Problem $2(10$ pts$)$

Revisit the setup for problem $1.$

$(7$ pts$)$ Use shell balances to obtain the profile for $v_x.$

$(3$ pts$)$ What is the force in the $x-$direction required on each plate to keep it stationary?

Express your answers in terms of $p_0{|}_x=L,p_0{|}_x=0,,$ L $($length in x$-$direction$),$ W $($width in z$-$direction$)$ and H $($separation between

the plates. Here, $p_0$ represents the pressure at $y=H,$ which varies in x $.$

PLEASE MAKE SURE YOU SOLVE ALL THE TWO QUESTIONS IN THE FILE