Finding the force of water in a pool on a vertical wall

In summary, the conversation discusses finding the force of water on the short vertical side of a swimming pool with dimensions 24 m by 9.0 m by 2.5 m. The formula F = P*A is used, where P = rho * g * h, and the integration of pressure by height is used to find the force. The correct answer is achieved when using 2.5 m as the depth and 9 m as the width. The conversation also addresses the confusion about the depth and how atmospheric pressure should be taken into account.
  • #1
chenying
48
0

Homework Statement


A swimming pool has the dimensions 24 m multiplied by 9.0 m multiplied by 2.5 m.

(a) When it is filled with water, what is the force (resulting from the water alone) on the bottom, on the short sides, and on the long sides?


Homework Equations



F = P*A

P = rho * g * h

The Attempt at a Solution



Ok, I have no idea what I am doing wrong, but I am trying to find the force of water on the short vertical side of the pool.

So, since pressure varies by height, I have to intergrate the pressure by height (h).

So P = [tex]\int\rho g dh[/tex]

and A = h*w where w = width of the pool

So F = [tex]\int\rho g dh h*w [/tex]

then you end up with [tex]\rho*w*g*(h^2)/2[/tex] from 0 to 9

and get 992250 Pa

I'm pretty sure what I did was correct, but I am not getting the right answer.

Can anyone help?
 
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  • #2
Seems good to me. Are you sure you didn't get your dimensions mixed up? That is, are you sure you used the right values for w and h?
 
  • #3
Well, for one thing, 2.5 m is the only sensible choice for the depth of the pool! If either of the other two is the depth, then that is one strange pool.
 
  • #4
Why would 2.5 be the sensible height? i thought it would be the width of the pool.
 
  • #5
Who has swum in a pool of 30' depth?

Edit: one other thing bothers me about the solution, the pressure at 0' depth is not 0 pressure but atmospheric pressure which I think should be accounted for if we are interested in the total pressure exerted on any of the surfaces, or am I confused?
 
  • #6
denverdoc said:
Who has swum in a pool of 30' depth?

Edit: one other thing bothers me about the solution, the pressure at 0' depth is not 0 pressure but atmospheric pressure which I think should be accounted for if we are interested in the total pressure exerted on any of the surfaces, or am I confused?

Oh, I guess that is rather large...

But yes, you are right, atmospheric pressure is the pressure at the surface, but the problem states to not take that into account.
 
  • #7
very well, I would try using 2.5 as the depth and 9 as the width as Cepheid suggests. See if you get the right answer
 
  • #8
I did and came out with the right answer. Thanks a lot!
 
  • #9
Thank Cepheid, he caught the error, but you're welcome.
 

Related to Finding the force of water in a pool on a vertical wall

1. What is the force of water in a pool on a vertical wall?

The force of water in a pool on a vertical wall is the pressure exerted by the water on the wall due to its weight and depth. This force is measured in units of newtons per square meter (N/m2), also known as pascals (Pa).

2. How do you calculate the force of water in a pool on a vertical wall?

The force of water in a pool on a vertical wall can be calculated using the formula F = ρgh, where F is the force in newtons, ρ is the density of water in kilograms per cubic meter (kg/m3), g is the acceleration due to gravity (9.8 m/s2), and h is the depth of the water in meters.

3. Does the height of the water affect the force on the vertical wall?

Yes, the height of the water does affect the force on the vertical wall. According to the formula F = ρgh, the force is directly proportional to the depth of the water. This means that as the height of the water increases, so does the force exerted on the wall.

4. What other factors can affect the force of water in a pool on a vertical wall?

In addition to the height of the water, the shape and size of the pool, the material and texture of the wall, and the temperature of the water can also affect the force exerted on the wall. These factors can change the density and viscosity of the water, which in turn affects the force.

5. Is it important to calculate the force of water on a vertical wall in a pool?

Yes, it is important to calculate the force of water on a vertical wall in a pool in order to ensure that the wall is strong enough to withstand the pressure exerted by the water. This is especially important for pools with high water levels or for walls made of weaker materials. It is also important for safety reasons, as a wall that cannot withstand the force of the water could potentially collapse and cause harm.

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