Water flows steadily through the variable area horizontal pipe shown in the figure below. The centerline velocity is given by $V=10(1+x)if\frac{t}{s},$ 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. If the pressure at section $(1)$ is $55$ psi, determine the pressure at $(2)$ by $($b$)$ integration of the pressure gradient obtained in $($a$)$ and $($c$)$ application of the Bernoulli equation.

$($a$)$

del$\frac{p}{d}$elx$=-194(1+x)l\frac{b}{f}{t}^3$

del$\frac{p}{d}$elx$=-1\mathrm{.}94(1+x)l\frac{b}{f}{t}^3$

del$\frac{p}{d}$elx$=194(1+x)l\frac{b}{f}{t}^3$

del$\frac{p}{d}$elx$=-194(1+10x)l\frac{b}{f}{t}^3$

$($b$)$ psi

$($c$)$ psi