Advanced Fluid Dynamics (ME335)
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School of Computing, Engineering and Mathematics
Division of Engineering and Product Design
Semester-One Examinations, January 2011
B.ENG. HONOURS DEGREE COURSE
ADVANCED FLUID DYNAMICS (ME335)
EXAMINER: PROF. S. SAZHIN
Instructions to Candidates:
 The time allowed is TWO hours
 Attempt ANY FOUR questions only
 The total number of questions is SIX
 Each question carries 25 marks
 This is a CLOSED-BOOK examination
Special Requirements:
 Formulae Sheets (Fluid Dynamics)
 Prandtl-Meyer Expansion Tables
 Tables for Oblique Shocks
January 2011
Page 1 of 5
Advanced Fluid Dynamics (ME335)
Question 1
(a) Given the two-dimensional velocity potential:
Determine the stream-function  and sketch the streamlines for the flow.
(10 marks)
(b) The incompressible inviscid flow around an infinitely long cylinder of radius a
whose axis is perpendicular to the free-stream, can be modelled by a twodimensional potential flow with the following stream-function:
where U = 2 m.s-1 and a = 5 cm.
(i)
Determine the velocity components
calculate the velocity at
and
and
, and hence or otherwise
(5 marks)
(ii) Along a streamline, Bernoulli’s equation states that:
By assuming that
as
of the cylinder is given by:
, show that the pressure on the surface
(8 marks)
(iii) Hence, or otherwise, find the maximum and minimum pressures on the
cylinder.
(2 marks)
Page 2 of 5
Advanced Fluid Dynamics (ME335)
Question 2
Oil, with a free-stream velocity of
, flows over a thin horizontal plate
wide and
long. The density of the oil is
and its kinematic viscosity
is equal to
.
(a) Determine whether or not the flow is laminar or turbulent.
(3 marks)
(b) Calculate the total double-sided resistance on the plate.
(7 marks)
(c) How will the answers to parts (a) and (b) change if the oil is replaced by water
with density equal to
and kinematic viscosity equal to
,
flowing with a free-stream velocity of
?
(5 marks)
(d) The ratio of the stream-wise velocity,
inside a boundary layer on a flat
plate to the free-stream velocity, , is given by:
where
plate.
is the boundary-layer thickness and
is a coordinate normal to the
Calculate the ratios of the displacement thickness, and the momentum thickness
to the boundary-layer thickness .
(10 marks)
Page 3 of 5
Advanced Fluid Dynamics (ME335)
Question 3
(a) Using the finite-difference approach, derive the expression for the first
derivative:
in a discretised form.
(5 marks)
(b) Using the finite-difference approach, derive the expression for the second
derivative:
in a discretised form.
(10 marks)
(c) Describe briefly the Gauss-Seidel point-by-point method.
(5 marks)
(d) Describe briefly the Gauss-Seidel line-by-line method.
(5 marks)
Question 4
Consider a plane wall 30 cm thick, one side of which is kept at T 1=300 K, while the
other is kept at T2=300 K. Find the distribution of temperature inside this wall, using
the finite-volume technique, for three computational cells. The distribution of
temperature inside the wall is controlled by the following equation:
(25 marks)
Page 4 of 5
Advanced Fluid Dynamics (ME335)
Question 5
A normal shock wave travels into stationary air with a velocity of 1400 m/s. The air is
at 17 ºC and 80 kPa. Calculate the stagnation pressure and temperature behind the
shock wave, assuming that
and
J/(kg K).
You may use the following relation, without deriving it, for the relation between
and
:
(25 marks)
Question 6
Figure Q6 below shows a two-dimensional aerofoil positioned at 4º incidence in a
flow of dry air
at a Mach number of 1.5 in an ambient static pressure of
0.8 bar.
Using shock-expansion theory, calculate the coefficient of lift of the body.
Figure Q6
(25 marks)
Page 5 of 5