Question

The surface pressure on Venus is 92.00 atm, and the acceleration due to gravity there is 0.894 g. In a future exploratory mission, an upright cylindrical tank of benzene is sealed at the top but still pressurized at 92.00 atm just above the benzene. The tank has a diameter of 1.75 m , and the benzene column is 10.30 m tall. Ignore any effects due to the very high temperature on Venus.

For all answers please use, F= ? Newtons, Use 4 sig figs in all answers. Thanks!

A) What total force is exerted on the inside surface of the bottom of the tank?

B) What force does the Venusian atmosphere exert on the outside surface of the bottom of the tank?

C)What total inward force does the atmosphere exert on the vertical walls of the tank?

Answer 1

(A) Pressure of benzene inside the tank, P = 92.0 atm = 92.0 x 101325 N/m^2 = 9321900 N/m^2

Surface area of the bottom of the tank, A = pi*r^2 = 3.141*(1.75/2)^2 = 2.405 m^2

So, the force exerted on the bottom of the tank = P x A

= 9321900 x 2.405 = 22417567.3 N = 22417.6 kN

(B) Outside pressure is also equal to 92.0 atm.

So, the force on the outside surface of the bottom of the tank = 22417.6 kN

(C) Surface area of the vertical wall of the cylinder = 2*pi*r*h = 2*3.141*(1.75/2)*10.30 = 56.62 m^2

So, the force on the vertical wall = 9321900 x 56.62 = 527805978 N = 527806 kN.