Determine force of water on plate

[Bluestribute]

Homework Statement

As water flows through the pipe at a velocity of 5 m/s, it encounters the orifice plate, which has a hole in its center. The pressure at A is 255 kPa , and at B it is 180 kPa, Assume water is ideal fluid, that is, incompressible and frictionless. Determine the force the water exerts on the plate. Consider the volume of water between A and B as a control volume and apply linear momentum equation.

Homework Equations

F = d/dt ∫ρVdv + ∫Vρ(V•n)dA

The Attempt at a Solution

Well, I have velocity of 5 m/s, which is constant.
The density of the water should remain constant throughout time and space
I have two pressures
The area I used was π(200mm - 75mm)²

But I don't know what to do with volume, the integrals, anything. I don't even know if I'm using the right equation. Is this a Conservation of Energy equation instead? I know that has explicit pressure terms . . . But the problem says linear momentum . . . So do I use ρA + ρA?

 

[Chestermiller]

To determine the force that the water exerts on the plate, you need to determine the force that the plate exerts on the water. To do that, you need to do a momentum balance. If the inlet and outlet flows and velocities are the same, what is the rate of change of momentum of the fluid in passing through the control volume? What is the net pressure force acting on the fluid in the control volume? What other force is acting on the fluid in the direction of flow?

Chet

 

[Bluestribute]

So are you saying the CS integral will simply be ρV²A, and the other term will be ρV(dv/dt). Since you said a rate of change. And I don't know how to relate explicitly density and velocity to force

 

[Chestermiller]

So are you saying the CS integral will simply be ρV²A, and the other term will be ρV(dv/dt). Since you said a rate of change. And I don't know how to relate explicitly density and velocity to force

The rate of change of momentum within the control surface is zero:

[ρV²A]_out-[ρV²A]_in=0

So you don't have to know ρ and you don't have to know V.