Centrifugal Pump Head Calculation
This question asks to calculate the new total head developed by a centrifugal pump when its speed changes. We are given the initial operating conditions (speed, heads) and the new speed. We need to apply the pump affinity laws.
Key Information:
- Initial speed ($N_1$): $1450 \text{ rpm}$
- Initial suction head: $5 \text{ m}$
- Initial delivery head: $12 \text{ m}$
- New speed ($N_2$): $1650 \text{ rpm}$
- Frictional head losses: negligible
Step-by-Step Solution
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Calculate the initial total head ($H_1$): The total head is the sum of the suction and delivery heads.
$H_1 = \text{Suction Head} + \text{Delivery Head}$
$H_1 = 5 \text{ m} + 12 \text{ m} = 17 \text{ m}$
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Apply the pump affinity law for head: The head developed by a centrifugal pump is proportional to the square of its speed ($N$).
$\frac{H_2}{H_1} = \left(\frac{N_2}{N_1}\right)^2$
Where $H_2$ is the new head at speed $N_2$. The given efficiency ($75\%$) and power ($6 \text{ kW}$) are not needed for this calculation.
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Calculate the new total head ($H_2$): Rearrange the formula to solve for $H_2$.
$H_2 = H_1 \times \left(\frac{N_2}{N_1}\right)^2$
Substitute the known values:
$H_2 = 17 \text{ m} \times \left(\frac{1650 \text{ rpm}}{1450 \text{ rpm}}\right)^2$
$H_2 = 17 \times \left(\frac{165}{145}\right)^2$
$H_2 = 17 \times \left(\frac{33}{29}\right)^2$
$H_2 = 17 \times \frac{1089}{841}$
$H_2 \approx 17 \times 1.294887 \approx 22.013 \text{ m}$
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Select the closest option: The calculated head is approximately $22.01 \text{ m}$.
Important Questions from Pump Characteristics
- Impeller speed of a centrifugal pump is increased by $30\%$. The power requirement of the pump increases by $n$ times. The value of $n$ is ________. (Rounded off to two decimal places)
- 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 ________.
