Show a detailed analysis of the problem starting from the fundamental equations. List all assumptions you make.

2. ( 45 pts) z2z1DKL,entranceKL,valveKLellbowKL,exitL=7.85m(elevationdifference)=2.03cm(pipediameter)=0.50(pipeentrance)=17.5(valve)=0.92(eachelbow-thereare5)=1.05(pipeexit)=176.5m(totalpipelength)=0.25mm(piperoughness) a) A water pump is used to pump water from one large reservoir to another large reservoir that is at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure, as sketched in the figure above. The dimensions and minor loss coefficients are provided in the figure. The pumps performance is approximated by the expression =H0 aV2, where shutoff head H0=24.4m of water column, coefficient a=0.0678m/Lpm2, available pump head Havailable is in units of meters of water column, and capacity V is in units of liters per minute (Lpm). Estimate the capacity delivered by the pump. Answer: 11.6Lpm b) For the pump and piping system in part (a), plot required pump head Hrequired (mof water column) as a function of volume flow rate V (Lpm). On the same plot, compare available pump head Havailable versus V, and mark the operating point. Discuss. c) Suppose that free surface of the inlet reservoir in part (a) is 3.0m lower in elevation, such that z2z1=10.85m. All the constants and parameters are identical to those of part (a) except for the elevation difference. Calculate the volume flow rate for this case and compare with the result of part (a). d) April's supervisor asks her to find a replacement pump that will increase the flow rate through the piping system of Problem 2a by a factor of 2 or greater. April looks through some online brochures and finds a pump with the performance data shown in table below. All dimensions and parameters remain the same as in Problem 1 -only the pump is changed. (a) Perform a least-squares curve fit (regression analysis) of Havalable versus V2, and calculate the best-fit values of coefficients H0 and a that translate the tabulated data of table below into the parabolic expression Havailable=H0aV2. Plot the data points as symbols and the curve fit as a line for comparison. (b) Use the expression obtained in part (a) to estimate the operating volume flow rate of the new pump if it were to replace the existing pump, all else being equal. Compare to the result of Problem 1 and discuss. Has April achieved her goal? (c) Generate a plot of required net head and available net head as functions of volume flow rate and indicate the operating point on the plot