You are assigned the design of a cylindrical, pressurized water tank for a futur

Question

You are assigned the design of a cylindrical, pressurized water tank for a future colony on Mars, where the acceleration due to gravity is 3.71 meters per second per second. The pressure at the surface of the water will be 100 kPa , and the depth of the water will be 14.1 m . The pressure of the air in the building outside the tank will be 88.0 kPa .

A) Find the net downward force on the tank's flat bottom, of area 1.50 m2 , exerted by the water and air inside the tank and the air outside the tank.

Express your answer numerically in Newtons, to three significant figures.

Explanation / Answer

There is a downward force (due to the pressure of water plus enclosed air above it) and an upward force (due to the outside air pressure beneath the bottom).

Downward: F = rho g h A + 130*10^3 N/m^2 * A
= 1000 kg/m^3 * 3.71 m/s^2 * 14.1 m * 1.50m^2 + 100000 N/m^2 * 1.50 m^2
= 228466.5 N

Upward: F = p A = 88000 N/m^2 * 1.50 m^2 = 132000 kN


So the net downward force is

F = 965 kN

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