$1.(50$ pts$)$ Water at $25$ oC drains from a large tank, by gravity, through a pipe. The outlet of the drain pipe is open to the

atmosphere, and is located $7\mathrm{.}23$ m below the surface of the large tank. The pipe itself is $5\mathrm{.}66$ m long and $2\mathrm{.}35$ cm in

diameter. The average surface roughness height inside the pipe is $0\mathrm{.}0540$ mm$.$ The pipe inlet at the tank is a reentrant inlet.

There are two smooth $90$ o threaded elbows in the pipe. Note: Use the Churchill equation, not the Colebrook equation.

$($a$)$ Estimate the volume flow rate in L$/$min$.$ Note: You may need to iterate. I strongly suggest using software to solve this

problem. However, show a sketch with your chosen control volume and show the equations you use, etc., even if you

solve this problem with software.

$($b$)$ Repeat, except ignore minor losses in the piping system. Calculate the percentage error caused by this approximation. $1.(50$ pts$\backslash ()\backslash$quad $\backslash )$ Water at $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ drains from a large tank, by gravity, through a pipe. The outlet of the drain pipe is open to the atmosphere, and is located $7\mathrm{.}23$ m below the surface of the large tank. The pipe itself is $5\mathrm{.}66$ m long and $2\mathrm{.}35$ cm in diameter. The average surface roughness height inside the pipe is $0\mathrm{.}0540$ mm $.$ The pipe inlet at the tank is a reentrant inlet. There are two smooth $\backslash (90^\{\backslash$circ$\}\backslash )$ threaded elbows in the pipe. Note: Use the Churchill equation, not the Colebrook equation.

$($a$)$ Estimate the volume flow rate in $\backslash (\backslash$mathrm$\{$L$\}/\backslash$mathrm$\{$min$\}\backslash ).$ Note: You may need to iterate. I strongly suggest using software to solve this problem. However, show a sketch with your chosen control volume and show the equations you use, etc., even if you solve this problem with software.

$($b$)$ Repeat, except ignore minor losses in the piping system. Calculate the percentage error caused by this approximation.