Different Pressures in Fluid Mechanics

The pressure on a fluid can be measured depending on two systems where one system measure pressure above the absolute zero pressure scale and the other measure below the absolute zero pressure scale. Hence there are different pressure terminologies in fluid mechanics.

The different kinds of pressure are:

1. Absolute Pressure
2. Gauge Pressure
3. Vacuum Pressure

Relationship between different pressures are shown in figure-1 below.

1.Absolute Pressure

Absolute pressure is the pressure that is measured with reference to the absolute zero level in the pressure scale. The figure-1 shows absolute pressure with reference to absolute zero level. Absolute pressure can never be negative. It is represented by ‘p’.

Note: Atmospheric pressure is the pressure present in the atmosphere. Absolute zero pressure or vacuum level is the space where there is no pressure acting.

2. Gauge Pressure

A gauge pressure is determined by means of a pressure measuring instrument where the datum taken would be atmospheric pressure. On the scale, the atmospheric pressure is marked as zero.

When the pressure is same as atmospheric pressure, the gauge pressure would be zero. Guage pressure can show a value less than zero(negative). If guagepressure is represented by Pg, then,

Pg = P-Pa Eq.1

Where, Pa = Local Atmospheric Pressure

3. Vacuum Pressure

Vacuum pressure is the pressure below the atmospheric pressure.Vacuum pressure is used when the gauge pressure is negative. Positive vacuum pressure means the gauge pressure is negative.

The vacuum pressure is represented by Pvacuum. Then,

Pvacuum = Pa – P Eq.2

Note: The atmospheric pressure at sea level at a temperature of 15 degree Celsius is 101.3 kN/m² or 10.13N/cm² in SI unit. The atmospheric pressure head is 760mm of mercury or 10.33 of water.

Determination of Gauge Pressure and Absolute Pressure

A simple problem is used to explain the determination of pressures.

Problem: The density of a given fluid is 1530kg/m³ at an atmospheric pressure equivalent to 750mm of merrcury. Determine the gauge pressure and absolute pressure at a depth 3m below the surface of the fluid.

Solution: As per Hydrostatic law, the rate of increase of pressure in a vertically downward direction acting on a point on the fluid must be equal to the specific weight of the fluid at that point. Based on the law:

By integrating both the sides,

Where, Z= Height of the point from the free surface or Pressure Head; p = atmospheric pressure; g = gravitational force;

Given data from the problem:

1. Depth of the liquid = Z1 = 3m
2. Density of the liquid = 1530kg/m³
3. Zo = atmospheric pressure head = 750mm of Hg = 0.75 m of Hg

From eq.4,

Atmospheric Pressure Pa = density x g x z

i.e. Pa = density of mercury x 9.81 x Zo

Density of Mercury = specific gravity of mercury x density of water

= 13.6 x 1000kg/m³

i.e Pa = 13.6 x 1000 x 9.81 x 0.75 = 100062 N/m²

The pressure at a point 3m below the surface of the fluid is given by;

P1 = density of fluid x g x Z1 = 1530 x 9.81 x 3 = 45028N/m²

The pressure obtained is positive. Hence,

Gauge Pressure, Pg = 45028N/m²
Absolute Pressure = Guage Pressure + Atmospheric Pressure

= 45028 + 100062 = 145090N/m²

Absolute Pressure, P = 145090 N/m²