Question

What will be the gauge pressure and the absolute pressure of water at depth 12m below the surface?

Answer 1

As a very first step, one could define both the given terms, namely, gauge pressure and absolute pressure. From their respective definitions, you may realize that the absolute pressure is the sum of gauge pressure and atmospheric pressure. Now, you could accordingly find the answer.

Formula used:
Absolute pressure = gauge pressure + atmospheric pressure
Gauge pressure,
${{G}_{p}}=\rho gh$

Complete step-by-step solution:
In the question, we are asked to find the gauge pressure and absolute pressure at a certain depth of 12m below the surface.
Before finding the values, we have to be well aware of the difference between gauge pressure and absolute pressure. The main difference lies in their respective zero points. For the case of absolute pressure, the zero point is the absolute zero while in the case of gauge pressure, the zero point is the atmospheric pressure. So, basically, absolute pressure would be the sum of gauge pressure and atmospheric pressure. That is,
Absolute pressure = gauge pressure + atmospheric pressure ……………………………………… (1)
We could also define the gauge pressure as the pressure exerted by the liquid column above the point under consideration alone. It is given by,
${{G}_{p}}=\rho gh$ ………………………………………… (2)
Substituting the values we get,
${{G}_{p}}={{10}^{3}}\times 9.8\times 12$
$\Rightarrow {{G}_{p}}=117kPa$ ……………………………………………. (3)
Substituting (3) in (1), we get the absolute pressure to be,
Absolute pressure = 117 + 100 =217kPa
Therefore, we found the values of gauge pressure and absolute pressure to be 117kPa and 217kPa respectively.

Note: In the equation (2), $\rho$ is the density of water and g is the acceleration due to gravity. We have accordingly substituted the known standard values for each of them. When we are supposed to measure or control a pressure that could be influenced by changes in atmospheric pressure, we find the gauge pressure and for the case where the pressure isn’t influenced by atmospheric pressure changes, then we measure the absolute pressure.