ME19b.
MIDTERM REVIEW.
Feb. 7, 2010.
EXAMPLE PROBLEM 1
Write down the general forms of the conservation equations in integral and dierential form, using vector notation.
Do not make any assumptions about the uid or the ow (i.e., do not assume the uid is N
ME19b.
MID. REVIEW SOLUTIONS.
Feb. 7, 2010.
EXAMPLE PROBLEM 1
Write down the general forms of the conservation equations in integral and dierential form, using vector notation.
Do not make any assumptions about the uid or the ow (i.e., do not assume the u
ME19b.
SOLUTIONS.
Feb. 25, 2010. Due Mar. 4
PROBLEM B23
In 1844, to commemorate a visit by the Tsar of Russia, the Duke of Devonshire, the greatest landowner in
Britain, wished to construct the tallest fountain ever built in the grounds of his great house
ME19b.
SOLUTIONS.
Feb. 18, 2010. Due Feb. 25
PROBLEM B18
The stability diagram for a laminar boundary layer on a at plate with zero pressure gradient (Blasius problem)
is given below:
200
160
2f
U2
6
Stable
120
x 10
Unstable
80
40
0
Stable
800
1600
2400
R
ME19b.
SOLUTIONS.
Feb. 11, 2010. Due Feb. 18
PROBLEM B14
Consider the long thin racing boats used in competitive rowing events. Assume that the major component of
resistance to motion is the skin friction drag on the hull of the boat. Estimate this drag f
ME19b.
SOLUTIONS.
Jan. 28, 2010. Due Feb. 4
PROBLEM B12
Consider the fully developed laminar pipe ow of an incompressible, non-Newtonian uid :
Flow
u(r)
r
R
x
This uid is such that the normal stress in the x direction is equal to p where p is the pressure
ME19b.
SOLUTIONS.
Jan. 21, 2010. Due Jan. 28
PROBLEM B8
Consider the laminar, viscous, planar ow of an incompressible uid contained between two parallel plates
a distance H apart. The coordinates x and y are measured parallel to and perpendicular to these
ME19b.
SOLUTIONS.
Jan. 14, 2010. Due Jan. 21
PROBLEM B5
A re nozzle is to be used at an elevation of 10 m above the level of a reservoir. The velocity of the jet is to
be 20 m/s and the ow is provided by a pump: The density of the water may be taken to be
ME19b.
SOLUTIONS.
Jan. 5, 2010. Due Jan. 14
PROBLEM B1
An incompressible, inviscid liquid ow (density, ) of depth, h1 , and velocity, V , ows under the action of gravity
through a sluice gate:
Liquid
Surface
Sluice
Gate
g
h1
F
V
h2
The depth downstream of
ME19b.
FINAL REVIEW.
Mar. 11, 2010.
EXAMPLE PROBLEM 1
A laboratory wind tunnel has a square test section with side length L. Boundary-layer velocity proles are
measured at two cross-sections and displacement thicknesses are evaluated from the measured pro
ME19b.
FINAL REVIEW SOLUTIONS.
Mar. 11, 2010.
EXAMPLE PROBLEM 1
A laboratory wind tunnel has a square test section with side length L. Boundary-layer velocity proles are
measured at two cross-sections and displacement thicknesses are evaluated from the me