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?
Expand 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
Time Analysis
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474. Affinity
477. Scaling Law
539. Impeller Diameter
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