Simplifying assumptions used in developing solutions should be
stated. In case of any uncertainty about the
meaning of the question, the assumed meaning should be clearly
stated.
It is an open-book examination and therefore you are free to
refer to any material.
(1) Navier-Stokes equations in dimensional form:
Write the NS equations in [25 marks]:
a) In vector notations b) In Einstein summation notation c) In
cylindrical coordinates d) Derive the NS equations in
non-dimensional form (Continutiy, Momentum and
Energy equations)
(2) A viscous liquid of constant density and viscosity falls due
to gravity between two parallel plates a distance 2h apart, as in
the figure. The flow is fully developed, that is,
w w(x) only. There are no pressure gradients, only gravity. Set
up and solve the Navier-Stokes equation for the velocity profile
w(x). [25 marks]
(3) A constant-thickness film of viscous liquid flows in laminar
motion down a plate
inclined at angle . The velocity profile is: [25 marks]
u = Cy (2h-y) v = w = 0
Find the constant C in terms of the specific weight and
viscosity and the angle . Find the volume flux Q per unit width in
terms of these parameters.
(4) Show that the linear Couette flow between plates as in the
figure has a stream function, but no velocity potential. Why is so?
[25 marks]
