Mechanical Energy Equation with Pump/Turbine

\frac{p _{1}}{γ} + \frac{V _{1}^{2}}{2 g} + z_{1} + h_{p} - h_{t} - h_{f} = \frac{p _{2}}{γ} + \frac{V _{2}^{2}}{2 g} + z_{2}

Bernoulli plus shaft work and losses. hp is head added by a pump, ht extracted by a turbine, hf=f(L/D)V²/2g plus minor losses K V²/2g. Power = γ Q hp / η.

$h_{p}$ (m): Pump head
$h_{f}$ (m): Loss head
$η$: Efficiency

Step-by-step solved example

Lift water 25 m, hf=4 m, V small, p_atm both surfaces. hp?

Pump adds hp between suction and discharge grade lines.

1. Terms
z2−z1=25, hf=4, Δp=ΔV=0.
2. hp
hp=25+4=29 m.
$h_{p} = 29 m$

Answer: hp = 29 m

10 practice questions

0/10 correct

1.A turbine head ht appears

2.Power to the fluid is

3.If η=0.75, fluid power 12 kW, shaft input is

4.Minor loss Kv²/2g uses K for

5.HGL is

6.A pump raises

7.Open reservoirs: p1=p2=patm and V≈0 so hp=

8.Units: γQh with γ in N/m³, Q m³/s, h m →

9.System curve hp vs Q is roughly

10.NPSH is a separate check at the