Question 14.2: Selection of Pump Impeller Size A washing operation at a pow...
Selection of Pump Impeller Size
A washing operation at a power plant requires 370 gallons per minute (gpm) of water. The required net head is about 24 ft at this flow rate. A newly hired engineer looks through some catalogs and decides to purchase the 8.25-in impeller option of the Taco Model 4013 FI Series centrifugal pump of Fig. 14–15. If the pump operates at 1160 rpm, as specified in the performance plot, she reasons, its performance curve intersects 370 gpm at H = 24 ft. The chief engineer, who is very concerned about efficiency, glances at the performance curves and notes that the efficiency of this pump at this operating point is only 70 percent. He sees that the 12.75-in impeller option achieves a higher efficiency (about 76.5 percent) at the same flow rate. He notes that a throttle valve can be installed downstream of the pump to increase the required net head so that the pump operates at this higher efficiency. He asks the junior engineer to justify her choice of impeller diameter. Namely, he asks her to calculate which impeller option (8.25-in or 12.75-in) would need the least amount of electricity to operate (Fig. 14–16). Perform the comparison and discuss.
For a given flow rate and net head, we are to calculate which impeller size uses the least amount of power, and we are to discuss our results.
Assumptions 1 The water is at 70°F. 2 The flow requirements (volume flow rate and head) are constant.
Properties For water at 70°F, \rho=62.30 lbm / ft ^{3} .
Analysis From the contours of brake horsepower that are shown on the performance plot of Fig. 14–15, the junior engineer estimates that the pump with the smaller impeller requires about 3.2 hp from the motor. She verifies this estimate by using Eq. 14–5,
Required bhp for the 8.25-in impeller option:
\begin{aligned}b h p=& \frac{\rho g \dot{V} H}{\eta_{\text {pump }}}=\frac{\left(62.30 lbm / ft ^{3}\right)\left(32.2 ft / s ^{2}\right)(370 gal / min )(24 ft )}{0.70} \\& \times\left(\frac{0.1337 ft ^{3}}{ gal }\right)\left(\frac{ lbf }{32.2 lbm \cdot ft / s ^{2}}\right)\left(\frac{1 min }{60 s }\right)\left(\frac{ hp \cdot s }{550 ft \cdot lbf }\right)=3.20 hp\end{aligned}
Pump efficiency: \eta_{\text {pump }}=\frac{\dot{W}_{\text {water horsepower }}}{\dot{W}_{\text {shaft }}}=\frac{\dot{W}_{\text {water horsepower }}}{\text { bhp }}=\frac{\rho g \dot{V} H}{\omega T _{\text {shaft }}} (14–5)
Similarly, the larger-diameter impeller option requires
Required bhp for the 12.75-in impeller option: bhp = 8.78 hp
using the operating point of that pump, namely, \dot{V}=370 gpm , H=72.0 ft , and \eta_{\text {pump }}=76.5 percent (Fig. 14–15). Clearly, the smaller-diameter impeller option is the better choice in spite of its lower efficiency, because it uses less than half the power.
Discussion Although the larger impeller pump would operate at a somewhat higher value of efficiency, it would deliver about 72 ft of net head at the required flow rate. This is overkill, and the throttle valve would be required to make up the difference between this net head and the required flow head of 24 ft of water. A throttle valve does nothing more than waste mechanical energy, however; so the gain in efficiency of the pump is more than offset by losses through the throttle valve. If the flow head or capacity requirements increase at some time in the future, a larger impeller can be purchased for the same casing.