# Pump Horsepower Calculator

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:

`P`_{s} = Q * H * ρ * g / η

Similarly, the **hydraulic power** can be estimated as:

`P`_{h} = Q * H * ρ * g

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

`η = P`_{h} / P_{s}

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

- Volumetric flow rate
`Q`

is in`m`

.^{3}/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 `N`

is a _{s}**dimensionless** quantity that is given by the equation:

`N`_{s} = N * Q^{0.5} / (g * H)^{0.75}

where the speed of pump `N`

is in radians per second.

Note that, while `N`

is dimensionless, its _{s}**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,

`N`_{s} = N * Q^{0.5} / H^{0.75}

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:

- Enter the
**discharge or fluid flow rate**,`Q`

. - Insert the
**differential head**,`H`

. - Fill in the
**density of the fluid**,`ρ`

. - Enter the
**efficiency of the pump**,`η`

. - The pump horsepower calculator then returns the value of
**shaft power**and**hydraulic power**.

Further, to estimate the **specific speed** of the pump:

- Enter the
**pump speed or revolutions**,`N`

. - 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:

- Enter the discharge or fluid flow rate,
`Q = 10 m`

.^{3}/h - Insert the differential head,
`H = 3 m`

. - Fill in the density of the fluid,
`ρ = 1000 kg/m`

.^{3} - Enter the efficiency of the pump,
`η = 0.79`

. - The shaft power equals to:

`P`_{s} = 10 * 3 * 9.81 * 1000 / 0.79 = 103.48 W

- The hydraulic pump power calculation can be performed as:

`P`_{h} = 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:

**Multiply**the discharge`Q`

with the differential head`H`

.**Multiply**the product with the density of the fluid and the acceleration due to the gravity constant.**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:

**Multiply**the discharge`Q`

with the differential head`H`

.**Multiply**the product with the density of the fluid and the acceleration due to the gravity constant.