Basic Laws of Fluid Mechanics (Basic Concept of Fluid Mechanics Part-1)

A Fluid is a substance which is capable of flowing under the action of shear force. The space between fluid molecules is relatively large. E.g. liquid, gases, vapor etc.

Their intermolecular forces are low and fluid continuously undergoes deformation.

Ideal Fluid: It has no viscosity, no surface tension & incompressible

Real Fluid: It possesses the properties like viscosity, surface tension & compressibility

For a static fluid shear force is zero. Solid objects regain their original shapes after the force is removed if the shear force is within the elastic limit.

Cohesive force: Attraction between two similar molecules is known as cohesive force.

Adhesive force: Attraction between two different molecules is known as adhesive force.

Density or mass density (ρ): It is defined as the ratio of mass of the fluid to its volume.It’s unit is kg/m³.

Note: Density of water 1000kg/m³

  Density variation with temperature and pressure.  

Temperature ↓ ⇒ Density(ρ) ↑

Pressure ↑ ⇒ Density(ρ) ↑ 

Specific weight or weight density (γ): It is defined as the ratio of weight of the fluid to its volume.It’s unit is N/m³.

Specific gravity or Relative density (s): It is defined as the ratio of specific weight of the fluid to specific weight of a standard fluid.Standard fluid is water in case of fluid and air in case of gas.

It’s is dimensionless.

Specific volume : It is defined as the ratio of volume per unit mass.It’s unit is m³/kg.

Fluid pressure at a point in stationary fluid is the force acting on any area or surface is perpemdicular to that surface.

P = dF/dA

If force is uniformly distributed over surface area then 
P = F/A
It’s unit is Pascal(Pa).

Pascal’s Law:

According to this law pressure at a point in static fluid( fluid at rest) is equal in all directions.

If fluid is static then by pascal’s law

Px = Py= Pz

Hydrostatic’s Law

According to this law, the rate of increase in pressure in a vertical direction is equal to the weight density of the fluid at that point.

Now integrating the above expression from z = 0 to z = h  then pressure at depth h is given by 

P = ρgh

Relationship between pressures

  • Absolute pressure = Atmospheric Pressure + Gauge Pressure
  • Absolute pressure = Atmoshpheric Pressure – Vaccum pressure

Now let’s discuss few cases to measure the gauge pressure.

1. We want to find the pressure at point B in the following figure:

As we have discussed above that pressure at C will be given by Hydrostatic law

Pc = ρgh

and by pascal’s law Pressure at any point in same level will be same i.e. 

Pb = Pc = ρgh

2. We want to find the pressure at point B in the following figure:

By pascals law pressure will be same along A-A’  line.

Now applying hydrostatic law we can write

 

3. We want to find the pressure between points A& B in the following figure:

By pascals law pressure will be same along C-C’  line.

Now applying hydrostatic law we can write

 

Now we will see a case from which questions usually comes in exams

4. We want to find the pressure at point B in the following figure:

By pascals law pressure will be same along C-C’  line.

Now applying hydrostatic law we can write

 

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