The velocity distribution for laminar flow between fixed parallel plates is given by:

$u=u_{\text{m}\text{a}\text{x}}[1-(\frac{2y}{h}{)}^2]$

where $h$ is the distance separating the plates and the origin is placed midway between the plates.

a$)$ Consider a flow of water at $15C$ with $u_{\text{m}\text{a}\text{x}}$ of $0\mathrm{.}51\frac{m}{s}$ and $h=0\mathrm{.}15mm,$ calculate the shear stress $($Pa$)$ on the upper plate

b$)$ Consider a flow of water at $15C$ with umax equal to $5\mathrm{.}1\frac{m}{s}$ and $h=1\mathrm{.}6mm,$ calculate the force $(N)$ on a $0\mathrm{.}31m^2$ section of the lower plate and give its direction.

Note: Use the following equation for the Newton's Law of viscosity.

${}_{yx}=-\frac{du}{dy}$