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 130 kPa , and the depth of the water will be 14.0 m . The pressure of the air in the building outside the tank will be 89.0 kPa .

Find the net downward force on the tank's flat bottom, of area 2.30 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

Given,

The pressure at the surface of the water tank, Ps = 130 kPa = 130 x 103

Acceleration due to gravity on Mars, gm = 3.71 m/s2

Depth of the water, h =14 m

The preesure in the air, Pair = 89 kPa = 89 x103 Pa

Area of the tank, A = 2.30 m2

The change in pressure, P = Pb - Ps = g h

The pressure at bottom, Pb = Ps+ P = Ps+ gh

The force on the bottom of the tank, Fb = PbA =( Ps+ gh ) A

The net downward force on the tank's flat bottom, Fnet = Fb - Fair = ( Ps+ gh ) A - Pair A

= ( Ps -Pair+ gh ) A

= [(130 x103) - (89x103) + (1000) (3.71) (14)] (2.30)

               = 2.13 x 105 N

Fnet = 213 kN

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