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

Question

Express your answer numerically in Newtons, to three significant figures. 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 125kPa , and the depth of the water will be 14.5m . The pressure of the air in the building outside the tank will be 93.0kPa . Find the net downward force on the tank's flat bottom, of area 2.45m 2 , 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

pressure at the surface of the water in the tank, Ps = 125 kPa

pressure at the bottom of the tank, Pb = Ps + pgh (where p = density)

Pb = 125 * 10^3 + 1000*9.8*14.5

Pb = 267.1 * 10^3

Pb = 267.1 kPa

Pressure outside the bottom of the tank, P_out = 93 kPa

area of the base of the cylinder, A = 2.45 m^2

net outward force acting on the base of the cylinder, F_out = (Pb - P_out) A

F_out = (267.1 * 10^3 - 93 * 10^3) 2.45

F_out = 426.545 * 10^3 N

F_out = 4.26 * 10^5 N..............upto three significant figures

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