Two immiscible incompressible fluids are flowing between two horizontal flat plates of length $L,$ width $W,$ and vertical separation $28.$ The flow rates are adjusted such that the thickness of each layer is $8.$ The fluid in the lower layer is more dense and more viscous than the fluid in the upper layer. Calculate:

$($a$)$ The variation of $v_x$ with $y$ in both layers of fluid

$($b$)$ The variation of ${}_m$ with $y$ in both layers

$($c$)$ The value of $y$ at which $v_x$ has its maximum value in both layers

The value of $\frac{P}{L}$ is the same in both layers.