PROBLEM $4(25$ points$)$

Two identical pumps have the characteristic curves shown in the table below. The pumps

are connected in series and deliver water through a $400-$mm$-$diameter, $1,000-$meter$-$long com$-$

mercial steel pipe into a reservoir where the water level is $25$ m above the pump. Neglecting

minor losses, calculate the discharge when the system contains two pumps connected in series.

The kinematic viscosity of water is $1*{10}^{-6}\frac{m^2}{s}.$

Through an empirical analysis, the friction factor for the identical pumps is calculated as

follows:

$f=\frac{0\mathrm{.}25}{[log(\frac{lon}{3\mathrm{.}70*D}+\frac{5\mathrm{.}74}{R{e}^{0\mathrm{.}90}}){]}^2}$

NOTE: Use a spreadsheet to help you solve the problem. Plot the graphs needed to solve

this problem and include them in your solution. Also, include the table from the spreadsheet

as part of your solution.

Problem $04$: For this problem, you must use a spreadsheet to speed up your calculations. Solving it primarily by hand will take a very

long time. For grading purposes, make sure to include a screenshot of your spreadsheet table with all the required variables $(Q,Hp,V,$

$Re,f,$ and HSH $)$ and the plot of the pump characteristic and pump system curves. You must indicate the operating point $($intersection

of the two curves$)$ as the answer for the problem.

Problem $04$: For this problem, you must use a spreadsheet to speed up your calculations. Solving it primarily by hand will take a very

long time. For grading purposes, make sure to include a screenshot of your spreadsheet table with all the required variables $(Q,Hp,V,$

$Re,f,$ and HSH $)$ and the plot of the pump characteristic and pump system curves. You must indicate the operating point $($intersection

of the two curves$)$ as the answer for the problem.