SME
Fluid Mechanics · Problem type
Net positive suction head and cavitation
Use this for “A pump draws 30 °C water (Pᵥ = 4.25 kPa) from an open sump 2 m below it with 1.2 m of suction losses. The pump needs 5 m NPSH. Will it cavitate?”
Chart
NPSH_A = hₚᵥ + zₛ − hL
9.935 + (−2) − 1.2 = +6.735
The flows in add and the flows out take away: NPSH_A = +6.735.
Surface pressure Pₐₜₘ = 101.325 kPa
Vapor pressure Pᵥ = 4.25 kPa
Density ρ = 996 kg/m³
Required NPSH NPSH_R = 5 m
NPSH margin ΔH = +1.735 m
This is an example. Type your own values to start a new problem.
hₚᵥ (m)
=
Pₐₜₘ (kPa)
−
Pᵥ (kPa)
ρ (kg/m³)
×
9.81
NPSH_A (m)
=
hₚᵥ (m)
+
(
zₛ (m)
)
−
hL (m)
ΔH (m)
=
NPSH_A (m)
−
NPSH_R (m)
Formulas
hₚᵥ
=
Pₐₜₘ − Pᵥ
ρ
× 9.81
9.935
=
101,325 − 4,250
996 × 9.81
NPSH_A = hₚᵥ + zₛ − hL
+6.735 = 9.935 + (−2) − 1.2
ΔH = NPSH_A − NPSH_R
+1.735 = 6.735 − 5
Formulas are worked in Pa. The step-by-step shows the conversions.
Assumptions
•
An open sump at atmospheric pressure, its surface velocity head 0.
•
Pᵥ is the vapor pressure at the water’s temperature, from the saturated-water table.
•
zₛ is the liquid surface above the pump inlet: negative when the pump sits above the sump.
•
The pump cavitates when NPSH_A falls to NPSH_R or below.
Step-by-step
WE KNOW
Pₐₜₘ = 101.325 kPa, Pᵥ = 4.25 kPa, ρ = 996 kg/m³, zₛ = −2 m, hL = 1.2 m, NPSH_R = 5 m
FIND
pressure head (hₚᵥ), available NPSH (NPSH_A), NPSH margin (ΔH)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to Pa).
Pₐₜₘ = 101.325 kPa = 101,325 Pa (1 kPa = 1000 Pa)
Pᵥ = 4.25 kPa = 4,250 Pa (1 kPa = 1000 Pa)
Step 2 · Find pressure head (hₚᵥ)
Use hₚᵥ = (Pₐₜₘ − Pᵥ) ÷ (ρ × 9.81)
The pressure above boiling, as a head of the liquid: divide by ρg.
hₚᵥ
=
101,325 − 4,250
996 × 9.81
hₚᵥ
=
97,075
9,770.76
hₚᵥ = 9.935 m
Step 3 · Find available NPSH (NPSH_A)
Use NPSH_A = hₚᵥ + zₛ − hL
Start from the head above boiling, add the height of liquid over the inlet, take the losses.
NPSH_A = 9.935 + (−2) − 1.2
NPSH_A = +6.735 m
Step 4 · Find NPSH margin (ΔH)
Use ΔH = NPSH_A − NPSH_R
The margin is what the line gives over what the pump needs; 0 or less means the pump cavitates.
ΔH = 6.735 − 5
ΔH = +1.735 m
Check
Put the numbers back in. Both sides should match.
9.935
=
101,325 − 4,250
996 × 9.81
✓
+6.7353 = 9.9353 + (−2) − 1.2 ✓
+1.7353 = 6.7353 − 5 ✓
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