Physics Help Forum Hydrostatic force on side of tank

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 Jun 24th 2018, 04:44 PM #1 Junior Member   Join Date: Jun 2018 Posts: 2 Hydrostatic force on side of tank Hi, I would like to know how to calculate the force on side of a water storage tank. Given the water tank size is L=5m, W=4m, H=3m. The tank is fill with water up to 3m high. What is the hydrostatic force exerted on the wall of the storage tanks at a) 1m high b) 2m high c) 3m high d) and at the base of the tank? Appreciate your help.
 Jun 24th 2018, 10:00 PM #2 Senior Member   Join Date: Apr 2017 Posts: 362 The force on the wall of a tank or on the bottom, comes from the height of water above the point you are considering ... The easiest way to consider this is to remember that 10.33 m of water gives one atmosphere in pressure .... so if you take a lung full of air at the surface , and swim down to a depth of 10.33m , the air in your lungs will be compressed to half the original volume ... you experience 2 atmospheres pressure at that depth .... In your tank the deepest water is 3m ...at that depth pressure is 3/10.33 about 0.29 atm. At 2 meters pressure is 2/10.33 about 0.19 atm ... so the pressure on the wall varies , falling to zero at the water surface .... I'm sure another member can solve this problem in a more tidy manner... Last edited by oz93666; Jun 24th 2018 at 10:03 PM.
Jun 25th 2018, 02:50 AM   #3
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 Originally Posted by piupiu Hi, I would like to know how to calculate the force on side of a water storage tank. Given the water tank size is L=5m, W=4m, H=3m. The tank is fill with water up to 3m high. What is the hydrostatic force exerted on the wall of the storage tanks at a) 1m high b) 2m high c) 3m high d) and at the base of the tank? Appreciate your help.
The pressure difference relative to the adjacent atmospheric layer due to a liquid is

$\displaystyle \Delta P = \rho g \Delta z$

where $\displaystyle \rho$ is the density of the fluid, g is the gravitational acceleration (9.81 m/s$\displaystyle ^2$) and $\displaystyle \Delta z$ is the depth. If you assume that there's terrestrial air above the water, the pressure of the adjacent layer is 101325 Pa. Then, the pressure difference from this value can be calculated if you substitute for the density of water and the Earth's gravitational acceleration.

 Jun 25th 2018, 06:01 AM #4 Junior Member   Join Date: Jun 2018 Posts: 2 I am referring to the hydrostatic force not pressure.
Jun 25th 2018, 07:09 AM   #5
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 Originally Posted by piupiu I am referring to the hydrostatic force not pressure.
Okay, but force is just pressure multiplied by area, so once you have the pressure the force is easily obtained by multiplying it by the surface area of the tank at the height required.

Jun 25th 2018, 07:13 PM   #6
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 Originally Posted by piupiu Hi, I would like to know how to calculate the force on side of a water storage tank..
OK ..fair enough .. lets take the side 3m by 5m ....=15 square meters

So you want to find the force that is pushing on that whole wall

We saw in my previous post the pressure under 3 m of water depth is 0.2904 Atmospheric pressure , or 29.4 KPa (KN/m squared)...

But at the top of the tank the pressure is zero , and as you move down the pressure increase linearly to the max 29.4 at 3 m

So the average pressure on the wall is 29.4/2 = 14.7 KN/m squared

And the area of the wall is 15 msq ...

So force is ...15 x 14.7 = 220.5 KN or 22.05 tonnes weight

The force pushing this wall out is equivalent to the weight of 22 tonnes in earth gravity ...I kid you not ...that is correct!

And the force pushing downwards on the bottom of the tank is 60 tonnes

If the tank is resting on a flat solid surface this is no problem , the surface pushes back supporting the bottom ....

But if the tank was supported by it's edges as it might be if on a tower , the the bottom of the tank had better be strong enough to hold the weight of 60 cars without buckling! and this is a relatively small 4 by 5 meter bottom.

 Tags force, hydrostatic, side, tank

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