Exercise set

Water and Wastewater Pump Station Duty, Power, NPSH, and VFD Exercises

Solved pump-station exercises for duty point, pump power, static head, curve margin, NPSH, motor current, VFD speed and release gates.

Branch: Environmental Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.0.0 · reviewed

These exercises practise water and wastewater pump-station hydraulic duty decisions: flow conversion, pump input power, static head, total dynamic head, pump curve margin, NPSH, motor current, VFD speed, affinity laws, wet-well drawdown and pump acceptance gates.

The goal is to verify the installed operating point, not nameplate capacity. A pump can have enough nominal flow and still fail because head is higher than assumed, wet-well level drops, NPSH margin is low, VFD speed is limited or motor current approaches its guard.

Assume water density unless stated otherwise. Field release should use installed pump curves, measured wet-well levels, pressure logs, current readings, VFD parameters, valve positions and acceptance-test records.

Release Evidence Notes

Pump evidence should identify flow, total dynamic head, speed, impeller condition, wet-well level and motor current at the same operating point.

Power evidence should separate hydraulic power from input power. Efficiency, motor efficiency and VFD losses should be visible when energy or electrical margin matters.

NPSH evidence should use worst credible suction condition: low wet-well level, warm liquid, high flow and known suction losses.

VFD evidence should show minimum speed limits, self-cleansing velocity, cooling constraints, pressure control and current limits.

Engineering Boundary Notes

This page covers pump duty and power. Pipe headloss, valves and surge transients belong in the pipe/transient exercise set. Standby availability, runtime balance, leakage trend and release checklist closure belong in the reliability exercise set.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Pump duty point	1-5	flow, area, velocity, static head and TDH	Confirm the duty point used for selection.
Power and efficiency	6-9	hydraulic power, input power, energy and current	Check motor, VFD and energy margin.
NPSH and operating envelope	10-14	suction margin, wet-well drawdown and speed change	Decide whether operating limits are acceptable.
Pump release	15-18	curve margin, guarded current and acceptance gates	Release, restrict or retest the pump station.

Exercise 1: Flow Conversion

A pump station flow is:

Q=78\ \text{L/s}

Convert to cubic meters per second.

Solution

Use:

1\ \text{L/s}=0.001\ \text{m}^3/\text{s}

Thus:

Q=78(0.001)=0.078\ \text{m}^3/\text{s}

Engineering Comment

Consistent units prevent large pump-power and velocity errors.

Plausibility Check

One thousand liters make one cubic meter, so tens of liters per second are hundredths of a cubic meter per second.

Exercise 2: Pipe Area at Pump Discharge

Discharge pipe diameter is:

D=0.30\ \text{m}

Find cross-sectional area.

Solution

Area:

A=\dfrac{\pi D^2}{4}=\dfrac{\pi(0.30)^2}{4}=0.0707\ \text{m}^2

Engineering Comment

Area is needed before checking discharge velocity and system curve.

Plausibility Check

A $300$ mm pipe has an area a little above $0.07\ \text{m}^2$ .

Exercise 3: Pump Discharge Velocity

Flow is:

Q=0.078\ \text{m}^3/\text{s}

Area is:

A=0.0707\ \text{m}^2

Find velocity.

Solution

Velocity:

v=\dfrac{Q}{A}=\dfrac{0.078}{0.0707}=1.10\ \text{m/s}

Engineering Comment

Velocity should be checked against self-cleansing, headloss, abrasion, odor and surge criteria.

Plausibility Check

About $0.08\ \text{m}^3/\text{s}$ in a $300$ mm pipe gives velocity close to one meter per second.

Exercise 4: Static Head from Level Difference

Discharge hydraulic grade is:

42.5\ \text{m}

Wet-well operating level is:

18.0\ \text{m}

Find static head.

Solution

Static head:

H_s=42.5-18.0=24.5\ \text{m}

Engineering Comment

Wet-well level changes can move the pump duty point during a run.

Plausibility Check

The discharge grade is about twenty-five meters above wet-well level.

Exercise 5: Total Dynamic Head

Static head is:

24.5\ \text{m}

Pipe friction loss is:

16.0\ \text{m}

Minor losses are:

3.5\ \text{m}

Find TDH.

Solution

Total dynamic head:

TDH=24.5+16.0+3.5=44.0\ \text{m}

Engineering Comment

Pump acceptance should verify flow at this total dynamic head, not at zero static lift.

Plausibility Check

The terms sum directly to a TDH in the mid-forties.

Exercise 6: Hydraulic Power

A pump delivers:

Q=0.075\ \text{m}^3/\text{s}

against:

H=32\ \text{m}

Use:

\rho=1000\ \text{kg/m}^3,\qquad g=9.81\ \text{m/s}^2

Find hydraulic power.

Solution

Hydraulic power:

P_h=\rho gQH=1000(9.81)(0.075)(32)=23544\ \text{W}

So:

P_h=23.5\ \text{kW}

Engineering Comment

Hydraulic power is lower than input power because pump and drive efficiency are not perfect.

Plausibility Check

Moderate flow against tens of meters of head gives tens of kilowatts.

Exercise 7: Pump Input Power

Hydraulic power is:

P_h=23.5\ \text{kW}

Pump efficiency is:

\eta=0.72

Find input power.

Solution

Input power:

P_i=\dfrac{P_h}{\eta}=\dfrac{23.5}{0.72}=32.6\ \text{kW}

Engineering Comment

Motor sizing should include motor efficiency, service factor and operating envelope.

Plausibility Check

Dividing by efficiency below one raises the required input power.

Exercise 8: Daily Energy Use

Input power is:

P=32.6\ \text{kW}

Daily runtime is:

t=9.5\ \text{h/day}

Find daily energy.

Solution

Energy:

E=Pt=32.6(9.5)=309.7\ \text{kWh/day}

Engineering Comment

Energy evidence should be checked against pump starts, level control and wet-weather operation.

Plausibility Check

About thirty-three kilowatts for about ten hours is about three hundred kilowatt-hours.

Exercise 9: Motor Current Guard

Motor full-load current is:

I_{FL}=62\ \text{A}

Release requires measured current below $95\%$ of full load. Find guarded limit.

Solution

Guarded limit:

I_g=0.95(62)=58.9\ \text{A}

Engineering Comment

The current guard should be checked at final speed, valve position and wet-well condition.

Plausibility Check

Five percent below $62$ A is just under $59$ A.

Exercise 10: Motor Current Status

Guarded current limit is:

58.9\ \text{A}

Measured current is:

57.0\ \text{A}

Check status.

Solution

Since:

57.0<58.9

the current gate passes.

Engineering Comment

A pass is valid only for the tested hydraulic duty point.

Plausibility Check

Measured current is below the guard by $1.9$ A.

Exercise 11: Wet-Well Drawdown Head Increase

Wet-well level drops by:

2.4\ \text{m}

Find static-head increase and pressure equivalent.

Solution

Head increase:

\Delta H=2.4\ \text{m}

Pressure:

\Delta p=\rho g\Delta H=1000(9.81)(2.4)=23544\ \text{Pa}=23.5\ \text{kPa}

Engineering Comment

Pump margin should be checked at the lowest allowed wet-well level.

Plausibility Check

Each meter of water is about $9.8$ kPa, so $2.4$ m is about $24$ kPa.

Exercise 12: NPSH Margin

Available NPSH is:

NPSH_A=6.2\ \text{m}

Required NPSH is:

NPSH_R=4.8\ \text{m}

Find margin.

Solution

Margin:

M=6.2-4.8=1.4\ \text{m}

Engineering Comment

NPSH should be reviewed at maximum flow and worst suction condition.

Plausibility Check

Available NPSH exceeds required NPSH by more than one meter.

Exercise 13: NPSH Release Gate

NPSH margin is:

1.4\ \text{m}

The release rule requires:

1.0\ \text{m}

Check release.

Solution

Since:

1.4>1.0

the NPSH gate passes.

Engineering Comment

The pass does not cover future fouling or lower wet-well levels unless those were included.

Plausibility Check

The margin exceeds the rule by $0.4$ m.

Exercise 14: VFD Speed Flow Estimate

Full-speed flow is:

Q_1=90\ \text{L/s}

VFD speed is:

80\%

Estimate flow.

Solution

Using affinity law:

Q_2=Q_1\dfrac{N_2}{N_1}=90(0.80)=72\ \text{L/s}

Engineering Comment

System curve and minimum velocity may limit actual speed reduction.

Plausibility Check

Flow scales approximately linearly with speed.

Exercise 15: VFD Head Estimate

Full-speed head is:

H_1=44\ \text{m}

Speed is:

80\%

Estimate pump head by affinity law.

Solution

Head scales with speed squared:

H_2=H_1(0.80)^2=44(0.64)=28.2\ \text{m}

Engineering Comment

The pump may not meet static head at reduced speed if the system requires more head.

Plausibility Check

Head falls faster than flow because of the squared speed relation.

Exercise 16: Pump Curve Flow Margin

Required flow is:

78\ \text{L/s}

Pump curve gives:

86\ \text{L/s}

at measured head. Find margin.

Solution

Margin:

M=86-78=8\ \text{L/s}

Percentage:

\dfrac{8}{78}=10.3\%

Engineering Comment

Impeller wear, valve throttling or higher roughness can consume a ten-percent margin.

Plausibility Check

The pump is slightly above required duty, so margin near ten percent is reasonable.

Exercise 17: Minimum Flow Gate

Minimum continuous stable flow is:

Q_{min}=35\ \text{L/s}

VFD low-speed operation produces:

Q=32\ \text{L/s}

Check gate.

Solution

Since:

32<35

the low-speed setting fails the minimum-flow gate.

Engineering Comment

Running below minimum stable flow can cause heating, vibration or recirculation damage.

Plausibility Check

The operating flow is three liters per second below the minimum.

Exercise 18: Pump Duty Release Gate

A pump acceptance package has:

Gate	Requirement	Current result
curve flow margin	at least $8\%$	$10.3\%$
motor current	below guarded limit	pass
NPSH margin	at least $1.0$ m	$1.4$ m
minimum VFD flow	at least $35$ L/s	$32$ L/s

Decide whether to release.

Solution

Curve, current and NPSH gates pass. Minimum VFD flow fails:

32<35

The pump duty package is not releasable without a speed limit or revised operating rule.

Engineering Comment

An acceptable full-duty point does not prove that all VFD operating modes are safe.

Plausibility Check

One hard gate fails, so the release must be held or restricted.

Validation Package Checklist

A strong pump-station duty solution should check:

whether flow, head, speed and current are measured at the same duty point;
whether wet-well level and static head represent the worst operating case;
whether pump curve margin includes wear and valve condition;
whether input power includes efficiency assumptions;
whether NPSH margin uses worst suction condition;
whether VFD low-speed operation meets minimum-flow and velocity limits;
whether acceptance gates are all closed before release.

Common Release Mistakes

Common mistakes include using nameplate flow instead of installed duty, checking pump power with mixed units, ignoring wet-well drawdown, accepting VFD speed reduction without minimum-flow review, checking NPSH only at nominal conditions, treating current margin as hydraulic margin, and releasing the pump because full-speed duty passes while low-speed operation fails.

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