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.
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
Power
Here:
- specific weight of the fluid - flow rate - total head