Bernoulli Total Head
Bernoulli Total Head
Bernoulli’s equation expresses a fluid’s total energy as a single head — the sum of elevation, pressure and velocity heads — conserved along a streamline.
The total head is H = z + p/(ρ·g) + v²/(2g). where z is the elevation, p the pressure, ρ the density, g gravity and v the velocity.
Inputs
z := 12 m=12 m
p := 150 kPa=150000 Pa
rho := 1000 kg/m^3=1000 kg/m^3
g := 9.81 m/s^2=9.81 m/s^2
v := 3 m/s=3 m/s
Sum the elevation, pressure and velocity heads.
H := z + p/(rho·g) + v^2/(2·g)=27.75 m
Results
The total head stays constant along an ideal streamline, with energy trading between the three forms. Real flows lose head to friction, which pumps must replace.
Assumptions & limitations
- Incompressible, steady, inviscid flow.
- Along one streamline.
- No friction losses.