$2$

Problem $10\mathrm{.}011-$ Sketch of the modified pressure profile $2$

Consider steady, incompressible, laminar, fully developed, planar Poiseuille flow between two parallel, horizontal plates $($velocity and pressure profiles are shown in the figure$).$ At some horizontal location $x=x_1,$ the pressure varies linearly with vertical distance $z,$ as sketched. Choose an appropriate datum plane $(z=h).$

$5$

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Discuss how modified pressure varies with downstream distance $x.$ In other words, does modified pressure increase, stay the same, or decrease with $x?$ If $P$ increases or decreases with $x,$ how does it do so $($e$.$g$.,$ linearly, quadratically, exponentially$)?$ Use a sketch to illustrate your answer. $($Please upload your response$/$solution using the controls provided below.$)$