L-shaped tank problem; forces due to water pressure

[Any Help]

Homework Statement

HELP! L-shaped tank problem! figure: http://www.webassign.net/hrw/hrw7_14-33.gif

The L-shaped tank shown below is filled with water and is open at the top.
(a) If d = 7.0 m, what is the force on face A due to the water?
(b) What is the force on face B due to the water?

Homework Equations

F=PA
P=pgh

The Attempt at a Solution

I've got the (a) part right: pgd*A = 1000*9.8*14*49 = 6722800.

However, I don't have a clue how I can get pressure on face B!

 

[mfb]

You should work with units.

What is the pressure (not force) at the top of B? What is the pressure at the bottom? Optional: What is the pressure at a height x above the bottom? How can you combine this information?

 

[Zypheros_Knight]

The tank is open from the top,dont you think atmospheric pressure should be added? Do you remember the law which states that fluids in closed systems transmit the same pressure at every surface of the closed vessel?

 

[gneill]

However, I don't have a clue how I can get pressure on face B!

If your course materials don't give you a "canned" formula for finding the net force on underwater vertical surfaces then presumably you'll be expected to derive them. What is your math background? Is a bit of calculus an option here?

The tank is open from the top,dont you think atmospheric pressure should be added?

No for two reasons:
1) The question specifically asks for the force due to the water.
2) The force due to air pressure will exist on both sides of an external tank wall, cancelling out.

 

[Zypheros_Knight]

Pressure at Bottom=ρgh
=1000*9.81*21
=206010 Pa
Pressure at Top=137340 Pa

Find the average and then substitute in P=F/A, face B's geometrical center is exactly at 3.5m so you can find the average force.

DONT QUOTE ME!

 

[mfb]

Providing full answers is against the forum rules, but your answer is wrong anyway. The pressure varies across the surface of B.

 

[Zypheros_Knight]

If your course materials don't give you a "canned" formula for finding the net force on underwater vertical surfaces then presumably you'll be expected to derive them. What is your math background? Is a bit of calculus an option here?No for two reasons:
1) The question specifically asks for the force due to the water.
2) The force due to air pressure will exist on both sides of an external tank wall, cancelling out.

I think calculus is not an option here as this is just high-school physics and sorry for my presumption, I thought that the question required the total force in one direction.( BTW for your second reason the resultant force is zero! Just 'Force' is a vector so you have to be specific otherwise the resultant force at B is 0 N if you know what I mean)

 

[Zypheros_Knight]

Providing full answers is against the forum rules, but your answer is wrong anyway. The pressure varies across the surface of B.

Oh sorry then...BTW I know what you mean but the question asks for ''Average Force'' at B
Edited: Now it doesn't give a full answer hope I helped!

 

[Any Help]

https://www.physicsforums.com/members/zypheros_knight.605857/ mfb gneill
can't we make an integral for force between 2d and 3d
then F=integral(density.g.d.A) with boundaries from 2d to 3d

 

[gneill]

https://www.physicsforums.com/members/zypheros_knight.605857/ mfb gneill
can't we make an integral for force between 2d and 3d
then F=integral(density.g.d.A) with boundaries from 2d to 3d

You can. Although it might be more instructive to take a general case first. It's a standard result that you can then use whenever this sort of problem pops up.

 

[Any Help]

You can. Although it might be more instructive to take a general case first. It's a standard result that you can then use whenever this sort of problem pops up.

then it will be density.g.A.(9d^2-4d^2)/2=1000x9.8x49x245/2= 58824500N please check my answer if I'm solving it correctly

 

[Zypheros_Knight]

then it will be density.g.A.(9d^2-4d^2)/2=1000x9.8x49x245/2= 58824500N please check my answer if I'm solving it correctly

Its wrong,BTW is this a high-school based question or a college based one because both will have different requirements? And please show your working (I haven't reached integration in my course!)

 

[gneill]

then it will be density.g.A.(9d^2-4d^2)/2=1000x9.8x49x245/2= 58824500N please check my answer if I'm solving it correctly

Can you go into detail about how you arrived at your formula? I suspect that you've made a slip regarding how the wall area fits into your result.

 

[Zypheros_Knight]

Can you go into detail about how you arrived at your formula? I suspect that you've made a slip regarding how the wall area fits into your result.

The wall area is 49 m2 but I can't figure out what integration method he used

 

[Any Help]

Can you go into detail about how you arrived at your formula? I suspect that you've made a slip regarding how the wall area fits into your result.

Can you go into detail about how you arrived at your formula? I suspect that you've made a slip regarding how the wall area fits into your result.

The wall area is 49 m2 but I can't figure out what integration method he used

forget it, okay area =49 now what ??

 

[Zypheros_Knight]

forget it, okay area =49 now what ??

Please tell us what level answer is required? Looks like you don't know about integration here's a link to a good place to start(https://www.wyzant.com/resources/lessons/math/calculus/integration)

 

[gneill]

forget it, okay area =49 now what ??

Your formula is pretty close to correct, but I believe you made a error when you introduced the area during your derivation. I really do suggest that you do the derivation for a general case, forgetting the multiples of d for the moment. Just assign a starting and ending depth to two variables. No numbers for now, just symbols.

 

[mfb]

then it will be density.g.A.(9d^2-4d^2)/2=1000x9.8x49x245/2= 58824500N please check my answer if I'm solving it correctly

Two ways to check:

- if you would have worked with units as I suggested in post #2 you would have noted your mistake directly at the point where you introduced it because the units stop matching there
- while B is a bit deeper than A, the pressure there is not completely different, and A and B have the same area. The value for B should be a bit higher, but certainly not 10 times the result for A.