Question

The correct relationship between gauge pressure, atmospheric pressure and absolute pressure is
$$\begin{gathered} A)Gauge\text{ pressure = Atmospheric pressure - Absolute pressure} \\ \text{B)}Gauge\text{ pressure = Atmospheric pressure + Absolute pressure} \\ \text{C)Absolute pressure = Atmospheric pressure + Gauge pressure} \\ \text{D)None of the above} \end{gathered}$$

Answer 1

Hint: In order to solve this question, firstly we will apply the concept of Pascal’s principle i.e. $P_{abs}=P_g+P_{atm}$. Then we will compare the given options to find the required answer.

Complete Step-by-Step solution:
As we know that the Tire gauges are simply designed to read zero at atmospheric pressure and positive when pressure is greater than atmospheric. Similarly, atmospheric pressure adds to blood pressure in every part of the circulatory system.
According to Pascal’s principle, the total pressure in a fluid is the sum of the pressures from different sources. Pascal also found that the pressure at a point in a resting fluid is the same in all directions; the pressure on all planes going through a particular point will be the same. This truth is also known as the law of Pascal.
In brief, it is very common for pressure gauges to ignore atmospheric pressure – that is to zero at atmospheric pressure. Consequently, total pressure or absolute pressure is the sum of gauge pressure and atmospheric pressure.
$P_{abs}=P_g+P_{atm}$
Where,
$$\begin{gathered} P_{abs}=absolute\text{ pressure} \\ {P}_g=Gauge\text{ pressure} \\ {\text{P}}_{atm}=Atmospheric\text{ pressure} \end{gathered}$$
Absolute pressure – It is the sum of gauge pressure and the atmospheric pressure.
Gauge pressure – This is the pressure compared to the pressure of the atmosphere. For pressure above atmospheric pressure, gauge pressure is positive, and negative for pressure below it.
Atmospheric pressure-The weight of the air above the surface is defined as the force per unit area exerted against a surface.
Therefore, we conclude that absolute pressure is the sum of gauge pressure and atmospheric pressure.
Hence, option C is correct.

Note- While solving this question, we must know the principle of Pascal i.e.In both directions the pressure at a point in the fluid at rest is the same. Also one should know the applications of Pascal’s principle i.e. It can be explained by hydraulic jacks, car brakes and even the lift produced on aircraft wings.