## 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**

**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**

**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