# Pump Horsepower Calculator

Created by Kenneth Alambra
Last updated: Aug 24, 2022

If you're looking for the correct amount of pump power that can deliver a specified discharge and pressure head, this pump horsepower calculator is for you. This tool allows you to estimate the pump's hydraulic power and shaft power that will suit your needs.

• What pump horsepower is;
• What the pump power formula is;
• Pump hp calculation example; and
• How to use this pump horsepower calculator.

## What is pump horsepower?

Pump horsepower is an overview of a pump's capacity to achieve its rated discharge (or volumetric flow rate output) and pressure head. In most cases, we use pumps to deliver water and other fluids to a higher location (e.g., from an underground water source to the top of a building).

The pump sucks water in and pushes it up to a higher level with the help of an impeller. An impeller is like a fan blade. But instead of moving air, it moves liquids. Inside a pump, we can also see a motor that propels the impeller.

Generally, a pump translates its motor power and torque to what we call shaft power. The motor's shaft is where the pump's impeller is directly connected. As water flows due to the impeller's motion, we convert the shaft power into the pump's hydraulic power. Due to friction and other mechanical inefficiencies, we lose some power during the translation.

We typically use horsepower as the unit of measure for the shaft and hydraulic power. And those are what pump horsepower is. If you're interested in converting power values to other units, you can check out our power converter.

To better understand the relationship between shaft power and hydraulic power, let's discuss how to calculate pump power in the next section of this text.

## How to calculate pump power

First, we briefly discuss the pump power formula for its hydraulic power, as shown below:

$P_h = Q\times H\times \rho\times g$

Where:

• $P_h$ is the pump hydraulic power in watts;
• $Q$ is the pump discharge rate in cubic meters per second;
• $H$ is the pressure head in meters;
• $\rho$ is the fluid's density in kilograms per cubic meter; and
• $g$ is the gravitational acceleration in meters per second squared.

From the formula above, we can see that the discharge and hydraulic head are both directly proportional to the hydraulic power. That means a pump that supplies more hydraulic power also delivers a stronger discharge and a higher pressure head.

Now, by considering the efficiency of the pump, we denote as $\eta$, we can find the pump shaft power, $P_s$, using this equation:

$P_s = \frac{P_h}{\eta}$

We can also determine a pump's efficiency if we know its hydraulic and shaft power. We only have to reorganize the variables to have this formula:

$\eta = \frac{P_h}{P_s}$

Other than the efficiency of a pump, we can also use its specific speed, $N_s$, to compare it with other pumps. We can use the following formula to determine $N_s$:

$N_s = \frac{N\times Q^{0.5}}{(g\times H)^{0.75}}$

Where:

• $N$ is the pump's revolution speed in rotations per minute;
• $Q$ is the discharge in gallons per minute;
• $g$ is the gravitational acceleration in feet per second squared; and
• $H$ is the pressure head in feet.

Nevertheless, these are the formulas we can use to estimate the correct pump horsepower to meet our requirements. Let's now use these formulas to consider an example.

## Pump hp calculation example

Let's say we need to determine the minimum pump power to deliver 0.2 cubic meters of water per second to a height of 10 meters. The supplier we contacted promised we could get any size of a pump at 0.9 efficiencies. With a water density of 1000 kg/m³ and gravitational acceleration of 9.81 m/s², we find the hydraulic power we need as follows:

\footnotesize \begin{align*} P_h &= Q\times H\times \rho\times g\\ &= 0.2\ \tfrac{\text{m³}}{\text{s}} \times 10\ \text{m}\times 1000\ \tfrac{\text{kg}}{\text{m³}}\times 9.81\ \tfrac{\text{m}}{\text{s²}}\\ &= 19620\ \text{W} \end{align*}

To convert it to mechanical horsepower or hp(l), we have to divide our hydraulic power in watts by $\small{745.7\ \tfrac{\text{W}}{\text{hp(l)}}}$, to get:
$\small{19,620\ \text{W}\div 745.7\ \tfrac{\text{W}}{\text{hp(l)}} = 26.31\ \text{hp(l)}}$.

On the other hand, to find the shaft power, we have:

\footnotesize \begin{align*} P_s &= \frac{P_h}{\eta}\\\\ &= \frac{26.31\ \text{hp(l)}}{0.9}\\\\ &= 29.234\ \text{hp(l)} \end{align*}

## How to use this pump horsepower calculator

To use our pump horsepower calculator, you can follow these steps:

2. Input the density of the fluid you need to transport. At this point, our pump calculator will already display the hydraulic power of the pump you need.
3. Type in the efficiency of the pump available to you to find the shaft power.

You can also use our tool in advanced mode by clicking on the Advanced mode button below it. In this mode, you can:

• Change the acceleration due to gravity - let's say you're on another planet; and
• Enter a value for your pump's revolution to find your pump's specific speed.
Kenneth Alambra
Pump parameters
Discharge (Q)
ft³/s
in
Density of fluid (ρ)
lb/cu ft
Efficiency (η)
Pump characteristics
Hydraulic power (Pₕ)
hp(l)
Shaft power (Pₛ)
hp(l)
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