Specific Speed Calculation for Centrifugal Pump
The specific speed ($N_s$) is a dimensionless index used to classify pump impellers. It relates the pump's speed ($N$), discharge ($Q$), and head ($H$) at its best efficiency point (BEP).
Formula for Specific Speed
The commonly used formula for specific speed is:
$N_s = \frac{N \times \sqrt{Q}}{H^{3/4}}$
Where:
- $N$ is the speed in revolutions per minute (rpm).
- $Q$ is the discharge rate in cubic meters per second (m$^3$/s).
- $H$ is the total head in meters (m).
Given Parameters
- Speed, $N = 1800$ rpm
- Discharge, $Q = 50$ L s$^{-1}$
- Total Head, $H = 25$ m
Calculation Steps
- Convert Discharge Units: Convert the discharge from L/s to m$^3$/s.
$Q = 50 \text{ L s}^{-1} = 50 \times 10^{-3} \text{ m}^3 \text{ s}^{-1} = 0.05 \text{ m}^3 \text{ s}^{-1}$
- Calculate Specific Speed: Substitute the values into the specific speed formula.
$N_s = \frac{1800 \times \sqrt{0.05}}{(25)^{3/4}}$
- Evaluate Terms:
- $\sqrt{0.05} \approx 0.2236$
- $25^{3/4} \approx 11.1803$
- Compute Final Value:
$N_s = \frac{1800 \times 0.2236}{11.1803} \approx \frac{402.48}{11.1803} \approx 36.00$
The calculated specific speed is approximately 36.00 rpm. This value lies within the range specified (35.9 to 36.1).
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
- 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 ________.
