Question
A six-stage centrifugal pump delivers water at the rate of $150$ L.s$^{-1}$ against a net pressure rise of $5003$ kN.m$^{-2}$. The pump impeller rotates at $1450$ rpm. If the acceleration due to gravity is $9.81$ m.s$^{-2}$, the specific speed of the pump is __________ (Answer in integer)
To find the specific speed, Ns, of the centrifugal pump, we use the formula:
Ns = N√Q / (H3/4)
where N is the rotational speed in rpm, Q is the flow rate in m3/s, and H is the head in meters.
First, convert the net pressure rise (ΔP) to head (H) using:
H = ΔP / (ρg)
where ρ is the density of water (considered as 1000 kg/m3) and g is acceleration due to gravity (9.81 m/s2).
ΔP = 5003 kN/m2 = 5003000 N/m2
H = 5003000 / (1000 × 9.81) ≈ 510 m
Convert the flow rate to cubic meters per second:
Q = 150 L/s = 0.150 m3/s
Now, substitute the values into the specific speed formula:
N = 1450 rpm
Ns = 1450√0.150 / (5103/4)
Ns ≈ 1450 × 0.3873 / 117.29
Ns ≈ 636
The specific speed of the pump is within the expected range of 631 to 637.
Ns = N√Q / (H3/4)
where N is the rotational speed in rpm, Q is the flow rate in m3/s, and H is the head in meters.
First, convert the net pressure rise (ΔP) to head (H) using:
H = ΔP / (ρg)
where ρ is the density of water (considered as 1000 kg/m3) and g is acceleration due to gravity (9.81 m/s2).
ΔP = 5003 kN/m2 = 5003000 N/m2
H = 5003000 / (1000 × 9.81) ≈ 510 m
Convert the flow rate to cubic meters per second:
Q = 150 L/s = 0.150 m3/s
Now, substitute the values into the specific speed formula:
N = 1450 rpm
Ns = 1450√0.150 / (5103/4)
Ns ≈ 1450 × 0.3873 / 117.29
Ns ≈ 636
The specific speed of the pump is within the expected range of 631 to 637.
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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)
- 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 ______________.
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