Design an experiment to determine hp for a pump.

Question

Design an experiment to determine [latex]h_{p}[/latex] for a pump.

Accepted Answer

Experimentalists seek to design tests that are theoretically motivated while easily performed and interpreted. To determine [latex]h_{p}[/latex] for a pump, for example, one would seek to eliminate all minor losses as well as the gravita-tional effects if possible. Consider, for example, Figure 10.16 for which the pipe flow equation is

[latex] \left(\frac{p_{1}}{ ho _{1}}+\frac{1}{2}\alpha _{1}\overline{ u }^{2}_{1} ight)-\left(\frac{p_{2}}{ ho _{2}}+\frac{1}{2}\alpha _{2}\overline{ u }^{2}_{2} ight)[/latex]

[latex] =f\left(Re,\frac{e}{D} ight)\left(\frac{L_{1}}{D} ight)\frac{\overline{ u }^{2}_{1} }{2}+f\left(Re,\frac{e}{D} ight)\left(\frac{L_{2}}{D} ight)\frac{\overline{ u }^{2}_{2} }{2}-h_{p}[/latex]

and from which [latex]h_{p}[/latex] can be solved in terms of measurable quantities. Of course, balance of mass requires that [latex]Q_{1} = Q_{2}[/latex] and thus [latex]\overline{ u }_{1} = \overline{ u }_{2}[/latex] in a constant

Control Volume and Semi-empirical Methods FIGURE 10.16 Simple experimental setup to determine the geometric loss (actually gain) due to a particular pump. cross-section pipe. If the flow is the same at 1 and 2, either turbulent or laminar, then our data reduction simplifies. Indeed, if we are able to measure the inlet [latex]p_{3}[/latex] and outlet [latex]p_{4}[/latex] pressures very near the pump, then

[latex] \frac{p_{3}-p_{4}}{ ho }=-h_{p} ightarrow h_{p}=\frac{p_{4}-p_{3}}{ ho },[/latex]

where [latex]p_{4}\gt p_{3}[/latex] due to the pump. Hence, the gain (or, a negative loss) due to a pump is determined primarily by the pressure jump across the pump.

Question 10.9: Design an experiment to determine hp for a pump.

Related Answered Questions