$3\mathrm{.}2\mathrm{.}3$ WP Water flows steadily through the variable area horizon$-$

tal pipe shown in Fig. P$3\mathrm{.}2\mathrm{.}3.$ The centerline velocity is given by

$V=10(1+x)hat(i)f\frac{t}{s},$ where $x$ is in feet. Viscous effects are neglected.

$($a$)$ Determine the pressure gradient, del$\frac{p}{d}$elx $($as a function of $x),$

needed to produce this flow. $($b$)$ If the pressure at section $(1)$

is $50$ psi, determine the pressure at $(2)$ by $($i$)$ integration of the

pressure gradient obtained in $($a$),($ii$)$ application of the Bernoulli

equation.

FIGURE P$3\mathrm{.}2\mathrm{.}3$