Question $7$

$7\mathrm{.}75$ Points

A Branch $a$ is also composed of $2-$in Schedule $40$ steel pipe and includes a heat exchanger with a resistance coefficient of $K=7\mathrm{.}5$ based on the velocity head in the pipe. Branch b is a bypass line composed of $\frac{11}{4}-$in schedule $40$ steel pipe. The length of pipe in branch $b$ is $20$ ft $.$ Because of the size of heat exchanger, the length of pipe in branch a is very short and friction losses in this branch can be neglected. Neglect energy losses at the tee junctions but consider all elbows $($standard elbows$).$ All three valves are fully open.

To fulfill the design requirements, the design engineer has estimated the trial friction factor of $0\mathrm{.}0248$ for branch b$.$ For this system

a$.$ Determine the volume flow rate in each branch.

b$.$ Also, indicate that the trial friction factor has been estimated from an acceptable range.

c$.$ Also, indicate that $f=0\mathrm{.}0248$ is an accurate estimation for the friction factor.

Note $1$: $g=32\mathrm{.}2f\frac{t}{s^2}$

Note $2$: $1f\frac{t^3}{s}=449$gal$/$min