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 m/s2. The pressure at the surface of the water will be 110 kPa , and the depth of the water will be 13.7 m . The pressure of the air outside the tank, which is elevated above the ground, will be 85.0 kPa .

Find the net downward force on the tank's flat bottom, of area 2.50 m^2 , exerted by the water and air inside the tank and the air outside the tank. Assume that the density of water is 1.00 g/cm^3

Express your answer in newtons.

Answer 1

From the question, it's clear that we need to calculate the net pressure acting at the bottom of the surface of the cylinder. One key point given in the question is that the water tank is elevated from the ground. As now there will be pressure due to air outside the tank, acting in the opposite direction to that of the hydrostatic pressure (Pressure due to static water) and surface pressure (pressure due to the air inside the tank).

Given details:

Height of water in the tank (h)= 13.7 m

Density of water () = 1.00 g/cm^3 = 1000 Kg/m^3

Area of the bottom of the tank (A) = 2.50 m^2

Acceleration due to gravity(g) = 3.71 m/s^2

The pressure at the surface of the water is due to the air present inside the tank.

   = 110 kPa             ...(1)

The pressure due to water at the bottom of the tank.

              

            .....(2)

The pressure due to air outside the tank.

= 85.0 kPa              .......(3)

From the above figure and eqns. (1),(2) and (3), the net pressure acting at the bottom of the tank is:

The net force acting at the bottom of the tank is: