Steady State Energy Equation

The system energy per unit mass E may be of several types:
E = Einternal + Ekinetic + Epotential + Eother
Eother= chemical reactions, nuclear reactions, and electrostatic or magnetic field effects. And it will be neglected here.

Einternal = internal energy due to pressure

Ekinetic = kinetic energy due to flow(velocity)

Epotential= z = potential energy due to position.
For steady flow with one inlet and one outlet, both assumed one-dimensional:

Where: hq = the heat transferred to the fluid per unit mass
= the shaft work isolates that portion of the work which
is done by a machine (pump impeller, fan blade, piston, etc.) protruding through the fluid per unit mass .
= the viscose work, this term may vanish or be negligible for all parts of the control surface which are solid confining walls, V = 0 from the viscous no-slip condition; hence Ws= zero identically.
Note:
• H1= head at inlet= , differs from the downstream value.
H2 ( head at outlet) only if there is heat transfer, shaft work, or viscous work as the fluid passes between sections 1 and 2.
• that q is positive if heat is added to the control volume
• ws and wv are positive if work is done by the fluid on the surroundings.
Flow measurments
1. Venture meters: are flow measurement instruments which use a converging section of pipe to give an increase in the flow velocity and a corresponding pressure drop from which the flow rate can be deduced. They have been in common use for many years, especially in the water supply industry