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Chapter 12: Problem 26

A centrifugal pump having an impeller diameter of \(1 \mathrm{m}\) is to be constructed so that it will supply a head rise of 200 mat a flowrate of \(4.1 \mathrm{m}^{3} / \mathrm{s}\) of water when operating at a speed of \(1200 \mathrm{rpm} .\) To study the characteristizs of this pump, a \(1 / 5\) scale, geometrizally similar model operated at the same speed is to be tested in the laboratory. Determine the required model discharge and head rise. Assume that both model and prototype operate with the same effciency (and therefore the same flow coefficient)

Short Answer

Expert verified
The required model discharge is \(0.0328 m^3/s\), and the required head rise is \(8 m\).

Step by step solution

01

Calculate discharge for model

Use the law of corresponding velocities for pumps. This states that the ratio of the discharges (or flow rates) of the model and prototype is the cube of the ratio of their dimensions. Given that the size ratio between the model and prototype is 1/5, the discharge of the model (\(Q_M\)) is given by \(Q_M = Q_P \times (D_M/D_P)^3\), substituting all known values gives \(Q_M = 4.1 m^3/s \times (1/5)^3\)
02

Calculate head rise for model

Use the law of corresponding pressures for pumps. This states that the ratio of the head (pressure) rise of the model and prototype is the square of the ratio of their dimensions. Hence, the head rise of the model (\(H_M\)) is given by \(H_M = H_P \times (D_M/D_P)^2\), substituting all known values gives \(H_M = 200 m \times (1/5)^2\)
03

Evaluate Calculation

Evaluate the values obtained from step 1 and step 2 to find the model discharge and model head rise

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