The Effects of Doubling Pump Speed Professor Seymour Fluids uses a small closed-loop water tunnel to perform flow visualization research. He would like to double the water speed in the test section of the tunnel and realizes that the least expensive way to do this is to double the rotational

Question

The Effects of Doubling Pump Speed

Professor Seymour Fluids uses a small closed-loop water tunnel to perform flow visualization research. He would like to double the water speed in the test section of the tunnel and realizes that the least expensive way to do this is to double the rotational speed of the flow pump. What he doesn’t realize is how much more powerful the new electric motor will need to be! If Professor Fluids doubles the flow speed, by approximately what factor will the motor power need to be increased?

Accepted Answer

For a doubling of ω, we are to calculate by what factor the power to the pump motor must increase.
Assumptions 1 The water remains at the same temperature. 2 After doubling pump speed, the pump runs at conditions homologous to the original conditions.
Analysis Since neither diameter nor density has changed, Eq. 14–38c reduces to

Ratio of required shaft power: [latex] \frac{\operatorname{bhp}_{ B }}{\operatorname{bhp}_{ A }}=\left(\frac{\omega_{ B }}{\omega_{ A }} ight)^{3} [/latex] (1)

Affinity laws: [latex] \frac{b h p_{ B }}{\operatorname{bhp}_{ A }}=\frac{ ho_{ B }}{ ho_{ A }}\left(\frac{\omega_{ B }}{\omega_{ A }} ight)^{3}\left(\frac{D_{ B }}{D_{ A }} ight)^{5} [/latex] (14–38c)

Setting [latex] \omega_{ B }=2 \omega_{ A } ext { in Eq. } 1 ext { gives } b h p_{ B }=8 bhp _{ A } [/latex]. Thus the power to the pump motor must be increased by a factor of 8. A similar analysis using Eq. 14–38b shows that the pump’s net head increases by a factor of 4. As seen in Fig. 14–75, both net head and power increase rapidly as pump speed is increased.

Affinity laws: [latex] \frac{H_{ B }}{H_{ A }}=\left(\frac{\omega_{ B }}{\omega_{ A }} ight)^{2}\left(\frac{D_{ B }}{D_{ A }} ight)^{2} [/latex] (14–38b)

Discussion The result is only approximate since we have not included any analysis of the piping system. While doubling the flow speed through the pump increases available head by a factor of 4, doubling the flow speed through the water tunnel does not necessarily increase the required head of the system by the same factor of 4 (e.g., the friction factor decreases with the Reynolds number except at very high values of Re). In other words, our assumption 2 is not necessarily correct. The system will, of course, adjust to an operating point at which required and available heads match, but this point will not necessarily be homologous with the original operating point. Nevertheless, the approximation is useful as a first-order result. Professor Fluids may also need to be concerned with the possibility of cavitation at the higher speed.

Question 14.10: The Effects of Doubling Pump Speed Professor Seymour Fluids ...

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