What is jet impact on moving plate?

Short Answer:

Jet impact on a moving plate refers to the process when a high-velocity fluid jet strikes a plate that is in motion. The plate may move in the same direction or opposite direction of the jet. The force exerted on the plate and the work done depend on the relative velocity between the jet and the plate. When the plate moves in the direction of the jet, the impact force reduces compared to a stationary plate.

This concept is important in fluid mechanics and is applied in the design of impulse turbines, jet propulsion systems, and other hydraulic machines. It helps in understanding how kinetic energy of a jet is converted into mechanical energy by moving surfaces like turbine blades or buckets.

Detailed Explanation :

Jet Impact on Moving Plate

The jet impact on a moving plate is an important principle in fluid mechanics that explains the transfer of momentum and energy from a fluid jet to a surface in motion. It is a direct application of Newton’s second law of motion, which states that the rate of change of momentum is equal to the force applied. When a high-speed jet of fluid strikes a moving plate, part of the jet’s kinetic energy is transferred to the plate, causing a force and doing work on it.

This concept is used to study how water or other fluids exert force on moving surfaces such as turbine blades, paddles, and buckets. It plays a key role in understanding the working of impulse turbines like the Pelton wheel and in calculating the efficiency of energy transfer between the fluid and the moving surface.

Types of Jet Impact on Moving Plate

The impact of a jet on a moving plate can occur under different conditions depending on the direction and velocity of motion of the plate. The two common cases are:

  1. Jet Impact on a Flat Moving Plate
  2. Jet Impact on a Curved Moving Plate
  1. Jet Impact on Flat Moving Plate

When a jet of water strikes a flat plate moving in the same direction as the jet, the effective impact force depends on the difference between the jet velocity and the plate velocity.

Let,

  •  = Velocity of jet (m/s)
  •  = Velocity of plate (m/s)
  •  = Density of fluid (kg/m³)
  •  = Area of jet (m²)

The mass flow rate of the jet is:

The relative velocity between the jet and the plate is reduced because the plate is moving in the same direction as the jet. Hence, the impact force (F) acting on the plate is given by:

If the plate moves in the opposite direction of the jet, the relative velocity increases and the impact force becomes greater.

The work done (W) by the jet on the plate per second is given by:

This work represents the useful energy transferred from the fluid jet to the moving plate.

The efficiency (η) of energy transfer is:

The maximum efficiency occurs when the plate velocity , giving a maximum efficiency of 50%.

  1. Jet Impact on Curved Moving Plate

In many practical machines like Pelton turbines, the plate (bucket or vane) is curved to allow smooth deflection of the jet. The deflection helps in extracting more energy from the jet.

When the jet is deflected by a curved plate moving in the same direction as the jet, the change in momentum is greater than for a flat plate. The angle of deflection is usually 120° to 180°.

For a plate moving with velocity , the force on the plate is given by:

where  is the angle through which the jet is deflected.

The work done per second is:

The efficiency becomes:

For a deflection of 180° (), , giving maximum efficiency at , similar to a flat plate case, but with double the energy transfer due to reversal of flow.

Factors Affecting Jet Impact on Moving Plate

  1. Velocity of Jet (V):
    A higher jet velocity increases the kinetic energy and the impact force.
  2. Velocity of Plate (u):
    The relative velocity between jet and plate decides the actual force and work done.
  3. Direction of Motion:
    When the plate moves in the same direction as the jet, the force decreases. If it moves opposite, the force increases.
  4. Shape of Plate:
    Curved plates are more efficient as they allow smooth flow deflection with less loss.
  5. Deflection Angle:
    The greater the angle of deflection, the more is the change in momentum and the higher is the impact force.

Practical Applications

  1. Hydraulic Turbines:
    The Pelton wheel turbine works on this principle where the jet of water impacts curved moving buckets, producing rotation.
  2. Jet Propulsion Systems:
    The principle is reversed in jet propulsion, where the reaction of expelled fluid causes motion.
  3. Fluid Testing Apparatus:
    Jet impact experiments in laboratories measure forces on moving or stationary surfaces.
  4. Water Jet Systems:
    Used in cutting, cleaning, and propulsion mechanisms that utilize kinetic energy of fluids.
  5. Paddle Wheel Systems:
    The impact of moving water on rotating paddles converts water flow energy into mechanical energy.
Conclusion:

The jet impact on a moving plate demonstrates how kinetic energy of a fluid jet can be converted into mechanical work. The force and work done depend on the relative velocity between the jet and plate. For maximum efficiency, the plate should move at half the velocity of the jet. This concept forms the foundation for the working of hydraulic turbines, jet engines, and fluid power systems. Understanding this helps engineers design efficient systems for power generation and propulsion.