4. Introduction
Impact of a jet is defines as the force produced by a jet of water as it strikes an object
(namely flat plate or hemispherical cup) due to the momentum of the jet. This force affects
the rate of momentum flow in the jet.
One of the applications of jet impact is used to generate electricity. Impact of jet is used to
rotate the turbine (Pelton wheel for example) in the generator. The water jet is applying
force tangential to the wheel.
Dr. Abdullah Al-Faruk 4
5. Impulse-Momentum principle
The Impulse-Momentum principle sates that “the impulse exerted on any body is equal to
the resulting changes in momentum of the body.”
This principle is a modified form of Newton’s second law of motion:
𝐹𝑥 =
𝑑
𝑑𝑡
𝑃𝑥 , where, 𝑃𝑥 = 𝑚𝑉
𝑥
𝐹𝑥 𝑑𝑡 = 𝑑 𝑃𝑥
The term 𝐹𝑥 𝑑𝑡 is impulse and the term 𝑑 𝑃𝑥 is the resulting change of momentum. Thus,
the product of a force and the time over which it is exerted is called impulse.
Dr. Abdullah Al-Faruk 5
6. Impulse-Momentum principle
The linear momentum equation for a control volume,
𝐹 =
𝑑
𝑑𝑡 𝐶𝑉
𝑉 𝜌𝑑∀ +
𝐶𝑆
𝑉 𝜌 𝑉. 𝑛 𝑑𝐴
For steady flow through the control volume,
𝐹 =
𝐶𝑆
𝑉 𝜌 𝑉. 𝑛 𝑑𝐴
where 𝑉. 𝑛 = 𝑉 cos 𝜃 is the normal component of velocity at an arbitrary control surface.
For uniform velocity distribution and normal (1-D) in/exit of flows through the surface
𝐹 = 𝑚 𝑉 𝑜𝑢𝑡
− 𝑚 𝑉 𝑖𝑛
where 𝑚 = 𝜌𝐴𝑉 is the mass flow rate.
For one inlet and one outlet of the control volume
𝐹 = 𝑚 𝑉out − 𝑉in
Dr. Abdullah Al-Faruk 6
7. Impulse-Momentum principle
If any force is exerted on a fluid, the fluid exerts an equal and opposite reaction force. As a
result, the force associated with momentum change of a fluid.
It can be interpreted as either an external force applied to the fluid (providing momentum to
the fluid in the direction of that force), or a force being applied by the fluid on its
surroundings, thereby depleting the fluid of momentum in the direction of that force.
For example, if water in a pipe is initially heading in the +𝑥 direction and takes a 180° turn:
• It can be interpreted as the pipe is applying a force, and therefore adding momentum to the
water in the −𝑥 direction. This force causes the 𝑥 component of the water’s velocity to
decrease and eventually become negative.
• Equivalently, it can be said that the water is applying a force to the pipe, and therefore losing
momentum in the +𝑥 direction.
Dr. Abdullah Al-Faruk 7
