Fluid Dynamics

Contents

**List and explain various Forces which are acting on the Fluid Elements** 1

**Recall the significance of Bernoulli Equation in Fluid Flow** 2

**Calculate the Discharge Rate and Velocity Flow of Venturimeter in different Conditions** 3

**Recall the working phenomena of Orifice meter** 4

**Determine the Discharge through Orifice meter** 5

**Recall the working phenomena of Pitot-tube** 6

**Calculate the Discharge through the Pitot-tube** 6

**Calculate the Discharge Rate of Nozzle in different Condition** 8

**Calculate the Discharge through the Weirs and Notches** 10

**Recall the Momentum Equation and Impulse Momentum Equation** 11

**Describe the expression for the Force exerted by a Flowing Fluid on a Pipe bend** 12

**Recall the phenomena of Free Liquid Jet and derive its Equation** 13

**Recall Time of Flight, Maximum Height and Horizontal Range of Jet** 14

**Calculate Time of Flight, Maximum Height and Horizontal Range of Jet** 14

**Recall the phenomena of Impact of Jet** 15

**Describe and calculate the Force exerted by Jet on a Flat Fixed Plate** 16

**Describe and calculate the Force exerted by Jet on a Inclined Fixed Plate** 17

**Describe and calculate the Force exerted by Jet on a Curved Fixed Plate** 18

**Recall the phenomena of Impact of Jet on a Moving Plate** 19

**Describe and calculate the Force exerted by Jet on a Flat Moving Plate** 20

**Describe and calculate the Force exerted by Jet on a Series of Flat vanes mounted on a Wheel** 21

**List and explain various Forces which are acting on the Fluid Elements**

There are several forces that act on fluid elements in fluid mechanics, which are important to understand in order to describe the behavior of fluid flows. The following are some of the most important forces:

- Pressure force: This is the force exerted by the fluid on the surrounding walls of a container or a pipe. The pressure in a fluid is a scalar quantity that depends on the depth of the fluid and the density of the fluid. The pressure force acts in all directions and is proportional to the area over which it is acting.
- Gravitational force: This is the force exerted by the gravitational field on the fluid elements. The magnitude of the gravitational force depends on the mass of the fluid element and the strength of the gravitational field. In most fluid mechanics problems, the gravitational force is considered to act in the downward direction.
- Viscous force: This is the force that opposes the relative motion between adjacent fluid layers. Viscosity is a measure of a fluid’s resistance to flow, and the viscous force depends on the velocity gradient of the fluid and the viscosity of the fluid. The viscous force acts in the direction opposite to the velocity of the fluid element.
- Surface tension force: This is the force that acts on the surface of a fluid, and is caused by the attractive forces between the molecules of the fluid. Surface tension is a measure of the resistance of a fluid to an increase in its surface area.
- Inertial force: This is the force that arises from the acceleration of a fluid element. The inertial force acts in the direction of acceleration and its magnitude depends on the mass of the fluid element and the acceleration of the fluid.

These are some of the most important forces that act on fluid elements in fluid mechanics. Understanding the behavior and interaction of these forces is essential for the analysis of fluid flows and for the design and operation of various fluid systems.

**Recall the significance of Bernoulli Equation in Fluid Flow**

The Bernoulli equation is a fundamental principle in fluid mechanics that relates pressure, velocity, and height in a fluid flow. It states that, for a steady and incompressible flow, the sum of the pressure energy, the kinetic energy, and the potential energy per unit volume of a fluid is constant along a streamline. This principle is named after the Swiss mathematician Daniel Bernoulli, who first formulated it in 1738.

The Bernoulli equation is used to describe the behavior of fluid flows in a wide range of applications, including pipe flows, aircraft wing design, and blood flow in the circulatory system. The equation can be used to calculate pressure drop, flow rate, and other parameters in fluid systems. It is particularly useful in the design and analysis of hydraulic systems and piping networks, as it allows engineers to calculate the pressure head and velocity at different points in the system.

The Bernoulli equation can also be used to understand the behavior of fluids in real-world applications. For example, it can explain why an aeroplane can fly, why a boat can move against the flow of a river, and why a wing produces lift. By analyzing the pressure and velocity distributions along a streamline, the Bernoulli equation helps engineers to optimize the performance of fluid systems and to design more efficient and effective fluid-handling systems.

In summary, the Bernoulli equation is a key tool in fluid mechanics that provides a comprehensive understanding of fluid flow behavior. It is widely used in many fields of engineering and science and is essential for the design and analysis of fluid systems.

**Recall the Venturimeter**

A Venturimeter is a device used to measure the flow rate of a fluid in a pipe. It is based on the principle of continuity, which states that the flow rate of a fluid must remain constant along a streamline in a steady flow. The Venturi Meter consists of a converging section and a diverging section, connected by a throat. The converging section reduces the velocity of the fluid, causing a corresponding increase in pressure, while the diverging section increases the velocity of the fluid, causing a corresponding decrease in pressure.

When a fluid flows through a Venturi Meter, the pressure difference between the inlet and the throat is proportional to the velocity of the fluid. The flow rate can be calculated by measuring the pressure drop across the throat and using the Bernoulli equation. By measuring the pressure difference at two points in the Venturimeter, it is possible to determine the fluid velocity, which can then be used to calculate the flow rate.

The Venturimeter is a simple and efficient way to measure fluid flow rates in pipes, and it is widely used in many industries, including water treatment, chemical processing, and oil and gas. It is also a popular device in laboratory experiments, as it is relatively easy to construct and provides accurate flow rate measurements.

In summary, the Venturimeter is a widely used device for measuring fluid flow rates in pipes. Its design is based on the principles of continuity and the Bernoulli equation, and it provides a simple and efficient way to determine the flow rate of a fluid in a pipe.

**Calculate the Discharge Rate and Velocity Flow of Venturimeter in different Conditions**

To calculate the discharge rate and velocity flow of a Venturimeter in different conditions, one must first understand the relationship between pressure and velocity in fluid flow. This relationship is described by the Bernoulli equation, which states that the pressure of a fluid decreases as its velocity increases.

The discharge rate of a Venturimeter can be calculated using the continuity equation, which states that the product of the cross-sectional area of a pipe and the velocity of the fluid flowing through it must remain constant. For a Venturimeter, the cross-sectional area decreases at the throat, causing the velocity of the fluid to increase. This increase in velocity corresponds to a decrease in pressure, which can be measured using a manometer or other pressure-measuring device.

The velocity flow of the fluid through a Venturimeter can be calculated by measuring the pressure difference between the inlet and the throat, and using the Bernoulli equation. The velocity of the fluid can be determined from the pressure drop and the density of the fluid.

It is important to note that the discharge rate and velocity flow of a Venturimeter will depend on the fluid properties, such as density and viscosity, as well as the design of the Venturimeter, including the shape and dimensions of the converging and diverging sections and the throat.

To calculate the discharge rate and velocity flow of a Venturimeter in different conditions, one must measure the pressure difference between the inlet and the throat and use the Bernoulli equation and continuity equation. These calculations will provide a quantitative understanding of the fluid flow through a Venturi Meter, which can be useful in a variety of industrial and laboratory applications.

**Recall the working phenomena of Orifice meter**

An Orifice meter is a device used to measure the flow rate of fluid flowing through a pipe. It works by restricting the flow of fluid through a small opening, called the orifice, in the pipe. This restriction creates a pressure drop, which is proportional to the fluid velocity and the square of the fluid flow rate.

The working principle of an Orifice meter is based on the Bernoulli equation, which states that the pressure of a fluid decreases as its velocity increases. The pressure drop across the orifice can be measured using a differential pressure transducer or manometer, and the fluid flow rate can be calculated from the pressure drop and the fluid properties, such as density and viscosity.

In an Orifice meter, the fluid enters the pipe at a higher velocity, and then slows down as it passes through the orifice, resulting in a pressure drop. The pressure difference between the inlet and outlet of the orifice is proportional to the square of the fluid velocity, and can be used to calculate the fluid flow rate.

The design of an Orifice meter includes several important parameters, such as the size and shape of the orifice, the type of fluid, the fluid temperature and pressure, and the measurement conditions. It is important to select the appropriate orifice size and shape based on the fluid flow rate and fluid properties, in order to obtain accurate measurements.

In summary, the Orifice meter works by creating a restriction in the fluid flow, which results in a pressure drop proportional to the fluid velocity and flow rate. The pressure drop is measured, and the fluid flow rate is calculated using the Bernoulli equation and fluid properties. The Orifice meter is widely used in industrial and laboratory applications to measure fluid flow rates in pipes.

**Determine the Discharge through Orifice meter**

The discharge through an Orifice meter can be determined by calculating the fluid flow rate through the orifice, which is proportional to the pressure drop across the orifice and the fluid properties. The calculation of the discharge rate through an Orifice meter involves several steps, as follows:

- Measurement of pressure drop: The pressure drop across the orifice is measured using a differential pressure transducer or manometer, and is expressed as the difference between the upstream and downstream pressures.
- Calculation of fluid velocity: The fluid velocity can be calculated from the pressure drop using the Bernoulli equation and the fluid properties, such as density and viscosity.
- Calculation of discharge rate: The fluid flow rate through the orifice can be calculated from the fluid velocity and the orifice area. The discharge rate is expressed in units of volume per unit time, such as cubic meters per second or cubic feet per second.
- Correction for fluid properties: The discharge rate calculated from the fluid velocity and orifice area is based on the fluid properties at the time of measurement. It is important to correct the discharge rate for changes in fluid temperature and pressure, in order to obtain accurate results.
- Correction for orifice shape: The discharge rate calculated from the fluid velocity and orifice area assumes that the orifice is circular in shape and has sharp edges. If the orifice has a different shape or rounded edges, the discharge rate must be corrected for these effects.

In summary, the discharge through an Orifice meter can be determined by measuring the pressure drop across the orifice, calculating the fluid velocity from the pressure drop, and calculating the fluid flow rate from the fluid velocity and orifice area. The discharge rate must be corrected for changes in fluid properties and orifice shape, in order to obtain accurate results.

**Recall the working phenomena of Pitot-tube**

A Pitot-tube is a type of fluid measurement instrument used in fluid mechanics to measure the fluid velocity or pressure. It consists of a small tube with one end open and another end that is pointed in the direction of the fluid flow. The open end measures the static pressure of the fluid, while the pointed end measures the total or dynamic pressure of the fluid.

The working principle of a Pitot-tube is based on the Bernoulli’s equation, which states that the pressure in a fluid decreases as its velocity increases. When the fluid flows into the pointed end of the Pitot-tube, it creates an impact pressure which is a combination of both static and dynamic pressure. This impact pressure can be used to calculate the fluid velocity by using the Bernoulli’s equation.

Pitot-tubes are commonly used in fluid flow measurement in various industrial applications, including fluid metering in pipelines, airspeed measurement in aircraft, and flow rate measurement in fluid systems. The accuracy of a Pitot-tube is influenced by factors such as fluid viscosity, fluid temperature, and Reynolds number.

**Calculate the Discharge through the Pitot-tube**

To calculate the discharge through a Pitot-tube, one needs to know the fluid velocity at a specific point in the flow. The fluid velocity can be obtained by using the impact pressure measured by the Pitot-tube and Bernoulli’s equation.

The impact pressure is measured by the difference between the dynamic pressure and the static pressure, and it can be expressed as:

Δp = p_{d} – p_{s} = 1/2 * ρ * v^{2} – p_{s}

where p_{d} is the dynamic pressure, p_{s} is the static pressure, ρ is the fluid density, and v is the fluid velocity.

By rearranging the above equation, the fluid velocity can be obtained as:

v = √(2 * Δp / ρ)

Once the fluid velocity is known, the discharge through the Pitot-tube can be calculated as:

Q = A * v

where A is the cross-sectional area of the flow.

It’s important to note that the Pitot-tube measurement is only valid for a point measurement, and the results will not be representative of the entire flow field. To obtain a more accurate flow rate measurement, multiple Pitot-tubes or other flow measurement techniques may be necessary.

**Recall the Flow Nozzle**

The Flow Nozzle is a device used in fluid mechanics to measure the discharge rate of a fluid flowing through a pipe. It is commonly used in industries such as water treatment, power plants, and chemical processing to monitor and control the flow of fluids. The Flow Nozzle is designed as a convergent-divergent shape which is inserted into a pipe carrying fluid. The flow of fluid through the nozzle causes a drop in pressure which can be measured and used to calculate the flow rate. The design of the Flow Nozzle and the shape of the convergent and divergent sections play a crucial role in determining the discharge rate. The accuracy of the Flow Nozzle depends on the correct design and installation of the device and the proper calibration of the instrument used to measure the pressure drop.

**Calculate the Discharge Rate of Nozzle in different Condition**

The discharge rate of a nozzle can be calculated by measuring the pressure drop across the nozzle and using this value to determine the flow rate. The pressure drop across a nozzle is proportional to the square of the velocity of the fluid and can be measured with a pressure gauge. The discharge rate of a nozzle can be calculated using the following equation:

Q = Cd * A * (2 * (P_{1} – P_{2}) / ρ)^{0.5}

Where:

Q = Discharge rate (m^{3}/s)

Cd = Coefficient of discharge

A = Area of the nozzle (m^{2})

P_{1} = Pressure of fluid upstream of the nozzle (Pa)

P_{2 }= Pressure of fluid downstream of the nozzle (Pa)

ρ = Density of fluid (kg/m^{3})

The coefficient of discharge, Cd, is a dimensionless value that takes into account the design and shape of the nozzle. It is a measure of the efficiency of the nozzle in converting the pressure drop into a velocity increase. The value of Cd can be determined experimentally or obtained from charts and tables based on the type of nozzle. The discharge rate of a nozzle can vary depending on the conditions under which the fluid is flowing. These conditions include the pressure and temperature of the fluid, the density of the fluid, and the velocity of the fluid. The discharge rate can be calculated for different conditions by adjusting the value of the coefficients and the pressure drop across the nozzle.

**Recall Weir and Notches**

A weir is a hydraulic structure that is used to measure the flow rate of fluid in open channels. It is a barrier placed across the width of a channel, and fluid flows over the top of the weir. A notch is similar to a weir but with a specific shaped opening in the barrier, which causes the fluid to flow through the notch in a controlled manner.

The height of the fluid above the weir or notch is proportional to the flow rate, which can be calculated using the principle of continuity, which states that the flow rate must be constant across any given cross-section of a channel. The discharge rate can be determined by measuring the height of the fluid above the weir or notch and using the appropriate formula.

Weirs and notches are commonly used in the fields of hydrology, irrigation, and water management to measure the flow rate of water in rivers, streams, and canals. They can also be used to regulate the flow of water in irrigation systems and to control the flow of water in hydraulic power plants.

**Classify Weir and Notches**

Weirs and notches are hydraulic structures used to measure the discharge rate of fluid flowing through them.

Classification of Weirs:

- Rectangular Weirs
- Trapezoidal Weirs
- Cipolletti Weirs
- V-notch Weirs
- Broad-crested Weirs

Classification of Notches:

- Triangular Notches
- Rectangular Notches
- Trapezoidal Notches
- V-notch Notches
- Curved Notches.

The classification is based on the shape and configuration of the weir or notch, which affects the discharge rate measurement. The choice of weir or notch depends on the application, the type of fluid, and the flow conditions.

**Calculate the Discharge through the Weirs and Notches**

A weir and notch are two types of flow measurement devices used in fluid mechanics. A weir is a type of dam or barrier that is placed in a channel or stream to control or measure the flow of water. Notches are similar to weirs, but instead of a barrier, a V-shaped opening is cut into the channel or stream.

Weirs and notches are classified based on the shape of the opening and the flow conditions. The most common types of weirs are rectangular weirs, triangular weirs, and trapezoidal weirs. The most common types of notches are rectangular notches, triangular notches, and V-notches.

The discharge rate through a weir or notch is calculated by determining the height of the liquid above the opening, known as the head, and using this information to calculate the flow rate. The formula used to calculate the discharge rate varies depending on the type of weir or notch. For example, the discharge rate through a rectangular weir can be calculated using the formula: Q = 2.49 h^{(2/3)} where Q is the discharge rate and h is the head. The discharge rate through a V-notch can be calculated using the formula: Q = 2.49 h^{(5/2)} where Q is the discharge rate and h is the head.

**Recall the Momentum Equation and Impulse Momentum Equation**

The Momentum Equation and Impulse Momentum Equation are two fundamental principles in fluid mechanics that describe the changes in momentum of a fluid due to external forces.

The Momentum Equation states that the rate of change of momentum of a fluid element in a control volume is equal to the net force acting on the fluid element. This equation is represented mathematically as:

∂(ρV)/∂t + ∇.(ρVV) = -∇p + ρg + ∑F

where,

∂(ρV)/∂t = rate of change of momentum

ρ = fluid density

V = fluid velocity

∇.(ρVV) = convective acceleration term

∇p = pressure force

ρg = gravitational force

∑F = total net external forces acting on the fluid

The Impulse Momentum Equation is a modified form of the Momentum Equation, where the rate of change of momentum is expressed as an impulse or change in momentum over a specific time period. This equation is represented mathematically as:

Δ(ρV) = – Δp + δn Δt + ∑FΔt

where,

Δ(ρV) = change in momentum

Δp = change in pressure

ρgΔt = change in gravitational potential energy

∑FΔt = change in external forces

These equations are important for understanding the behavior of fluid flows and for calculating fluid velocity and pressure changes due to external forces. They are used in a variety of applications, including the design of hydraulic systems, the calculation of fluid flow rates, and the analysis of fluid dynamics in pipes, tanks, and other containers.

**Describe the expression for the Force exerted by a Flowing Fluid on a Pipe bend**

In fluid mechanics, the force exerted by a flowing fluid on a pipe bend is a crucial aspect that needs to be considered while designing pipelines. The force exerted by the fluid can result in significant stresses and deformations on the pipe, leading to potential failure of the pipeline. The expression for the force exerted by a flowing fluid on a pipe bend is given by the Momentum Equation and Impulse Momentum Equation.

The Momentum Equation is a mathematical expression that describes the conservation of momentum in a flowing fluid. It states that the rate of change of momentum of a fluid element is equal to the net force acting on the fluid element. The Momentum Equation can be used to calculate the force exerted by a fluid on a pipe bend by considering the fluid element as the fluid flowing through the bend.

The Impulse Momentum Equation is another mathematical expression that is used to calculate the force exerted by a fluid on a pipe bend. This equation states that the change in momentum of a fluid is equal to the impulse applied to the fluid. The impulse is given by the product of the force and the time over which the force is applied.

By using the Momentum Equation and Impulse Momentum Equation, the force exerted by a flowing fluid on a pipe bend can be calculated and accounted for in the design of pipelines. This helps in ensuring the safe and efficient functioning of pipelines and prevents potential failures due to fluid forces.

**Recall the phenomena of Free Liquid Jet and derive its Equation**

Free Liquid Jet is a type of fluid flow where a stream of liquid is ejected from an orifice and becomes a continuous, self-contained jet. The jet is considered “free” because it is not confined or guided by any external structure. Some common examples of free liquid jets include fountain sprays, waterfalls, and geysers.

The equation that describes the behavior of a free liquid jet is the Bernoulli equation, which is based on the principle of energy conservation. According to the Bernoulli equation, the pressure of a fluid decreases as its velocity increases. In the case of a free liquid jet, the pressure at the orifice is lower than the pressure of the surrounding fluid, causing the liquid to be expelled from the orifice and form a jet.

The velocity of the jet can be calculated by considering the conservation of mass and the principle of continuity. The principle of continuity states that the volume flow rate of a fluid must remain constant along its path. In the case of a free liquid jet, this means that the cross-sectional area of the jet must decrease as its velocity increases. Combining the principle of continuity with the Bernoulli equation, it is possible to derive an equation that describes the velocity of the free liquid jet.

The equation for the velocity of a free liquid jet can be expressed as:

V = (2gH)^{0.5}

where V is the velocity of the jet, g is the acceleration due to gravity, and H is the height difference between the orifice and the end of the jet.

In summary, a free liquid jet is a fluid flow that occurs when a stream of liquid is expelled from an orifice and becomes a continuous, self-contained jet. The behavior of the free liquid jet is described by the Bernoulli equation, which takes into account the conservation of energy and the principle of continuity. The velocity of the jet can be calculated using the equation V = (2gH)^{0.5}.

**Recall Time of Flight, Maximum Height and Horizontal Range of Jet**

In fluid mechanics, the time of flight, maximum height, and horizontal range of a free liquid jet are important parameters that describe the behavior of the jet.

- Time of Flight: Time of flight refers to the amount of time it takes for a free liquid jet to reach its maximum height. It is a measure of the vertical motion of the jet and is typically calculated by dividing the maximum height by the vertical velocity of the jet.
- Maximum Height: Maximum height refers to the highest point that a free liquid jet reaches before it begins to fall back towards its starting point. This height is determined by the initial velocity of the jet, the acceleration due to gravity, and the height of the orifice.
- Horizontal Range: Horizontal range refers to the maximum horizontal distance that a free liquid jet can travel from its starting point. This distance is determined by the initial velocity of the jet, the angle of the jet relative to the horizontal, and the acceleration due to gravity.

In summary, the time of flight, maximum height, and horizontal range of a free liquid jet are important parameters that describe the behavior of the jet. The time of flight is the amount of time it takes for the jet to reach its maximum height, while the maximum height is the highest point that the jet reaches before it begins to fall back towards its starting point. The horizontal range is the maximum horizontal distance that the jet can travel from its starting point. These parameters are useful in various applications, including the design of fountains, waterfalls, and geysers, among others.

**Calculate Time of Flight, Maximum Height and Horizontal Range of Jet**

To calculate the time of flight, maximum height, and horizontal range of a free liquid jet, the following steps can be followed:

- Time of Flight: The time of flight can be calculated using the following equation:

t = (2H/g)^{0.5},

where t is the time of flight, H is the maximum height of the jet, and g is the acceleration due to gravity.

- Maximum Height: The maximum height can be calculated using the following equation:

H = (V_{0}^{2} * sin^{2}(θ))/2g,

where V_{0} is the initial velocity of the jet, θ is the angle of the jet relative to the horizontal, and g is the acceleration due to gravity.

- Horizontal Range: The horizontal range can be calculated using the following equation:

R = (V_{0}^{2} * sin(2θ))/g,

where V_{0} is the initial velocity of the jet, θ is the angle of the jet relative to the horizontal, and g is the acceleration due to gravity.

In summary, the time of flight, maximum height, and horizontal range of a free liquid jet can be calculated by using the equations t = (2H/g)^{0.5}, H = (V_{0}^{2} * sin^{2}(θ))/2g, and R = (V_{0}^{2}* sin(2θ))/g, respectively. These equations allow engineers and designers to predict the behavior of a free liquid jet and make design decisions based on the desired outcome.

**Recall the phenomena of Impact of Jet**

In fluid mechanics, the impact of a jet refers to the process of a fluid jet striking a solid surface and the resulting effects on the fluid and the surface. The impact of a jet is a common phenomenon that occurs in many industrial applications, such as water treatment plants, irrigation systems, and fire suppression systems, among others.

When a fluid jet strikes a solid surface, the kinetic energy of the fluid is transferred to the surface, causing the fluid to decelerate rapidly. This deceleration results in an increase in pressure, which can cause the fluid to spread out and form a puddle on the surface. The pressure increase can also cause the fluid to rebound from the surface and form a spray or mist. The shape and behavior of the jet after impact depend on several factors, including the velocity of the jet, the fluid properties, and the surface properties.

The impact of a jet can also have significant effects on the solid surface. For example, the increased pressure and velocity of the fluid can cause erosion or damage to the surface. In some cases, the fluid can also penetrate the surface and cause damage to internal structures.

In summary, the impact of a jet refers to the process of a fluid jet striking a solid surface and the resulting effects on the fluid and the surface. The impact of a jet can cause the fluid to spread out, form a puddle, rebound, and form a spray or mist, and can also cause erosion or damage to the surface. Understanding the impact of a jet is important in many industrial applications to ensure safe and effective operation.

**Describe and calculate the Force exerted by Jet on a Flat Fixed Plate**

The force exerted by a jet on a flat fixed plate refers to the force that the fluid exerts on the surface due to the impact of the jet. This force can be calculated using the equation of continuity and Bernoulli’s equation.

To calculate the force exerted by a jet on a flat fixed plate, the following steps can be followed:

- Determine the velocity and area of the jet before and after impact: The velocity of the jet before impact can be calculated using the equation of continuity, which states that the mass flow rate must be conserved. The area of the jet before and after impact can also be determined.
- Apply Bernoulli’s equation: Bernoulli’s equation states that the total energy of a fluid particle is constant along a streamline. By applying Bernoulli’s equation to the fluid particle before and after impact, the pressure difference between the two points can be calculated.
- Calculate the force exerted by the jet: The force exerted by the jet on the flat fixed plate can be calculated using the equation:

F = (p_{1} – p_{2}) * A,

where F is the force exerted by the jet, p_{1} is the pressure before impact, p_{2} is the pressure after impact, and A is the area of the jet after impact.

In summary, the force exerted by a jet on a flat fixed plate can be calculated by determining the velocity and area of the jet before and after impact, applying Bernoulli’s equation to calculate the pressure difference between the two points, and then using the equation F = (p_{1} – p_{2}) * A to calculate the force exerted by the jet. This information can be used in various industrial applications to design and optimize fluid systems and to ensure safe and efficient operation.

**Describe and calculate the Force exerted by Jet on a Inclined Fixed Plate**

The force exerted by a jet on an inclined fixed plate refers to the force that the fluid exerts on the surface due to the impact of the jet when the plate is inclined at a certain angle. This force can also be calculated using the equation of continuity and Bernoulli’s equation.

To calculate the force exerted by a jet on an inclined fixed plate, the following steps can be followed:

- Determine the angle of inclination: The angle of inclination is the angle between the surface of the inclined plate and a horizontal plane. This angle is important in determining the force exerted by the jet on the surface.
- Determine the velocity and area of the jet before and after impact: The velocity of the jet before impact can be calculated using the equation of continuity, and the area of the jet before and after impact can be determined.
- Apply Bernoulli’s equation: Bernoulli’s equation can be used to calculate the pressure difference between the fluid particle before and after impact.
- Calculate the force exerted by the jet: The force exerted by the jet on the inclined fixed plate can be calculated using the equation:

F = (p_{1} – p_{2}) * A * cos(θ),

where F is the force exerted by the jet, p_{1} is the pressure before impact, p_{2} is the pressure after impact, A is the area of the jet after impact, and θ is the angle of inclination.

In summary, the force exerted by a jet on an inclined fixed plate can be calculated by determining the angle of inclination, determining the velocity and area of the jet before and after impact, applying Bernoulli’s equation to calculate the pressure difference between the two points, and then using the equation F = (p_{1} – p_{2}) * A * cos(θ) to calculate the force exerted by the jet. This information can be used in various industrial applications to design and optimize fluid systems and to ensure safe and efficient operation.

**Describe and calculate the Force exerted by Jet on a Curved Fixed Plate**

The force exerted by a jet on a curved fixed plate refers to the force that the fluid exerts on the surface due to the impact of the jet when the plate is curved. The calculation of this force can be done using the equation of continuity, Bernoulli’s equation, and the principle of conservation of momentum.

To calculate the force exerted by a jet on a curved fixed plate, the following steps can be followed:

- Determine the velocity and area of the jet before and after impact: The velocity of the jet before impact can be calculated using the equation of continuity, and the area of the jet before and after impact can be determined.
- Apply Bernoulli’s equation: Bernoulli’s equation can be used to calculate the pressure difference between the fluid particle before and after impact.
- Apply the principle of conservation of momentum: The principle of conservation of momentum states that the total momentum of a system is conserved if no external forces are acting on the system. This principle can be applied to the fluid particle before and after impact to calculate the force exerted by the jet on the curved surface.
- Calculate the force exerted by the jet: The force exerted by the jet on the curved fixed plate can be calculated using the equation:

F = m * (v_{2} – v_{1}) / t,

where F is the force exerted by the jet, m is the mass of the fluid particle, v_{1} is the velocity of the fluid particle before impact, v_{2} is the velocity of the fluid particle after impact, and t is the time required for the fluid particle to move from one point to another.

In summary, the force exerted by a jet on a curved fixed plate can be calculated by determining the velocity and area of the jet before and after impact, applying Bernoulli’s equation to calculate the pressure difference between the two points, applying the principle of conservation of momentum, and then using the equation F = m * (v_{2} – v_{1}) / t to calculate the force exerted by the jet. This information can be used in various industrial applications to design and optimize fluid systems and to ensure safe and efficient operation.

**Recall the phenomena of Impact of Jet on a Moving Plate**

The impact of a jet on a moving plate refers to the interaction between a fluid jet and a plate that is moving relative to the fluid. This phenomenon can occur in various industrial applications such as in hydro power plants, water treatment plants, and cooling systems. Understanding the impact of a jet on a moving plate is important for the design and optimization of these systems.

The impact of a jet on a moving plate can be described as follows:

- The fluid jet is directed towards the moving plate.
- As the fluid jet strikes the moving plate, it changes its velocity and direction.
- The fluid particles on the plate create a dynamic pressure that acts in the direction opposite to the plate’s motion.
- The dynamic pressure causes the fluid jet to deflect from its original path, resulting in a reduction of its velocity.
- The fluid jet continues to move along the surface of the moving plate until it reaches a point of stable equilibrium.

The impact of a jet on a moving plate can have various effects on the fluid and the plate. For example, the interaction between the fluid and the moving plate can cause a change in the velocity and direction of the fluid, which can result in a reduction of the fluid’s energy. Additionally, the dynamic pressure created by the impact can cause a change in the fluid’s pressure distribution, which can result in a reduction in the fluid’s flow rate.

In summary, the impact of a jet on a moving plate refers to the interaction between a fluid jet and a plate that is moving relative to the fluid. The impact of the jet can cause a change in the velocity and direction of the fluid, a reduction in the fluid’s energy, and a change in the fluid’s pressure distribution. Understanding this phenomenon is important for the design and optimization of fluid systems.

**Describe and calculate the Force exerted by Jet on a Flat Moving Plate**

The force exerted by a fluid jet on a flat moving plate refers to the effect of the impact of the jet on the plate. This force can be calculated to determine the effect of the impact on the plate, which is important for the design and optimization of fluid systems.

The calculation of the force exerted by a jet on a flat moving plate can be performed using the following steps:

- Determine the velocity of the fluid jet before it strikes the moving plate. This can be calculated using the principle of continuity or by measuring the velocity of the jet using a flow meter or other instrument.
- Determine the velocity of the moving plate. This can be measured using a velocity meter or other instrument.
- Calculate the relative velocity of the fluid jet and the moving plate. The relative velocity is equal to the difference between the velocity of the fluid jet and the velocity of the moving plate.
- Calculate the dynamic pressure created by the impact of the fluid jet on the moving plate. The dynamic pressure is equal to half of the density of the fluid multiplied by the square of the relative velocity.
- Calculate the force exerted by the fluid jet on the moving plate using the dynamic pressure. The force is equal to the dynamic pressure multiplied by the area of the plate.

It is important to note that the force exerted by a fluid jet on a flat moving plate is dependent on various factors, including the velocity of the fluid jet, the velocity of the moving plate, and the density of the fluid. By performing the calculations described above, it is possible to determine the effect of the impact of the fluid jet on the flat moving plate and optimize the design of fluid systems.

In summary, the force exerted by a fluid jet on a flat moving plate refers to the effect of the impact of the jet on the plate. The calculation of this force involves determining the velocity of the fluid jet and the moving plate, calculating the relative velocity, calculating the dynamic pressure, and then multiplying the dynamic pressure by the area of the plate. This calculation is important for the design and optimization of fluid systems.

**Describe and calculate the Force exerted by Jet on a Series of Flat vanes mounted on a Wheel**

The force exerted by a fluid jet on a series of flat vanes mounted on a wheel refers to the effect of the impact of the fluid jet on the vanes. This force is important to consider when designing fluid systems that involve the impact of a fluid jet on a series of vanes, such as in turbines or pumps.

The calculation of the force exerted by a fluid jet on a series of flat vanes mounted on a wheel can be performed using the following steps:

- Determine the velocity of the fluid jet before it strikes the vanes. This can be calculated using the principle of continuity or by measuring the velocity of the jet using a flow meter or other instrument.
- Calculate the impact angle between the fluid jet and the vanes. This can be done by measuring the angle between the fluid jet and the vanes using an instrument such as a protractor.
- Calculate the change in velocity of the fluid jet as it strikes the vanes. This can be done using the principles of fluid mechanics and the impact angle.
- Calculate the dynamic pressure created by the impact of the fluid jet on the vanes. The dynamic pressure is equal to half of the density of the fluid multiplied by the square of the change in velocity.
- Calculate the force exerted by the fluid jet on the vanes using the dynamic pressure. The force is equal to the dynamic pressure multiplied by the area of the vanes.

It is important to note that the force exerted by a fluid jet on a series of flat vanes mounted on a wheel is dependent on various factors, including the velocity of the fluid jet, the impact angle, the density of the fluid, and the area of the vanes. By performing the calculations described above, it is possible to determine the effect of the impact of the fluid jet on the vanes and optimize the design of fluid systems.

In summary, the force exerted by a fluid jet on a series of flat vanes mounted on a wheel refers to the effect of the impact of the fluid jet on the vanes. The calculation of this force involves determining the velocity of the fluid jet, calculating the impact angle, calculating the change in velocity, calculating the dynamic pressure, and then multiplying the dynamic pressure by the area of the vanes. This calculation is important for the design and optimization of fluid systems that involve the impact of a fluid jet on a series of vanes.