## Related questions with answers

A centrifugal water pump running at speed $\omega$=800 rpm has the following data for flow rate, Q, and pressure head, $\Delta p$.

$\begin{matrix} \text{Q (}{ft^{3}/min)} & \text{0} & \text{50} & \text{75} & \text{100} & \text{120} & \text{140} & \text{150} & \text{165}\\ \text{}{\Delta p (psf)} & \text{7.54} & \text{7.29} & \text{6.85} & \text{6.12} & \text{4.8} & \text{3.03} & \text{2.38} & \text{1.23}\\ \end{matrix}$

The pressure head is a function of the flow rate, speed, impeller diameter D, and water density $\rho$. Plot the pressure head versus flow rate curve. Find the two $\Pi$ parameters for this problem, and, from the above data, plot one against the other. By using Excel to perform a trendline analysis on this latter curve, generate and plot data for pressure head versus flow rate for impeller speeds of 600 rpm and 1200 rpm.

Solution

Verified**Given:**

$\begin{aligned} \Delta p=\Delta p(Q, \omega, D, \rho) \end{aligned}$

**Find:**

The dimensionless parameters, plot one dimensionless parameter against the other one.

**Assumptions and principles:**

In order to find the non dimensional form of the function, Buckingham Pi Theorem will be used. With this theorem in six easy steps non dimensional groups for the given function will be obtained.

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