Suppose the pump of Probs. 14–31E and 14–33E is used in a piping system that has the system requirement H_required = (z₂ – z₁) 1 bV̇², where elevation difference z₂ – z₁ = 11.3 ft, and coefficient b = 0.00986 ft/(gpm)². Estimate the operating point of the system, namely, V̇_operating (gpm) and H_operating (ft).

Data from Problem 14–33E

For the centrifugal water pump of Prob. 14–31E, plot the pump’s performance data: H (ft), bhp (hp), and η_pump (percent) as functions of V̇ (gpm), using symbols only (no lines). Perform linear least-squares polynomial curve fits for all three parameters, and plot the fitted curves as lines (no symbols) on the same plot. For consistency, use a first-order curve fit for H as a function of V̇², use a second order curve fit for bhp as a function of both V̇ and V̇², and use a third-order curve fit for η_pump as a function of V̇, V̇², and V̇³. List all curve-fitted equations and coefficients (with units) for full credit. Calculate the BEP of the pump based on the curve-fitted expressions.

Data from problem 14–31E

The performance data for a centrifugal water pump are shown in Table P14–31E for water at 77°F (gpm = gallons per minute). 

For each row of data, calculate the pump efficiency (percent). Show all units and unit conversions for full credit. 

Estimate the volume flow rate (gpm) and net head (ft) at the BEP of the pump.

Transcribed Image Text:

TABLE P14-31E V, gpm 0.0 4.0 8.0 12.0 16.0 20.0 24.0 H, ft 19.0 18.5 17.0 14.5 10.5 6.0 0.0 bhp, hp 0.06 0.064 0.069 0.074 0.079 0.08 0.078