## Affinity Law

Consider a 1,500 rpm pump moving a fluid at a rate of 15 L/s. If the same pump were to increase the volumetric flow rate to 20 L/s through the same pipe/impeller diameter, what is the new speed in rpm?

Hint
$$\left ( \frac{Q}{ND^3} \right )_2= \left ( \frac{Q}{ND^3} \right )_1$$$where $$Q$$ is the volumetric flowrate, $$N$$ is the rotational speed, and $$D$$ is the impeller diameter. Hint 2 Since the diameter is constant, the equation becomes: $$\left ( \frac{Q}{N} \right )_2= \left ( \frac{Q}{N} \right )_1$$$
Using the scaling/affinity laws:
$$\left ( \frac{Q}{ND^3} \right )_2= \left ( \frac{Q}{ND^3} \right )_1$$$where $$Q$$ is the volumetric flowrate, $$N$$ is the rotational speed, and $$D$$ is the impeller diameter. Since the diameter is constant, the equation becomes: $$\left ( \frac{Q}{N} \right )_2= \left ( \frac{Q}{N} \right )_1$$$
$$\left ( \frac{Q_1}{N_1} \right )= \left ( \frac{Q_2}{N_2} \right )$$$$$\left ( \frac{15L/s}{1500rpm} \right )= \left ( \frac{20L/s}{N_2} \right )$$$
$$N_2=\frac{20\cdot 1500rpm}{15}=2000\:rpm$$\$
2000 rpm