$60,000l\frac{b}{h}$ of a petroleum fraction will be cooled from $250F$ to $150F$ using water with a range of $85F$ to $120F.$ For each stream, the inlet pressure will be $50$ psia and a maximum pressure drop of $10$ is specified. A fouling factor of $0\mathrm{.}002h*f{t}^2.\frac{F}{B}t$ is required for each stream. The petroleum fraction is not corrosive and its properties may be assumed constant at the values given below.

$\backslash$table$[[$Petroleum Fraction Property,Value$],[C_P(Bt\frac{u}{l}bm*F),0\mathrm{.}52],[k(Bt\frac{u}{h}*ft*F),0\mathrm{.}074],[(cp),2\mathrm{.}75],[s,0\mathrm{.}82],[Pr,46\mathrm{.}7]]$

$($a$)$ Develop an initial configuration for a shell$-$and$-$tube heat exchanger with plain $($un$-$finned$)$ tubes to meet this service.

$($b$)$ Perform the rating calculations for the initial configuration developed in part $($a$).$

$($c$)$ Based on the results of the rating calculations in part $($b$),$ specify what changes, if any, should be made to the configuration of the heat exchanger for the next trial.