A two dimensional jet in the form of a liquid sheet impinges

A two dimensional jet in the form of a liquid sheet impinges on a semicircular object as shown Figure P3.21. Develop an expression for the restraining force.

Solution

We know that the force exerted on a body is equal to the rate of change of momentum.

Now for the above situation, we have a liquid of volume AV going into the semicircle every seconds. That is,mass of the liquid being pushed in = AVp where p is the density of the liquid. Now this mass undergoes change of velocity from V to -V

That is, net change of 2V

Therefore net momentum change = 2ApV^2

This has to be equal to the force being exerted on the semicircular object from the right.

Therefore, F = 2ApV^2