MECH4620 2024_T3 TUTORIAL 1 PROBLEMS
(DUE 5 PM FRIDAY WEEK 3)
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THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MECHANICAL AND MANUFACTURING ENGINEERING
MECH4620 COMPUTATIONAL FLUID DYNAMICS
Tutorial Problems (T1)
(Due 5 pm, Friday Week 3)
1. Consider a parallel plate flow problem where the mass fluxes are acting on an
infinitesimal control volume along the Cartesian coordinate system.
Figure 1. Incoming and outgoing mass fluxes over a infinitely small control volume.
(a) According to the control volume approach as described in Fig. 1, derive the mass
conservation equation.
Figure 2. Normal and shear stresses over an infinitely small control volume along the x-direction.
MECH4620 2024_T3 TUTORIAL 1 PROBLEMS
(DUE 5 PM FRIDAY WEEK 3)
2 | P a g e
(b) Provide now that the flow is incompressible, what can be concluded based on the
mass conservation equation in (a).
(c) According to the control volume approach as described in Fig. 2, derive the x- momentum equation and deduce the y-, z-momentum equations by similarity, given
that the fluid is Newtonian in the absence of body forces with constant fluid
properties. The following expressions for the normal and tangential viscous stresses
are provided:
2 = − + + + + xx u u v w p x x y z ; = + yx u v y x
and = + zx u w z x
2. For parallel plate flows, the problem is often solved in two dimensions due to flow
similarities.
(a) Based on the three-dimensional form of the mass conservation and x-, y-momentum
equations with constant fluid properties, reduce them into two-dimensional
expressions. Define each term in the x-momentum equation.
(b) For laminar flows, the outlet velocity profile for a two-dimensional parallel plate
channel flow is often approximated by the channel width, fluid viscosity and
pressure gradient.
Find the fully-developed outlet flow profile expression of the channel with the
following boundary conditions:
0 ( ) 2 H u at y no slip= =
0 0 ( ) u at y symmetry y = =
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