Conservation Laws

In fluid dynamics, 4 laws are used to analyse the fluid flow.

• Laws of mechanics
• Conservation of mass
• Conservation of energy
• Conservation of momentum

These laws are applied to a specific volume of the fluid in motion, and it’s called as control volume.

Control volume

A volume, through which a fluid flows.

• It’s a fixed volume
• Can either be real or imaginary

Conservation of mass

Mass cannot be created nor destroyed.

Conservation of energy

Energy cannot be created nor destroyed, but can be converted from one form to another.

Conservation of momentum

Unless a resultant force is exerted on a mass, it cannot gain or lose momentum.

Momentum

Derivations

Continuity equation

From the conservation of mass law, the below equation can be derived for an incompressible fluid:

Here:

• - Flow rate
• - Cross-sectional area
• - velocity

Bernoulli’s equation

For an incompressible fluid in steady flow, total head on a point is constant throughout a streamline. Can be derived from the conservation of energy law.

Here:

• - Datum head. Height to the point from a reference level.
• - Pressure head.
• - Velocity head. Kinetic energy per unit weight.

Note

• Head is the energy per unit weight.
• Piezometric head is equal to where is the piezometric pressure.

Steady flow momentum equation

Here:

• - Force exerted on the fluid within the control volume
• - Rate of change of momentum of the inflow fluid
• - Rate of change of momentum of the outflow fluid