Hi everyone, im stuck on this question regarding immersed fluids, any help on this would be great thank you !
Question>
A tank (4m wide, 4m long and 2m high) is filled with is filled with 3000 litres of fluid A, 4000 litres of fluid B and 2000 litres of fluid C. The density of fluid A is 1200 kg/m3, the density of fluid B is 1100 kg/m3, and the density of fluid C is 800kg/m3. If the tank contains all three fluids, what is the force on each side of the tank?
Question>
A tank (4m wide, 4m long and 2m high) is filled with is filled with 3000 litres of fluid A, 4000 litres of fluid B and 2000 litres of fluid C. The density of fluid A is 1200 kg/m3, the density of fluid B is 1100 kg/m3, and the density of fluid C is 800kg/m3. If the tank contains all three fluids, what is the force on each side of the tank?
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So it contains 9000 litres of fluid, or 9 m^3. So the fluid is 9/16 m deep. The pressure at depth h is rho*g*h. Assume the density is the weighted average of the three, integrate pressure over the depth in the tank, don't forget to multiply out by the width of the walls and bob's yr uncle init.
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Zero to 9/16
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Edit. multiply out by the width of only one wall, as asked by the question
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Ok, hang on. Look at the densities. If you mix them in the ratio of their proportions you can't get 3100 kg/m3. I make it 1066.7. Will do the rest too. Hold on
I would do it like this:
F = Width * Integral[rho * g * h]dh from 0 to 9/16
F = 4 * rho * 9.81 * (9/16)^2 / 2
Denisty = (3/9)*1200 + (4/9)*1100 + (2/9)*800
F = 6621.75 N
Please check. I take no responsibility for mistakes..!!!
____
Zero to 9/16
________
Edit. multiply out by the width of only one wall, as asked by the question
______
Ok, hang on. Look at the densities. If you mix them in the ratio of their proportions you can't get 3100 kg/m3. I make it 1066.7. Will do the rest too. Hold on
I would do it like this:
F = Width * Integral[rho * g * h]dh from 0 to 9/16
F = 4 * rho * 9.81 * (9/16)^2 / 2
Denisty = (3/9)*1200 + (4/9)*1100 + (2/9)*800
F = 6621.75 N
Please check. I take no responsibility for mistakes..!!!