Understanding the Pump Affinity Laws: Equations, Applications, and Examples
Pumps play a critical role in many industrial, commercial, and residential applications, such as water supply, heating, ventilation, and air conditioning (HVAC), and process and manufacturing operations. To ensure efficient and reliable pump operations, it is essential to understand the pump affinity laws, which relate pump performance parameters, such as flow rate, head, and power, to changes in pump speed, impeller diameter, and other design variables.
The pump affinity laws consist of three main equations, which express the following relationships:
Flow rate (Q) is proportional to pump speed (N). Q2/Q1 = N2/N1
Head (H) is proportional to the square of pump speed (N) and the square of impeller diameter (D). H2/H1 = (N2/N1)^2 x (D2/D1)^2
Power (P) is proportional to the cube of pump speed (N) and the cube of impeller diameter (D). P2/P1 = (N2/N1)^3 x (D2/D1)^3
These equations can be used to predict the performance of a pump under different operating conditions or design changes, such as speed control, impeller trimming, or system resistance variations. They can also be used to optimize pump operations by selecting the best combination of speed and impeller diameter to achieve the desired flow rate and head with minimum power consumption.
Worked Example
Let's take a look at a practical example of how to use the pump affinity laws to optimize pump operations. Suppose we have a centrifugal pump that delivers a flow rate of 100 m3/h and a head of 50 m when operated at a speed of 1500 rpm and an impeller diameter of 300 mm. The pump is powered by a motor that consumes 30 kW.
Now, let's assume that we want to increase the flow rate to 120 m3/h without changing the motor power or the system resistance. We can use the pump affinity laws to calculate the required speed and impeller diameter.
First, we can use equation 1 to find the new speed: N2/N1 = Q2/Q1 = 120/100 = 1.2 N2 = 1.2 x N1 = 1.2 x 1500 = 1800 rpm
Next, we can use equation 2 to find the new impeller diameter: D2/D1 = √(H2/H1) / (N2/N1) D2/D1 = √(50 x (120/100)^2) / (1800/1500) = 1.09 D2 = 1.09 x D1 = 1.09 x 300 = 327 mm
Finally, we can use equation 3 to check the new power consumption: P2/P1 = (N2/N1)^3 x (D2/D1)^3 P2/P1 = (1800/1500)^3 x (327/300)^3 = 1.42 P2 = 1.42 x P1 = 1.42 x 30 = 42.6 kW
We can see that the new pump speed and impeller diameter will increase the flow rate to the desired value but will also increase the power consumption by about 42%. If energy efficiency is a priority, we may want to consider alternative solutions, such as using a variable speed drive (VSD)
