Contents

## Introduction:

The normal stress in a fluid at rest is called pressure. the stresses at a point are defined as the force per unit area and are determined by dividing the force by the area on which it acts.

The normal component of force acting per unit area on a surface is called normal stress, and the tangent component of force is called shear stress.

When the fluid is confined within the solid boundaries, it exerts a force against the boundary surfaces. The applied force always acts in the direction normal to the surface in contact. Because the fluid at rest cannot maintain the shear stress and hence has no tangent component.

## Fluid Pressure at a Point:

Pressure or pressure intensity can be defined as the force exerted on a unit area. Thus, p = dF/dA where dF = an infinitesimal area dA . force acting on

## Pascal’s Law for Pressure at a Point:

According to Pascal’s law, the pressure at a point in a fluid system is distributed equally in all directions.

This means that the pressure at any point in rest or motion of a fluid is independent of the direction because no shear stress is present.

The pressure in a fluid system has a magnitude but is not specific. a point in the direction of the fluid system and, thus, is a scalar quantity.

This applies to fluid rest.

In the case of the fluid being reduced, the relative motion between the particles of the fluid will result in the establishment of shear stress.

The pressure at a point is then assumed to be the mean of the normal forces per unit area (stress) on three mutually perpendicular planes. Since these normal stresses are usually larger than the shear stresses, it is generally assumed that Pascal’s law still applies.

## Units of Pressure:

- 1 pa= 1N/m²
- 1 kgf/cm² = 9.80 * 10_4 N/mm²
- 1 Bar = 10_5 Pa
- 1 atm = 101325 Pa
- 1Psi = 6888.1 Pa, 1atm = 14.7 psi
- 1 torr = 1 mm Hg
- Pressure can also be represented in terms of the height of the liquid column. Ex.: 1 atm= 760 mm of Hg = 10.3 m of water.

## Different Types of Pressure:

- Atmospheric Pressure
- Absolute Pressure
- Gauge Pressure

### 1. Atmospheric Pressure:

The pressure exerted by atmospheric air normally on all the surfaces with which it is in contact is known as atmospheric pressure.

### 2. Absolute Pressure:

The pressure measured above absolute zero (or absolute vacuum) is known as absolute pressure.

### 3. Gauge Pressure:

The pressure measured above or below atmospheric pressure is known as gauge pressure. Thus, the gauge pressure can be negative or positive. Its value will be negative if the value of absolute pressure is less than atmospheric pressure and vice versa.

If the pressure of a fluid is less than atmospheric pressure, it is designated as vacuum pressure (or suction pressure or negative gauge pressure) and its gauge value is the amount by which it is lower than atmospheric pressure.

Absolute Pressure = Atmospheric Pressure + Gauge Pressure

Absolute Pressure = Atmospheric Pressure – Vacuum Pressure

Pressures are assumed to be gauge pressures unless specifically designated as absolute. For e.g. 100 kPa (abs) would refer to absolute pressures.

## Pressure Head:

The vertical height of the free surface above any point in a liquid at rest is known as the pressure head for that point.

Relationship between the heights of columns of different liquids which would develop the same pressure at any point, p = γ1h1 = γ2h2. If S1 and S2 are specific gravities of the two liquids then,

p= S1γwh1 = S2γwh2

S1h1=S2h2

### Pressure in a Compressible Fluid:

For a compressible fluid, the density varies with the pressure, therefore

where, P = pressure at elevation z1 ; p2 = pressure at elevation z2