# Pump Affinity Laws with a Sample Calculation

## What are Pump Affinity Laws?

Pump affinity laws or Pump Laws are used during hydraulic design to calculate volume capacity, head or power consumption of the centrifugal pumps with changing speed or wheel diameters. These laws are very important in pump design as these express the relationship between the variables that decide the pump performance.

The Pump affinity laws are basically a set of formulas that predict the impact of Change in Pump impeller Diameter and its Rotational Speed on the Pump Head (h), Pump Flow (Q) and Power Demand of the Pump (P). The affinity laws are applied both to centrifugal and axial flows. These laws can also be applied to fans, hydraulic turbines.

## Uses of Pump Affinity Laws

Pump Affinity laws are widely used to predict the pump performance at a different speed or with different impeller diameter provided pump performance curve at a certain speed or impeller diameter is known. You can refer to our video article on the same subject by clicking here. To get an update regarding more similar videos please click here and subscribe to our channel.

## Types of pump affinity law?

As mentioned above these laws study the impact of impeller diameter & rotational speed of the pump. Hence the affinity laws are framed

• Once keeping the diameter constant and
• Once keeping the rotational speed constant.

So based on these conditions below mentioned are the cases and relations on flow, head & power consumption of the pump.

## Pump Affinity law keeping the impeller diameter Constant

• The flow of the pump is directly proportional to the change in the speed of the pump. This means there will be the same amount of change in the flow of the pump as the rotational speed of pump changes.
• The Head of the pump is proportional to the square of speed. This means a change in pump rotational speed will lead to a change in the square root of the pump head.
• Power is proportional to the cube of the speed. This means that when the rotational speed of the pump is increased the power consumption of the pump will be increased by 8 times.

The above points can be presented mathematically as given below

## Pump Affinity laws keeping the pump speed constant

• The flow of the pump is directly proportional to the change in the impeller diameter of the pump. This means there will be the same amount of change in the flow of the pump as the impeller diameter of the pump is changed.
• The Head of the pump is proportional to the square of the impeller diameter. This means a change in pump impeller diameter will lead to change in the square root of the pump head
• Power is proportional to the cube of the impeller diameter. So, when the diameter of the pump is increased the power consumption of the pump will be increased by 8 times.

Mathematically the aforementioned points can be represented as given Fig. 3.

## Combined Pump Affinity Law

The flow, head, and power consumption of a pump changes can be combined as shown in Fig. 5 when both rotational speed & impeller diameter changes.

## Example Calculation Explaining Pump Affinity Law

Consider a pump of flow 1000m3/hr is designed for 1500rpm. The same pump is required to be operated at 3000rpm. Find the changed flow of the pump? Assume the diameter of the pump is kept constant.

### Solution:

As per the pump affinity law when impeller diameter is kept constant:

Q∝N or Q1/Q2=N1/N2; So, Q1 = 1000m^3/hr, N1 = 1500rpm, Q2 =? , N2 = 3000 rpm.

Hence, 1000/Q2=1500/3000; Q2=2000 m^3/hr

Hence for the same pumps if the RPM of pump is doubled flow will also get doubled.

In the same example let’s take Power consumption = 100Kw, so find P2 at changed RPM.
P∝N^3 or P1/P2=(N1^3)/(N2^3 )
So, 100/P2=(1500^3)/(2000^3 ) Or P2 = 800 kW.

Hence change in rpm will increase the power consumption of the pump 8 times.