$(1)$ Show that the pressure gradiont $d\frac{P}{d}y$ is constant. Here. $P$

is the "modified pressure", which is a convenient abbreviation

for the sum nt the prassure mid gravituoicnl irtms

ootion. I $(5$ prints$)$

$(2)$ Derive an equation for the steady$-$state velocity profile $v_y(x)$

of the fluid. $(5$ points$)$

$(3)$ Draw the velocity profile $v_y$ and the corresponding shear stress

profile ${}_{xy}.$ clarifying the change of sign in ${}_{xy}.10$ points$)$