How Is Force Calculated on a Plate Stopping Water in a Pipe?

[azure kitsune]

Homework Statement

Water flows at 7 m/s in a pipe of radius 5 cm. A plate having an area equal to the cross-sectional area of the pipe is suddenly inserted to stop the flow. Find the force exerted on the plate. Take the speed of sound in water to be 1.4 km/s. (Hint: When the plate is inserted, a pressure wave propagates through the water at the speed of sound v_s. The mass of water brought to a stop in time Δt is the water in a length of tube equal to v_sΔt.)

Homework Equations

P = F/A

The Attempt at a Solution

I am trying to attempt the problem in the following way: Consider a reference frame where the water is still. Then the insertion of the plate would actually be a plate moving at 7 m/s, causing the still water to start moving. However, I am not sure how to get the force from this. It's probably going to be from P = F/A. Can anyone help me get started on this problem?

 

[aim1732]

You can easily work it out using the hint. The amount of water stopped by the plate is v*dt*A where A=pi*r*r. Now you can find mass and momentum stopped using density and initial velocity of flowing water. Force is thus time rate of change of momentum. Since I can not think of a retarding force on water other than that by the plate, this may be the answer.