FLUID DYNAMICS: Body or volume forces, Surface forces, Line forces, FORCES ACTING ON FLUID IN MOTION, gravity force, pressure force, viscous force, turbulent flow, compressibility force, Reynolds’s equations of motion, Navier – Stokes equation, Euler’s equation of motion


A fluid in motion is subjected to several forces, which results in the variation of the acceleration and the energies involved in the flow of the fluid. The study of the forces and energies that are involved in the fluid flow is known as Dynamics of fluid flow.

The various forces acting on a fluid mass may be classified as:

1. Body or volume forces

2. Surface forces

3. Line forces.

Body forces: 

The body forces are the forces which are proportional to the volume of the body.

Examples: Weight, Centrifugal force, magnetic force, Electromotive force etc.

Surface forces: 

The surface forces are the forces which are proportional to the surface area which may include pressure force, shear or tangential force, force of compressibility and force due to turbulence etc.

Line forces: 

The line forces are the forces which are proportional to the length. Example is surface tension.

The dynamics of fluid flow is governed by Newton‟s second law of motion which states that the resultant force on any fluid element must be equal to the product of the mass and acceleration of the element and the acceleration vector has the direction of the resultant vector. The fluid is assumed to be in compressible and non- viscous.

Σ F = M. a

Where Σ F represents the resultant external force acting on the fluid element of mass M and a is total acceleration. Both the acceleration and the resultant external force must be along same line of action. The force and acceleration vectors can be resolved along the three reference directions x, y and z and the corresponding equations may be expressed as ;

Where Σ Fx , Σ Fy and Σ Fz are the components of the resultant force in the x, y and z directions respectively, and ax , ay and az are the components of the total acceleration in x, y and z directions respectively.


The various forces that influence the motion of fluid are due to gravity, pressure, viscosity, turbulence and compressibility.

The gravity force Fg is due to the weight of the fluid and is equal to Mg. The gravity force per unit volume is equal to “ρ g”.

The pressure force Fp is exerted on the fluid mass, if there exists a pressure gradiant between the two points in the direction of the flow.

The viscous force Fv is due to the viscosity of the flowing fluid and thus exists in case of all real fluids.

The turbulent flow Ft is due to the turbulence of the fluid flow.

The compressibility force Fc is due to the elastic property of the fluid and it is important only for compressible fluids.

If a certain mass of fluid in motion is influenced by all the above forces, then according to Newton‟s second law of motion

The net force Fx =M. ax = (Fg )x + ( Fp )x + ( Fv )x + ( Ft )x + ( Fc )x

i) if the net force due to compressibility (Fc) is negligible, 

the resulting net force Fx = (Fg) x + (Fp) x + (Fv) x + (Ft) x and the equation of motions are called Reynolds’s equations of motion.

ii) For flow where (Ft) is negligible, the resulting equations of motion are known as Navier – Stokes equation.

iii) If the flow is assumed to be ideal, viscous force (Fv) is zero and the equations of motion are known as Euler’s equation of motion.

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