Pump Power Calculation Using Affinity Laws
The power requirement ($P$) of a centrifugal pump is fundamentally linked to its impeller speed ($N$) through the affinity laws. The relationship governing power is:
$P \propto N^3$
This indicates that the power needed scales directly with the cube of the impeller's rotational speed.
Calculating Power Factor ($n$) for Speed Increase
Let the initial impeller speed be $N_1$ and the corresponding initial power be $P_1$. The impeller speed is increased by $30\%$. The new speed, $N_2$, is therefore:
$N_2 = N_1 + (0.30 \times N_1) = 1.30 N_1$
The factor $n$ represents the ratio of the new power ($P_2$) to the original power ($P_1$):
$n = \frac{P_2}{P_1}$
Applying the affinity law:
$n = \left( \frac{N_2}{N_1} \right)^3$
Substituting the relationship between $N_2$ and $N_1$:
$n = \left( \frac{1.30 N_1}{N_1} \right)^3 = (1.30)^3$
Final Power Factor Calculation
The value of $n$ is calculated as:
$n = 1.30 \times 1.30 \times 1.30 = 2.197$
Rounding this value to two decimal places, as required:
$n \approx 2.20$
Important Questions from Pump Characteristics
- A centrifugal pump having an overall efficiency of $75\%$ requires $6 \text{ kW}$ power at $1450 \text{ rpm}$ to deliver water against a suction head of $5 \text{ m}$ and a delivery head of $12 \text{ m}$. If the pump runs at $1650$ $\text{rpm}$ and frictional head losses are negligible, the total head developed by the pump in metres will be
- At a speed of 1800 rpm, a centrifugal pump discharges 50 L s$^{-1}$ at its best point of efficiency for a total head of 25 m. The specific speed of the pump in rpm (round off to 2 decimal places) is ________
- Discharge from a centrifugal pump operating at $1000$ rpm with a total head of $30$ m is $300$ L $min^{-1}$. The pump efficiency is $65\%$. If speed of the pump is increased to $1200$ rpm, the power required to operate the pump in kW is ________ (rounded off to $2$ decimal places).
Consider acceleration due to gravity = $9.81$ m $s^{-2}$. A six-stage centrifugal pump delivers 120 L $s^{-1}$ against a total head of 510 m. If the design speed of this pump is 1450 rpm, the specific speed of the pump will be ______________.
- The brake power of a centrifugal pump having an impeller diameter of 200 mm is 1.86 kW. If the impeller is replaced with another impeller of 180 mm diameter, the brake power of the pump in kW will be ________.
