Question

A tube of water is open on one end to the environment while the other end is closed. The height of the water relative to the base is 100 cm on the open end and 40 cm on the closed end. What is the absolute pressure of the water at the top of the closed end in units of atm

Answer 1

Answer:

1.06 atm

Explanation:

On the open end of the tube, the pressure will be the sum of atmospheric pressure and the pressure due to the height of water

The pressure due to a height of water = ρgh

where ρ is the density of water = 1000 kg/m^3

g is the acceleration due to gravity = 9.81 m/s^2

h is the height of the water column

The height of water column on the open end = 100 cm = 1 m

pressure on this end = ρgh = 1000 x 9.81 x 1 = 9810 Pa

Atmospheric pressure = 101325 Pa

The total pressure on the open end =  101325 Pa + 9810 Pa = 111135 Pa

The pressure due to the water column on the closed end = ρgh

The height of the water in the closed end = 40 cm = 0.4 m

The pressure due to this column of water = 1000 x 9.81 x 0.4 = 3924 Pa

The resultant pressure on the water on the top of the closed end of the tube = 111135 Pa - 3924 Pa = 107211 Pa

In atm unit, this pressure = 107211/101325 = 1.06 atm