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 145 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 87.0 kPa . A.Find the net downward force on the tank's flat bottom, of area 2.00 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

Reading between the lines, the cylinder is upright, and pressurized internally. It is in an environment that is also pressurized. The cylinder is 14.3 m high.

From the weight of the water alone, the pressure is:

Pfluid = gh
Pfluid is pressure in Pa or N/m²
is the density of the fluid in kg/m³
density of water at 20C = 0.998 g/cm³ = 998 kg/m³
Pfluid = 998 x 3.71 x 14.3 = 52947 Pa or 52.947 kPa

Pressure from the pressurized environments is
145k – 87k = 60k

adding that to the fluid pressure, total pressure at the bottom of the tank is
P = 60k pa + 52.947k pa = 112.947k Pa

Force = pressure x area = 112.947 x 2 = 225894Newtons.

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