Specific Speed and Unit Quantities Questions and Answers

Q: Which of the following is true?

Specific speed rises from impulse to reaction turbines and with the flow rate. The Pelton wheel has the lowest specific speed (a high head, low flow machine), the Francis turbine is in the medium range, and the Kaplan turbine has the highest, being used for low heads and large discharges. So the Francis specific speed is less than that of the Kaplan turbine. The options that put Kaplan below Francis or below Pelton, or Francis below Pelton, reverse this order.

Q: A centrifugal pump running at 500 rpm and at its maximum efficiency is delivering a head of 30 m at a flow of 60 liters per minute. If the rpm is changed to 1000, then the head H in meters and flow rate Q in liters per minute at maximum efficiency are estimated to be :

At 1000 rpm the pump gives H = 120 m and Q = 120 litres per minute.For the same pump running at its point of maximum efficiency, the affinity laws say that discharge varies as the speed and head as the square of the speed.\[ \begin{aligned} \frac{Q_2}{Q_1} &= \frac{N_2}{N_1} = \frac{1000}{500} = 2 \\ Q_2 &= 2 \times 60 = 120\ \text{L/min} \end{aligned} \]\[ \begin{aligned} \frac{H_2}{H_1} &= \left(\frac{N_2}{N_1}\right)^{2} = 4 \\ H_2 &= 4 \times 30 = 120\ \text{m} \end{aligned} \]H = 60 m comes from scaling the head linearly with speed, Q = 30 halves the flow instead of doubling it, and Q = 480 cubes the speed ratio, which is the law for power, not for flow.

Q: The specific speed (Ns) of a pump is:(When Symbols have their usual meanings)

The specific speed of a pump is \(\frac{N\sqrt{Q}}{H^{3/4}}\).A pump's specific speed is the speed of a geometrically similar pump delivering unit discharge against unit head. It is defined with the discharge Q, since that is what a pump delivers.The forms with \(\sqrt{P}\) and \(H^{5/4}\) define the specific speed of a turbine, which is rated by its power output, so options B and D, and the mixed form in A, do not apply to a pump.

Which of the following is true?

A.Specific speed of Francis turbine < Specific speed of Kaplan turbine
B.Specific speed of Kaplan turbine < Specific speed of Francis turbine
C.Specific speed of Kaplan turbine < Specific speed of Pelton wheel
D.Specific speed of Francis turbine < Specific speed of Pelton wheel

Exam Year(s)

DSSSB JE - 2023,

Answer: A

Specific speed rises from impulse to reaction turbines and with the flow rate. The Pelton wheel has the lowest specific speed (a high head, low flow machine), the Francis turbine is in the medium range, and the Kaplan turbine has the highest, being used for low heads and large discharges. So the Francis specific speed is less than that of the Kaplan turbine. The options that put Kaplan below Francis or below Pelton, or Francis below Pelton, reverse this order.

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A centrifugal pump running at 500 rpm and at its maximum efficiency is delivering a head of 30 m at a flow of 60 liters per minute. If the rpm is changed to 1000, then the head H in meters and flow rate Q in liters per minute at maximum efficiency are estimated to be :

A.H=120, Q=30
B.H=60, Q=120
C.H=120, Q=120
D.H=60, Q=480

Exam Year(s)

RSMSSB JE - 2025, RSMSSB - 2025,

Answer: C

At 1000 rpm the pump gives H = 120 m and Q = 120 litres per minute.

For the same pump running at its point of maximum efficiency, the affinity laws say that discharge varies as the speed and head as the square of the speed.

\[ \begin{aligned} \frac{Q_2}{Q_1} &= \frac{N_2}{N_1} = \frac{1000}{500} = 2 \\ Q_2 &= 2 \times 60 = 120\ \text{L/min} \end{aligned} \]

\[ \begin{aligned} \frac{H_2}{H_1} &= \left(\frac{N_2}{N_1}\right)^{2} = 4 \\ H_2 &= 4 \times 30 = 120\ \text{m} \end{aligned} \]

H = 60 m comes from scaling the head linearly with speed, Q = 30 halves the flow instead of doubling it, and Q = 480 cubes the speed ratio, which is the law for power, not for flow.

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The specific speed (Ns) of a pump is:

(When Symbols have their usual meanings)

A.\(\frac{N\sqrt{Q}}{H^{5/4}}\)
B.\(\frac{N\sqrt{P}}{H^{5/4}}\)
C.\(\frac{N\sqrt{Q}}{H^{3/4}}\)
D.\(\frac{N\sqrt{P}}{H^{3/4}}\)

Exam Year(s)

RSMSSB JE - 2025, RSMSSB - 2025,

Answer: C

The specific speed of a pump is \(\frac{N\sqrt{Q}}{H^{3/4}}\).

A pump's specific speed is the speed of a geometrically similar pump delivering unit discharge against unit head. It is defined with the discharge Q, since that is what a pump delivers.

The forms with \(\sqrt{P}\) and \(H^{5/4}\) define the specific speed of a turbine, which is rated by its power output, so options B and D, and the mixed form in A, do not apply to a pump.

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