Pump Head Power Calculator

Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

Speed Ratio: About this input

The ratio of the new pump speed to the base speed, dimensionless, used with the affinity laws to project flow, head and power at a different speed. Use 1 for no change.

Default 1 Range At least 0
Pump Efficiency: About this input

The pump hydraulic efficiency, in percent, that converts hydraulic power to the brake power the shaft must supply.

Unit percent Default 72 Range 0 to 100
Net Positive Suction Head Required: About this input

The net positive suction head the pump needs at its inlet to avoid cavitation, in feet, from the pump curve or nameplate. The available head must exceed it.

Unit ft Default 10 Range At least 0
Static Discharge Head: About this input

The vertical distance from the pump centerline to the discharge liquid level, in feet.

Unit ft Default 80
Suction Pipe Length: About this input

The straight length of suction pipe from the source to the pump, in feet, before the fitting allowance is applied.

Unit ft Default 20 Range At least 0
Suction Pipe Inside Diameter: About this input

The inside diameter of the suction pipe, in inches, which sets the suction velocity and the friction loss ahead of the pump. It must be greater than zero: at a bore of zero the velocity and the friction are unbounded rather than zero, so the model refuses the state instead of reporting a duty for a pipe that does not exist.

Unit in Default 6.065 Range At least 0
Static Suction Head: About this input

The vertical distance from the source liquid level to the pump centerline, in feet, entered positive when the source is above the pump, a flooded suction, and negative on a lift.

Unit ft Default 8
Motor Efficiency: About this input

The motor efficiency, in percent, that converts brake power at the shaft to the electrical input the motor draws.

Unit percent Default 92 Range 0 to 100
Discharge Pipe Length: About this input

The straight length of discharge pipe from the pump to the delivery point, in feet, before the fitting allowance is applied.

Unit ft Default 200 Range At least 0
Discharge Pipe Inside Diameter: About this input

The inside diameter of the discharge pipe, in inches, which sets the discharge velocity and the friction loss after the pump. It must be greater than zero, for the same reason as the suction pipe.

Unit in Default 4.026 Range At least 0
Atmospheric Pressure: About this input

The absolute atmospheric pressure at the site, in pounds per square inch absolute, used to compute the available net positive suction head. It falls with altitude.

Unit psia Default 14.7 Range At least 0
Fitting Allowance: About this input

An allowance for fittings and valves added to the measured pipe length, in percent, so the friction estimate covers minor losses. For example 30 adds 30 percent equivalent length.

Unit percent Default 30 Range At least 0
Hazenwilliams: About this input

The Hazen-Williams roughness coefficient of the pipe, a dimensionless value near 130 to 150 for smooth pipe, used to estimate the suction and discharge friction head.

Default 140 Range At least 0
Fluid: About this input

The fluid being pumped, such as water. It sets the specific gravity and vapor pressure used for the power and the available suction head.

Default Water 60 F Allowed Water 60 F, Water 100 F, Water 140 F, Water 180 F
Flow Rate: About this input

The flow the pump delivers, in gallons per minute, at the operating point being analysed.

Unit gpm Default 300 Range At least 0

Outputs

Net Positive Suction Head Available: About this output

The net positive suction head available at the pump inlet, in feet, from atmospheric pressure, static suction head, vapor pressure and suction friction.

Unit ft
Motor Input Power: About this output

The electrical power the motor draws, in kilowatts: brake power divided by the motor efficiency.

Unit kW
Model Status: About this output

The overall check on your entries, shown above the results. It reads OK when the inputs are usable, NOT VALID with a reason when an entry makes the model meaningless, or CHECK with a reason when a result is valid but worth a second look. Read it before you trust the numbers below.

No unit declared
Net Positive Suction Head Margin: About this output

NPSH available minus NPSH required, in feet. A positive margin means the pump is not expected to cavitate at this duty, and the status raises a check below 2 ft. When the model refuses your inputs, the page shows that reason in place of the results, so no margin is shown for a pipe with no bore.

Unit ft
Total Dynamic Head: About this output

The total head the pump must develop, in feet: the static lift plus the friction losses on both sides. It is the head paired with the flow to size the pump.

Unit ft
Suction Velocity: About this output

The fluid velocity in the suction pipe, in feet per second, from the flow and the suction diameter.

Unit ft/s
Suction Friction: About this output

The friction head lost in the suction pipe and its fittings, in feet.

Unit ft
Affinity Head At New Speed: About this output

The head projected at the new speed by the affinity laws, in feet, scaling with the square of the speed ratio.

Unit ft
Affinity Flow At New Speed: About this output

The flow projected at the new speed by the affinity laws, in gallons per minute, scaling with the speed ratio.

Unit gpm
Affinity Brake Power At New Speed: About this output

The brake power projected at the new speed by the affinity laws, in horsepower, scaling with the cube of the speed ratio.

Unit HP
Brake Power: About this output

The power the pump shaft must receive, in horsepower: hydraulic power divided by the pump efficiency.

Unit HP
Hydraulic Power: About this output

The useful power delivered to the fluid, in horsepower, from the flow, the total dynamic head and the fluid specific gravity.

Unit HP
Discharge Velocity: About this output

The fluid velocity in the discharge pipe, in feet per second, from the flow and the discharge diameter.

Unit ft/s
Discharge Friction: About this output

The friction head lost in the discharge pipe and its fittings, in feet.

Unit ft

What it is

The Pump Head and Power Calculator works out how much head a pump must develop to move a given flow through a given piping system, and how much power that takes. It reports the total dynamic head, the hydraulic power delivered to the fluid, the brake power the shaft must receive, the electrical input the motor draws, and the velocities and friction losses on each side of the pump.

It also computes the available net positive suction head and its margin against the value your pump requires, which is the check that guards against cavitation, and it projects flow, head and power at a different pump speed using the affinity laws.

It works in United States customary units: gallons per minute, feet of head, inches of pipe diameter, horsepower and kilowatts.

Use it for preliminary sizing. Final pump selection needs the manufacturer's certified pump curve, which this tool does not model.

Methodology

Purpose and model boundary

This model calculates a water system's total dynamic head, hydraulic/brake/motor power, suction conditions, and affinity-law projections from one operating flow. It also produces the system-head curve for the entered piping. It supports preliminary pump duty and cavitation-margin checks. It does not intersect a manufacturer pump curve, determine an actual operating point, model variable efficiency, select equipment, or replace a certified pump and NPSH evaluation.

Inputs and units

Inputs use US customary hydraulic units: flow in gpm; static discharge and suction heads, pipe lengths, and NPSH required in ft; suction and discharge inside diameters in inches; atmospheric pressure in psia; Hazen-Williams C; fitting allowance as percent added to pipe length; pump and motor efficiencies as percent; and a dimensionless speed ratio. The fluid selector chooses stored specific gravity and vapour pressure for water at 60, 100, 140, or 180 °F.

Governing relationships

Pipe velocities and Hazen-Williams friction heads are:

V = 0.4085 × Q / d²

h_f = 0.2083 × (100/C)^1.852 × Q^1.852 / d^4.8655 × [L × (1 + fitting allowance/100)] / 100

The workbook combines static and friction heads:

TDH = static discharge head - static suction head + suction friction + discharge friction

Power is calculated in US units:

hydraulic HP = SG × Q × TDH / 3960

brake HP = hydraulic HP / (pump efficiency/100)

motor input kW = brake HP × 0.7457 / (motor efficiency/100)

Available net positive suction head and margin are:

NPSH_available = (atmospheric pressure - vapour pressure) × 2.31 / SG + static suction head - suction friction

NPSH margin = NPSH_available - NPSH_required

For speed ratio r, the affinity projections are Q_new = Q × r, H_new = TDH × r², and BHP_new = brake HP × r³.

Calculation sequence

Look up fluid specific gravity and vapour pressure.
Calculate suction and discharge velocities.
Apply the fitting allowance to each entered pipe length and calculate Hazen-Williams friction.
Combine static-head difference and both friction losses to produce total dynamic head.
Calculate hydraulic horsepower, brake horsepower, and motor input kW from the entered efficiencies.
Calculate NPSH available and subtract entered NPSH required.
Apply the speed ratio to flow, head, and brake power using the affinity-law exponents.
Generate the system curve and evaluate status in the order below.

Outputs and interpretation

Total_Dynamic_Head is the primary result. Supporting results show suction/discharge velocity and friction, hydraulic and brake power, motor input, NPSH available and margin, and three speed-scaled affinity values. The system chart belongs to the entered piping and static head; it is not a pump performance curve and does not establish where a real pump will operate.

Validation and status logic

Condition	Returned status
Flow is zero or less	`NOT VALID: flow must be positive`
Pump efficiency or motor efficiency is zero or less	`NOT VALID: efficiencies must be positive`
Hazen-Williams `C` is zero or less	`NOT VALID: Hazen-Williams C must be greater than zero`
NPSH margin is less than 2 ft	`CHECK: NPSH margin below 2 ft, cavitation risk`
Discharge velocity is greater than 10 ft/s	`CHECK: discharge velocity above 10 ft/s`
Suction velocity is greater than 5 ft/s	`CHECK: suction velocity above 5 ft/s`
None of the preceding conditions applies	`OK`

The NPSH warning takes precedence over both velocity warnings; discharge velocity precedes suction velocity.

Assumptions and limitations

The calculation uses one entered flow rather than solving the intersection of a pump curve and system curve.
Hazen-Williams is used for water friction with a single C; it does not model viscosity-sensitive or non-water friction behavior.
Fittings are represented only as a percentage of straight pipe length, not individual equivalent lengths or K values.
Specific gravity and vapour pressure come from four illustrative water-property rows without interpolation. Actual temperature, altitude/barometric pressure, dissolved gas, and suction-vessel pressure must be supplied appropriately.
Pump and motor efficiencies are constant at the entered values. The workbook has no efficiency curve, minimum continuous stable flow, runout, shutoff, or motor service-factor check.
Affinity-law outputs assume geometrically similar operation and do not recalculate the system operating point or efficiency.
Manufacturer NPSH required is an input. The workbook's 2 ft margin warning is a screening threshold, not a universal acceptance criterion.

Restrictions and non-computing states

The fluid input is restricted to four declared water rows. This calculator rejects negative flow, pipe lengths and diameters, atmospheric pressure, fitting allowance, C, NPSH required, speed ratio, and efficiencies; efficiencies are capped at 100%. The workbook additionally requires positive flow, both efficiencies, and C. Zero pipe diameter is protected in the friction and velocity formulas and may yield a misleading zero for that line while status remains driven by the checks above, so a positive real diameter is required for meaningful use even though the workbook does not issue a dedicated diameter message.

Errors and warnings

An undeclared fluid or value outside its allowed range is rejected before the calculation runs. Workbook NOT VALID means the duty or efficiency basis cannot produce usable power results. Workbook CHECK preserves the outputs while flagging low NPSH margin or high velocity. A connection or calculation-service failure is not a pump-performance finding and must not be treated as a zero-head result.

References

No proprietary pump curve or manufacturer table is reproduced. Fluid properties shipped with the workbook are illustrative and user-editable. The relations implemented are cited below.

Williams, Gardner S., and Allen Hazen. Hydraulic Tables. John Wiley and Sons, 1905. (the origin of the Hazen-Williams friction relation used here)
Wikipedia. Hazen-Williams equation. https://en.wikipedia.org/wiki/Hazen%E2%80%93Williams_equation
Wikipedia. Net positive suction head. https://en.wikipedia.org/wiki/Net_positive_suction_head
Wikipedia. Affinity laws. https://en.wikipedia.org/wiki/Affinity_laws
Wikipedia. Cavitation, for what the suction head margin protects against. https://en.wikipedia.org/wiki/Cavitation

Use the pump manufacturer's certified curve and the real properties of your fluid for final selection.

Additional source notes migrated from Methodology

The workbook uses the US-unit Hazen-Williams relation, standard hydraulic-power conversion (3960), atmospheric/vapour head conversion (2.31 ft/psi for water adjusted by specific gravity), and pump affinity laws. The reviewer packet cites Engineering ToolBox on pumps, power, and head, Engineering ToolBox on NPSH available, and FIRGELLI's affinity-law calculator. Manufacturer certified curves govern final selection.

Frequently asked questions

Should the static suction head be positive or negative?

Positive when the source liquid level is above the pump centreline, which is a flooded suction, and negative when the pump has to lift from below. A flooded suction reduces the total dynamic head the pump must develop and increases the available net positive suction head, so the sign matters twice. In the shipped example the 8 foot flooded suction reduces the static duty from 80 feet to 72.

Why is nearly all my friction on the discharge side?

Usually because the discharge pipe is longer, narrower, or both. Hazen-Williams friction rises very steeply as diameter falls, so a modest reduction in pipe size produces a large increase in friction head. In the shipped example the discharge line is ten times longer and about a third narrower, and it accounts for 12.81 of the 12.99 feet of total friction.

What fluids can I model?

Water only, at four temperatures: 60, 100, 140 and 180 degrees Fahrenheit. There are no non-water fluids in the list. Each entry supplies a specific gravity and a vapour pressure that are illustrative values shipped with the workbook. For any other fluid, or for a viscous one, this tool will not give you a usable answer, since viscosity correction is not modelled.

Why did my suction head margin collapse when I raised the temperature?

Because vapour pressure rises steeply with temperature, and it is subtracted from atmospheric pressure when computing the available suction head. On the shipped example, moving from water at 60 degrees Fahrenheit to water at 180 drops the available head from about 41 feet to about 25. Hot liquids are the common cause of cavitation in an otherwise sound design.

The status warns about discharge velocity. Is my suction velocity fine?

Not necessarily. Only one status message is shown at a time, and the discharge velocity check sits ahead of the suction velocity check, so a discharge breach will mask a suction breach. Read the reported suction and discharge velocities directly rather than relying on the status to flag both.

How far can I trust the affinity law projections?

They are first-order estimates. Flow scales with the speed ratio, head with its square and power with its cube, which holds well for modest speed changes on a pump operating near its design point. They assume the pump curve keeps its shape and they take no account of the best efficiency point moving, so treat a large speed change as indicative only and check it against the manufacturer's curve.

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