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 115 kPa, and the depth of the water will be 14.3 m. The pressure of the air in the building outside the tank will be 95.0 kPa
Find the net downward force on the tank's flat bottom, of area 1.85 m^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

Given The pressure at the surface of the water tank is Ps = 115 kPa                                                                                       = 115 kPa(103Pa/kPa)                                                                                       = 115 x103Pa Acceleration due to gravity on Mars is gm = 3.71m/s2 Depth of the water is h =14.3 m The preesure in the air is Pair = 95.0 kPa                                                      =95 kPa(103Pa/kPa)                                                      = 95 x103Pa Area of the tank is A = 1.85m2                                                      =95 kPa(103Pa/kPa)                                                      = 95 x103Pa ---------------------------------------------------------------------------------------- The change in pressure is given by               P = Pb - Ps = g h The pressure at bottom is ---------------------------------------------------------------------------------------- The change in pressure is given by               P = Pb - Ps = g h The pressure at bottom is    Pb   = Ps+ P           = Ps+ gh The force on the bottom of the tank is      Fb = PbA            =( Ps+ gh ) A --------------------------------------------------------------------------------------- The net downward force on the tank's flat bottom is       Fnet= Fb - Fair               = ( Ps+ gh ) A - Pair A               = ( Ps -Pair+ gh ) A               = [(115x103Pa) - (95.0x103Pa) + (1000 kg/m3) (3.71m/s2) (14.3 m)] (1.85m2)                = 1.3515x 105 N                = 135.15 kN                = 135.15 kN

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