# Pump Horsepower Calculator

By Rahul Dhari
Last updated: Sep 23, 2021

The pump horsepower calculator is used to estimate the pump power, i.e., the power transmitted to the shaft. A pump is one of the most common hydraulic machinery and is used to move fluid by the means of mechanical action by its impeller. Some of its application includes maintaining water supply across the city, heating, ventilation, and cooling systems (HVAC), hydraulics and pneumatics, and electricity generation.

The pump power is a function of hydraulic power and efficiency. Given the importance of this component, it is imperative to understand the basic characteristics of a pump to ensure greater efficiency of the larger processes. You can find more information about pump efficiency and pump power calculations in subsequent paragraphs.

## Types of pump power – shaft and hydraulic power

A pump is a device used to move fluid using mechanical actions. The most common components of a pump are the impeller, casing, suction pipe, and delivery pipe. Pumping action involves drawing of fluid via the suction end of the pipe and moved across the body of the pump over to the delivery end of the pipe. To do so, the impeller, which is housed inside the casing, moves either by rotating or reciprocating motion, depending on the type of pump. The impeller is connected to the shaft, which is run by an electric motor. The pump shaft power is defined as the power applied to achieve the head and the volumetric flow rate. It is a function of volumetric flow rate `Q`, differential head `H`, the density of fluid `ρ`, efficiency `η`, and the gravitational constant `g`. Mathematically, that's:

`Ps = Q * H * ρ * g / η`

Similarly, the hydraulic power can be estimated as:

`Ph = Q * H * ρ * g`

The efficiency, therefore, can be rewritten as the ratio of hydraulic power to shaft power:

`η = Ph / Ps`

The above equations are valid given the parameters have the following units.

• Volumetric flow rate `Q` is in `m3/s`.
• Head `H` is in `metres`.
• Efficiency `η` is in the scale of `0 to 1`.

We know that the pumps in most cases do not operate at an efficiency of 100%. The parameter of specific speed is used to compare the performance of the pump to the ideal case, i.e., a geometrically similar pump delivering 1 cubic meter of fluid per second against 1 m head. The specific speed `Ns` is a dimensionless quantity that is given by the equation:

`Ns = N * Q0.5 / (g * H)0.75`

where the speed of pump `N` is in radians per second.

Note that, while `Ns` is dimensionless, its value changes depending on the units system used for its inputs. The above version of the equation is used in the calculator that gives dimensionless output for specific speed. However, a simpler version of the equation was introduced without the acceleration due to gravity `g` to use with English units. Mathematically,

`Ns = N * Q0.5 / H0.75`

The user has to make sure the units used are consistent for the above equation. Such that:

• Discharge `Q` is in gallons per minute;
• Head `H` is in feet; and
• Speed `N` is in rotations per minute.

## How to calculate shaft power?

To calculate the shaft power of a pump:

1. Enter the discharge or fluid flow rate, `Q`.
2. Insert the differential head, `H`.
3. Fill in the density of the fluid, `ρ`.
4. Enter the efficiency of the pump, `η`.
5. The pump horsepower calculator then returns the value of shaft power and hydraulic power.

Further, to estimate the specific speed of the pump:

1. Enter the pump speed or revolutions, `N`.
2. The specific speed of the pump is returned by the hydraulic horsepower calculator.

## Example of using the pump horsepower calculator

Let's take a look at a pump shaft power calculation: Determine the pump power supplying water at `10 cubic meters per hour` with the differential head of `3 m`. Take the efficiency of the pump as `79%`.

To calculate the shaft power of a pump:

1. Enter the discharge or fluid flow rate, `Q = 10 m3/h`.
2. Insert the differential head, `H = 3 m`.
3. Fill in the density of the fluid, `ρ = 1000 kg/m3`.
4. Enter the efficiency of the pump, `η = 0.79`.
5. The shaft power equals to:
`Ps = 10 * 3 * 9.81 * 1000 / 0.79 = 103.48 W`
1. The hydraulic pump power calculation can be performed as:
`Ph = 103.48 * 0.79 = 81.75 W`

## FAQ

### What is pump shaft power?

The power required to turn the shaft of the pump to deliver a certain differential head is known as the pump shaft power.

### How do I calculate pump shaft power?

To calculate the shaft power of a pump:

1. Multiply the discharge `Q` with the differential head `H`.
2. Multiply the product with the density of the fluid and the acceleration due to the gravity constant.
3. Divide the resultant with the efficiency of the pump.

### How do I calculate efficiency of the pump?

To calculate the efficiency of the pump: Divide the pump's hydraulic power with the shaft power.

### How do I calculate hydraulic power of a pump?

To calculate the hydraulic power of a pump:

1. Multiply the discharge `Q` with the differential head `H`.
2. Multiply the product with the density of the fluid and the acceleration due to the gravity constant.
Rahul Dhari
Pump parameters
Discharge (Q)
ft³/s
in
Density of fluid (ρ)
lb/cu ft
Revolutions (N)
rpm
Pump characteristics
Efficiency (η)
Hydraulic power (Pₕ)
hp(l)
Shaft power (Pₛ)
hp(l)
Specific speed (Nₛ)
Nₛ
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