Short Answer:

Impulse of a jet is defined as the force exerted by a jet of fluid when it strikes a surface and changes its momentum. It is the product of the rate of change of momentum and time during which the jet acts on the surface. The impulse represents the total effect of the jet over a short duration.

In simple terms, impulse of a jet refers to the total force developed when a high-velocity fluid jet hits an object, such as a plate or vane, causing a change in direction or velocity. It plays an important role in hydraulic turbines and jet propulsion systems where moving fluids perform mechanical work.

Detailed Explanation :

Impulse of a Jet

The impulse of a jet is a fundamental concept in fluid mechanics that describes how a moving jet of fluid exerts a force on a surface or an object when it strikes it. The impulse is caused by the change in momentum of the fluid due to the impact. When a fluid jet hits a stationary or moving surface, its velocity either changes direction or reduces in magnitude, resulting in a change of momentum. This change of momentum gives rise to an impulse or a force acting on the surface.

Mathematically, the impulse  is given by the relation:

where  is the force exerted by the jet, and  is the time duration during which the jet acts on the surface.

Since force is equal to the rate of change of momentum, we can also express impulse as:

where  is the mass of the fluid and  is the velocity. Hence, impulse represents the change in momentum of the jet over time.

Principle of Impulse of a Jet

The impulse of a jet is based on Newton’s Second Law of Motion, which states that the rate of change of momentum of a body is directly proportional to the applied force. When a fluid jet strikes a surface, it changes its momentum, and this change is responsible for developing a reactive force on the surface.

For example, when a jet of water from a nozzle strikes a plate, it exerts a force on the plate. The direction and magnitude of this force depend on the velocity, flow rate, and angle of impact of the jet. The total impulse is obtained by multiplying this force by the time for which it acts.

Expression for Force due to Impulse

If a jet of fluid with a velocity  and mass flow rate  (kg/s) strikes a surface, the force  exerted by the jet is given by:

where  and  are the velocities of the jet before and after impact respectively.

If the jet strikes a stationary flat plate normally (at 90°), the velocity after impact becomes zero, so:

Hence, impulse depends on the velocity and mass flow rate of the fluid jet.

Impulse on Different Types of Surfaces

1. Flat Plate (Normal Impact):
   When the jet strikes a flat plate normally, the entire momentum of the fluid is lost, and the reaction force on the plate is maximum.

1. Flat Plate (Inclined Impact):
   If the plate is inclined at an angle , only a component of velocity in the normal direction changes. The effective force becomes:

1. Curved Plate:
   In turbines, jets often strike curved vanes or blades. The jet changes direction smoothly, and the force is determined by the difference in velocity components before and after striking the vane. For a smooth 180° curve, the force becomes:

This type of impact is used in Pelton wheel turbines for high efficiency.

Applications of Impulse of a Jet

The concept of impulse of a jet is used in various hydraulic and mechanical systems, including:

1. Pelton Wheel Turbine:
   The Pelton turbine works entirely on the impulse principle. A jet of water strikes the buckets of the wheel, and the impulse causes rotation, converting fluid energy into mechanical energy.
2. Jet Propulsion Systems:
   The impulse of gases expelled from a nozzle provides thrust to rockets and jet engines. The change in momentum of exhaust gases generates an equal and opposite reaction force that propels the vehicle forward.
3. Hydraulic Machines:Devices like jet pumps and water jets use impulse principles to generate useful work.
4. Fluid Testing and Measurement:
   Impulse methods are used to measure the impact forces of fluid jets in laboratory experiments to study flow characteristics.

Factors Affecting Impulse of a Jet

1. Velocity of Jet: Higher velocity increases the momentum change and thus increases impulse.
2. Mass Flow Rate: Greater fluid discharge per second increases the total impulse.
3. Angle of Impact: The direction of the plate or vane changes how momentum is transferred.
4. Surface Shape: Curved surfaces provide smoother flow and higher efficiency.
5. Fluid Density: Denser fluids exert more force for the same velocity.

Conclusion:

The impulse of a jet is an essential concept in fluid mechanics that explains how moving fluids exert forces on surfaces through momentum change. It forms the working principle of impulse turbines, jet engines, and many hydraulic devices. Understanding impulse helps engineers design efficient systems that convert fluid energy into mechanical motion effectively and safely.