Question $3(20$ marks$)$

A $5-$in$-$diameter pipe with an estimated f of $0\mathrm{.}033$ is $110$ feet long and connects two reservoirs whose surface elevations differ by $12$ feet. The pipe entrance is flushed, and the discharge is submerged. $($a$)$ Compute the flow rate. $($b$)$ How much would the flow rate change if the last $10$ ft of the pipe were replaced with a smooth conical diffuser with a cone angle of $10$ o $?$