Question

A 1-m-tall barrel is closed on top except for a chin pipeextending 5 m up from the top. When the barrel is filledwith water up to the base of the pipe (I m deep) the waterpressure on the bottom of the barrel is 10 kPa. What isthe pressure on the bottom when water is added to fill thepipe to its top?

Answer 1

The diagram representing the scenario is shown below

The formula for calculating the pressure of a liquid in a vertical pipe is expressed as

Pressure = height x density of liquid x acceleration due to gravity

Considering the 1 m barrel,

height = 1

Pressure = 10kpa.

We need to convert 10kpa to pascal

Recall

1 kpa = 1000 pa

10 kpa = 10 x 1000 = 10000 pa

Thus,

pressure = 10000 pa

acceleration due to gravity = 9.8

By substituting these values into the formula, we have

10000 = density x 9.8 x 1

density = 10000/9.8 = 1020.41 kg/m^3

Considering the 5m pipe,

density = 1020.41

height = 5

Thus,

Pressure = 1020.41 x 9.8 x 5 = 50000.1 pa

Pressure on the bottom = sum of both pressures

Pressure on the bottom = 10000 + 50000.1

Pressure on the bottom = 60000.1 pa