical design characteristics to understand its performance and to identify opportunities for improvement. The analysis includes evaluating the fluid flow through the turbine, determining the hydraulic and mechanical efficiencies, and considering other factors that can affect the performance of the turbine.

# Explain Axial-Flow Turbines (Kaplan and Propeller Turbine)

Axial-flow turbines are a type of water turbine that utilise a flow of water that is parallel to the axis of rotation of the turbine. There are two main types of axial-flow turbines: Kaplan turbines and Propeller turbines.

Kaplan turbines are designed for high head and low flow applications, typically in hydroelectric power plants. The Kaplan turbine consists of a runner with adjustable blades that are set at an angle to the flow of water. The water enters the runner at the inlet, where it is directed onto the blades by a guide vane. As the water flows over the blades, it causes the runner to rotate, producing power.

The efficiency of the Kaplan turbine is determined by a number of factors, including the design of the runner, the blade angle, the flow rate and velocity of the water, and the head of the water. The efficiency of the turbine can be improved by optimising the design of the runner and the blade angle, and by controlling the flow rate and velocity of the water.

Propeller turbines are similar to Kaplan turbines, but are designed for low head and high flow applications. The Propeller turbine consists of a runner with fixed blades that are perpendicular to the flow of water. The water enters the runner at the inlet and is directed onto the blades, causing the runner to rotate and producing power.

The efficiency of the Propeller turbine is determined by a number of factors, including the design of the runner, the flow rate and velocity of the water, and the head of the water. The efficiency of the turbine can be improved by optimising the design of the runner, and by controlling the flow rate and velocity of the water.

In summary, axial-flow turbines are a type of water turbine that utilise a flow of water that is parallel to the axis of rotation of the turbine. There are two main types of axial-flow turbines: Kaplan turbines and Propeller turbines. The efficiency of these turbines is determined by a number of factors, including the design of the runner, the flow rate and velocity of the water, and the head of the water, and can be improved by optimising the design of the runner and by controlling the flow rate and velocity of the water.

# Describe working Proportions of Kaplan Turbine

Working proportions in Kaplan turbines refer to the design parameters that determine the performance and efficiency of the turbine. These proportions include the runner diameter, the blade angle, the number of blades, and the shape of the blades.

The runner diameter is the most important working proportion, as it directly affects the flow rate and velocity of the water. A larger runner diameter will result in a higher flow rate and velocity, which will in turn increase the power output of the turbine. However, the runner diameter must be carefully designed to ensure that the flow of water is smooth and uniform, and that the blades are not subjected to excessive stresses.

The blade angle is another important working proportion, as it determines the amount of power that can be extracted from the flow of water. The blade angle should be set at an optimal value that balances the trade-off between maximum power output and efficiency.

The number of blades is another important working proportion, as it affects the flow of water over the runner. A larger number of blades will result in a smoother flow of water, which will increase the efficiency of the turbine. However, a larger number of blades will also increase the size and cost of the turbine.

The shape of the blades is another important working proportion, as it affects the performance of the turbine. The shape of the blades should be carefully designed to ensure that the flow of water over the runner is smooth and uniform, and that the blades are not subjected to excessive stresses.

In summary, working proportions in Kaplan turbines refer to the design parameters that determine the performance and efficiency of the turbine. These proportions include the runner diameter, the blade angle, the number of blades, and the shape of the blades. The optimal values of these proportions must be carefully determined to ensure that the turbine operates at maximum efficiency and produces the desired power output.

# Explain the Specific Speed of a Turbine

The specific speed of a turbine is a dimensionless parameter that is used to characterise the hydraulic performance of a turbine. It is defined as the speed at which a geometrically similar turbine would operate if it were to deliver 1 unit of power from a unit head of water. The specific speed is expressed as a non-dimensional number and is used to classify the type of turbine and to predict its performance for a given set of operating conditions.

The specific speed is calculated using the following formula:

Ns = (nQ/√H)(1/2)

where:

Ns = specific speed

n = rotational speed of the turbine (in revolutions per minute)

Q = flow rate of water through the turbine (in cubic meters per second)

H = head of water (in meters)

The specific speed of a turbine is used to classify the type of turbine, with different types of turbines having different ranges of specific speeds. For example, Pelton turbines have a specific speed range of 40 to 80, Francis turbines have a specific speed range of 60 to 130, and Kaplan turbines have a specific speed range of 60 to 200.

The specific speed of a turbine is also used to predict its performance for a given set of operating conditions. For example, if the specific speed of a turbine is known, its power output, efficiency, and overall performance can be predicted based on the flow rate and head of water. This is useful in the design and selection of turbines for specific applications, as it allows engineers to compare the performance of different types of turbines and to choose the one that is best suited for their needs.

In summary, the specific speed of a turbine is a dimensionless parameter that is used to characterise the hydraulic performance of a turbine. It is used to classify the type of turbine and to predict its performance for a given set of operating conditions, making it an important tool for engineers in the design and selection of turbines for specific applications.

# Explain the Non-dimensional Specific speed (Shape number) of a Turbine

The non-dimensional specific speed, also known as the shape number, of a turbine is a dimensionless parameter that is used to characterise the geometric shape of the runner in a hydraulic turbine. It is defined as the specific speed of a turbine divided by the square root of its blade diameter. The shape number is expressed as a non-dimensional number and is used to classify the type of turbine and to predict its performance for a given set of operating conditions.

The shape number of a turbine is calculated using the following formula:

Sn = Ns / (D(1/2))

where:

Sn = shape number

Ns = specific speed of the turbine

D = diameter of the turbine runner (in meters)

The shape number of a turbine is used to classify the type of turbine, with different types of turbines having different ranges of shape numbers. For example, Pelton turbines have a shape number range of 5 to 10, Francis turbines have a shape number range of 4 to 6, and Kaplan turbines have a shape number range of 5 to 7.

The shape number of a turbine is also used to predict its performance for a given set of operating conditions. For example, if the shape number of a turbine is known, its efficiency, power output, and overall performance can be predicted based on the flow rate and head of water. This is useful in the design and selection of turbines for specific applications, as it allows engineers to compare the performance of different types of turbines and to choose the one that is best suited for their needs.

In summary, the non-dimensional specific speed, or shape number, of a turbine is a dimensionless parameter that is used to characterise the geometric shape of the runner in a hydraulic turbine. It is used to classify the type of turbine and to predict its performance for a given set of operating conditions, making it an important tool for engineers in the design and selection of turbines for specific applications.

# List and explain the different types of Unit Quantities

In fluid mechanics, unit quantities are used to describe the performance of hydraulic turbines. They are non-dimensional numbers that are obtained by dividing the power output of a turbine by a reference power and the square of the specific speed. There are several types of unit quantities, each of which provides different information about the performance of a turbine. These include:

1. Power Coefficient: The power coefficient is a measure of the efficiency of a turbine. It is defined as the ratio of the actual power output of the turbine to the theoretical power output if all the available energy from the fluid flow is converted into mechanical work. The power coefficient ranges between 0 and 1.
2. Efficiency: The efficiency of a turbine is defined as the ratio of the actual power output of the turbine to the theoretical power output if all the available energy from the fluid flow is converted into mechanical work. The efficiency ranges between 0 and 1.
3. Hydraulic Efficiency: The hydraulic efficiency is defined as the ratio of the actual hydraulic power output of the turbine to the theoretical hydraulic power output if all the available energy from the fluid flow is converted into hydraulic power.
4. Mechanical Efficiency: The mechanical efficiency is defined as the ratio of the actual mechanical power output of the turbine to the hydraulic power output.
5. Load Coefficient: The load coefficient is defined as the ratio of the actual power output of the turbine to the theoretical power output if all the available energy from the fluid flow is converted into mechanical work. The load coefficient ranges between 0 and 1.

These unit quantities are important for the design and analysis of hydraulic turbines, as they provide valuable information about the performance of the turbine and its efficiency. By analyzing the unit quantities, engineers can determine the most efficient design for a particular turbine, optimize its performance, and improve its efficiency.

# Explain Model Testing of the Turbines

Model testing of turbines is an important process in the design and development of hydro turbines. The main objective of model testing is to evaluate the performance of a hydro turbine under controlled conditions in a laboratory environment. The data obtained from model tests is used to make improvements in the design of the turbine and to predict its performance under full-scale operating conditions.

The process of model testing of a turbine involves creating a scaled-down model of the turbine and subjecting it to a flow of water that is similar in velocity and pressure to the full-scale turbine. The model turbine is instrumented with sensors to measure various parameters such as flow rate, head, power output, and efficiency. The model is then tested under a range of operating conditions to determine its performance.

The main components of a model testing setup include the test rig, the water supply system, the flow measurement system, the power measurement system, and the control system. The test rig is the most important component of the setup, as it provides a controlled environment for the model turbine to operate in. The water supply system provides a controlled flow of water to the model turbine, while the flow measurement system accurately measures the flow rate and head. The power measurement system measures the output power of the model turbine, and the control system provides a means to control the test conditions and collect data.

Model testing is a crucial step in the design and development of hydro turbines, as it provides valuable information about the performance of the turbine and helps to identify any potential problems that may arise. The results obtained from model testing are used to make improvements in the design of the turbine and to predict its performance under full-scale operating conditions.

# Explain the Cavitation in Turbine

The term “cavitation” refers to the formation and subsequent collapse of vapour-filled cavities within a fluid due to a decrease in pressure. In a turbine, cavitation occurs when the local pressure within the fluid falls below the vapour pressure of the fluid, resulting in the formation of vapour cavities. These cavities then collapse as the pressure increases, producing a high-velocity flow that can erode and damage the turbine components, leading to a decrease in efficiency and power output.

Cavitation can occur in different parts of a turbine, including the impeller, diffuser, and draft tube, and can result from a variety of causes, such as high fluid velocity, high fluid temperature, or a poorly designed or worn impeller. The severity of cavitation damage depends on several factors, including the type and size of the turbine, the fluid properties, and the operating conditions.

To minimize cavitation damage in a turbine, engineers must design the turbine components to reduce the occurrence of cavitation, as well as perform regular maintenance to check for any signs of wear or damage. Additionally, they may use cavitation modelling software or perform cavitation tests on physical models of the turbine to identify areas of high risk and optimize the design.

# Define Thomas Cavitation Factor

The Thomas cavitation factor is a dimensionless number that is used to predict the likelihood of cavitation in a turbine. It is defined as the ratio of the net head of the fluid entering the turbine to the vapour pressure head of the fluid. The net head is the difference between the inlet and outlet pressures, while the vapour pressure head is the height of the fluid column required to produce a vapour pressure equal to the vapour pressure of the fluid at the inlet conditions.

A higher Thomas cavitation factor indicates a higher likelihood of cavitation in the turbine, as it means that the net head of the fluid entering the turbine is lower relative to the vapour pressure head. On the other hand, a lower Thomas cavitation factor indicates a lower likelihood of cavitation, as it means that the net head is higher relative to the vapour pressure head.

The Thomas cavitation factor is an important design parameter for turbines, as it helps engineers predict and minimize the risk of cavitation damage. The factor can be used to optimize the design of the turbine components, such as the impeller, diffuser, and draft tube, to reduce the likelihood of cavitation and improve the efficiency and performance of the turbine.