Q$1$

Starting with an element of fluid of dimensions $z$ and $r,$ show the forces acting on the element for

fully developed flow. From this element write down the equation governing fluid flow. What

assumptions are made? It the pipe in question was an arterial wall what other assumptions are

made?

Q$2$

It can be shown that for fully$-$developed pipe flow $d\frac{P}{d}z$ is a constant. Derive an expression for this

constant.

Q$3$

Show that for fully developed flow the average velocity is half the maximum velocity.

Q$4$

Derive an expression for the volumetric flow rate for a circular pipe given that the flow is fully

developed. What is the shear stress at the wall?

Q$5$

A pressure drop of $7\mathrm{.}2Pa$ was measured for a $300mm$ long capillary with a diameter of $3mm$ carrying

plasma which has a viscosity of $1\mathrm{.}35{10}^{-3}P$ as$.$ Sketch the velocity profile. What is the maximum

velocity? If the fluid was non$-$Newtonian shear thinning, sketch how the velocity profile would

change qualitatively. What is the volumetric flow rate?

Q$6$

If a constriction on the capillary in Q$5$ existed in the form of a protrusion into the capillary of $1\mathrm{.}5mm$

which extended for $50mm.$ Estimate the shear stress on the cells in the constriction.