Chapter 14, Problem 33P

The performance data of a water pump follow the curve fit $H_{available}=H_0-a{\stackrel{\dot{}}{V}}^2$ . where the pump's shutoff head $H_0=0.76m$ , coefficient $a=0.453m/{\left(Lpm\right)}^2$ the units of pump head H are meters, and the units of $\stackrel{\dot{}}{V}$ are liters per minute (Lpm). The pump is used to pump water from one large reservoir to another large reservoir at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure. The system curve simplifies to $H_{available}=\left(z_2-z_1\right)+b{\stackrel{\dot{}}{V}}^2$ , where elevation difference $z_2-z_1=3.52m$ , and coefficient b = 0.0261m/(Lpm)2. Calculate the operating point Of the pump ( ${\stackrel{\dot{}}{V}}_{operating}$ and $H_{operating}$ ) in appropriate units (Lpm and meters, respectively).