Question $3$

Illustrate and describe $($without deriving the equations themselves, but while still referencing them$)$ the principles of operation of:

$($i$)$ Slipper bearings

$($ii$)$ Rayleigh step bearings

Fluid is flowing in a laminar regime between two parallel plates which are $2m$ in length $)=(2m$ and which have a clearance of $6mm$ between them $)=(6mm.$ The bottom plate is stationary while the top plate is moving in the opposite direction to the bulk fluid flow. A pressure difference of $0\mathrm{.}5$ barg acts as the driving force for the fluid flow $($in the positive $x-$direction as shown below$).$

$($iii$)$ Develop a symbolic expression for the velocity profile between the two plates.

$($iv$)$ Determine the maximum velocity which the top plate may have in order to retain a volumetric flowrate per unit plate width $(\frac{Q}{b})$ of the bulk fluid equal to $0\mathrm{.}00125\frac{m^3}{s}.m$

$($v$)$ If a uniform element of tracer is injected between the two plates at a position $x=1($spanning the full gap between the plates as shown below$),$ determine the time for the first tracer particle to exit the plates at $x=2.$

$($vi$)$ Discuss briefly the residence time distribution of the tracer between the plates.

Data

Fluid Viscosity

$0\mathrm{.}15$ Pa$.$s