How this instrument works
Hydraulic horsepower is the power a pump imparts to the fluid itself, not the power its motor draws from the wall. It comes straight from the definition of mechanical work: force times distance over time, restated for a pump as weight flow times height per minute. Multiply the flow rate by the head the pump must overcome and by how heavy the fluid is relative to water, and the result is the rate at which energy is added to the moving stream.
The constant 3960 in the formula is not arbitrary. A US gallon of water weighs about 8.34 pounds, and one mechanical horsepower is defined as 33,000 foot-pounds of work per minute. Divide 33,000 by 8.34 and the answer is 3960 — the gallon-feet of water a single horsepower can lift in one minute. Specific gravity rescales that constant for anything other than plain water: brine near 1.2 demands proportionally more power, gasoline near 0.74 demands less.
The number this instrument returns is a floor, not a purchase order. Hydraulic horsepower assumes a perfectly efficient pump, with no friction at the wear rings and no turbulence in the volute. Real centrifugal pumps recover only 60 to 85 percent of shaft power as hydraulic work, so the motor an engineer actually specifies must supply hydraulic horsepower divided by that efficiency — the brake horsepower stamped on the nameplate is always the larger figure.
- Enter the Flow rate, GPM — the volume the pump moves per minute, taken from its rated capacity or the system's expected demand.
- Enter the Total dynamic head, ft — the sum of static lift, elevation change, and pipe friction losses the pump has to push against.
- Set the Fluid specific gravity — leave it at 1 for water, raise it for brine or slurry, lower it for gasoline or other light fluids.
- Read the Hydraulic horsepower — the theoretical power delivered to the fluid; divide by expected pump efficiency to estimate motor size.
Worked example — sizing a 100 GPM lift-station pump
A municipal lift station moves 100 GPM against 50 ft of total dynamic head, and the fluid is plain water, so specific gravity is 1. The formula gives HP = (100 × 50 × 1) ⁄ 3960 = 5,000 ⁄ 3960 ≈ 1.263 hydraulic horsepower — the theoretical minimum power the water itself absorbs as it climbs through the pump and into the discharge line.
No pump reaches 100 percent efficiency, so an engineer sizing the motor divides that figure by the pump's expected efficiency. At a typical centrifugal efficiency of 70 percent, the required brake horsepower is 1.263 ⁄ 0.70 ≈ 1.80 hp, which is why a job like this would likely end up specifying a standard 2 hp motor rather than the bare hydraulic figure.
Questions
Why does the formula divide by 3960?
Because 3960 converts gallons per minute and feet of head directly into horsepower. One horsepower equals 33,000 foot-pounds of work per minute, and a US gallon of water weighs about 8.34 pounds; dividing 33,000 by 8.34 gives 3960, the gallon-feet of water one horsepower can lift each minute. Specific gravity then rescales that constant for fluids heavier or lighter than water.
Is hydraulic horsepower the same as the horsepower on a pump's nameplate?
No. The nameplate lists brake horsepower, the power the motor shaft actually supplies, which is always larger. Hydraulic horsepower is only the fraction of that power the fluid receives; the rest is lost to bearing friction, impeller slip, and turbulence inside the casing. Divide hydraulic horsepower by the pump's efficiency, typically 60 to 85 percent, to estimate the needed brake horsepower.
What counts as total dynamic head?
Total dynamic head is the sum of static head, the elevation the fluid must be lifted including any difference between suction and discharge levels, and friction head, the losses from pipe length, fittings, and valves along the way. It is not simply tank height; a long pipe run with several elbows can add many feet of head even across flat ground.
What specific gravity should I enter for water?
Enter 1, the reference value other fluid densities are compared against. Water near 4°C is defined as specific gravity 1.0, and ordinary tap or process water at room temperature stays close enough for pump sizing. Denser fluids such as brine, about 1.2, or dilute sulfuric acid, above 1.8, need a higher entry; lighter fluids such as gasoline, about 0.74, need a lower one.
Does this formula account for pump efficiency or NPSH?
No, and that omission is deliberate. This formula returns hydraulic horsepower, the theoretical energy transferred to the fluid assuming perfect efficiency; it says nothing about net positive suction head, cavitation risk, or mechanical losses inside the casing. Those need separate checks against the manufacturer's pump curve before a motor or impeller gets finalized.
Can I use this formula for fluids other than water, like oil or brine?
Yes, that is exactly what the specific gravity field is for. Set it to the fluid's density relative to water, 1.0, and the same formula scales correctly: a heavier fluid such as brine needs proportionally more horsepower to move the same flow through the same head, and a lighter fluid such as light crude oil needs less.