Calculation of Specific Speed of Centrifugal Pump

Step 1: Determine the flow rate of the centrifugal pump

Given, the centrifugal pump delivers 750 litres of water per second.

Step 2: Determine the head against which the pump is working

Given, the head against which the centrifugal pump is working is 15 metres.

Step 3: Determine the rotational speed of the centrifugal pump

Given, the rotational speed of the centrifugal pump is 725 rpm.

Step 4: Determine the specific speed of the centrifugal pump

Using the formula for specific speed of a centrifugal pump:

Specific speed (Ns) = (N √Q) / H3/4

Where,

N = rotational speed of the pump in rpm
Q = flow rate of the pump in m3/s
H = head against which the pump is working in metres

Substituting the given values, we get:

Specific speed (Ns) = (725 √(750/1000)) / (15)3/4

Specific speed (Ns) = 36.97

Therefore, the specific speed of the centrifugal pump delivering 750 litres of water per second against a head of 15 metres at 725 rpm is 36.97.

Explanation:

Specific speed is a dimensionless parameter used to characterize the hydraulic performance of a centrifugal pump. It is a measure of the pump's efficiency and its ability to handle different flow rates and heads. A higher specific speed indicates a pump that is better suited for higher flow rates and lower heads, while a lower specific speed indicates a pump that is better suited for lower flow rates and higher heads.

In this problem, we are given the flow rate, head, and rotational speed of the centrifugal pump. We can use the formula for specific speed to calculate its value. The specific speed obtained in this problem is 36.97, which indicates that the pump is better suited for moderate flow rates and moderate heads.

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