Statics, moment on submerged surface problem

[jasonnaylor]

Homework Statement

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Shown below is a slew gate controlling the flow of salt water flowing into fresh water in a submarine depressurising chamber (used to measure the pressure depth and which is compared to a control signal that has been calibrated).

On the inlet side, the depth of salt water is 2.93m and on the outlet side the freshwater is to a depth of 2m. Assuming the width of the plate is 2.2m, calculate the fluid moment at the centre of pressure location on the inlet face.
If the plate is 10mm thick and the hole is drilled 5mm to the right of the centre line, what will be the overall effect of the difference in pressure between inlet and outlet on the plate material. Assume the plate to have an E-value of 140GN/m2

Homework Equations

Total force= ρgAy

I have worked this out to be (1030)x(9.81)X((2.93X2.2)-(πd2/4))X (2.93/2) = 94.7KN

The Attempt at a Solution

[/B]
I have worked the total force to be (1030)x(9.81)X((2.93X2.2)-(πd2/4))X (2.93/2) = 94.7KN
Have no clue where to go next. Where would the centre of pressure be, it can't surely be the centroid as there's a pressure void where the hole lies.

 

[SteamKing]

Homework Statement

[/B]
Shown below is a slew gate controlling the flow of salt water flowing into fresh water in a submarine depressurising chamber (used to measure the pressure depth and which is compared to a control signal that has been calibrated).

On the inlet side, the depth of salt water is 2.93m and on the outlet side the freshwater is to a depth of 2m. Assuming the width of the plate is 2.2m, calculate the fluid moment at the centre of pressure location on the inlet face.
If the plate is 10mm thick and the hole is drilled 5mm to the right of the centre line, what will be the overall effect of the difference in pressure between inlet and outlet on the plate material. Assume the plate to have an E-value of 140GN/m2

Homework Equations

Total force= ρgAy

I have worked this out to be (1030)x(9.81)X((2.93X2.2)-(πd2/4))X (2.93/2) = 94.7KN

The Attempt at a Solution

[/B]
I have worked the total force to be (1030)x(9.81)X((2.93X2.2)-(πd2/4))X (2.93/2) = 94.7KN
Have no clue where to go next. Where would the centre of pressure be, it can't surely be the centroid as there's a pressure void where the hole lies.

I think I understand this part of your force calculation: (1030)x(9.81)X((2.93X2.2)
What is not clear to me is this part: (πd² / 4)) * (2.93 / 2). Why have you divided the depth of the saltwater by 2?

Isn't the surface of the water over the top of the pipe connecting the outlet plate and the inlet plate?

After all, the pipe has a diameter of 0.23 m and its centerline is located 0.75m above the bottom edge of the plates.

And to give you a hint about the center of pressure, no the center of pressure is not located at the centroid of the plate (minus the hole). You have to account for the variation of water pressure with depth on the plate in order to calculate the c.o.p.