ME19a.
SOLUTIONS.
Nov. 24, 2009. Due Dec. 4
PROBLEM 30 (Value 4 times the regular homework problems.)
Obtain a numerical solution to the planar, potential ow around a bend using the grid sketched below.
I = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
J=1
B
2
=0
3
ME19a.
SOLUTIONS.
Nov. 17, 2009. Due Nov. 24
PROBLEM 25
A two-dimensional potential (or free) vortex is located near an innite wall at a distance h from the wall:
U, p
h
Wall
The velocity and pressure of the ow far from the vortex are U and p respectively
ME19a.
SOLUTIONS.
Nov. 10, 2009. Due Nov. 17
PROBLEM 21
Water is sloshing back and forth between two innite vertical walls separated by a distance L:
y
Surface
x
h(x,t)
Water
Tank
L
The ow is assumed to be planar, incompressible, inviscid potential ow. Th
ME19a.
SOLUTIONS.
Nov. 3, 2009. Due Nov. 10
PROBLEM 17
A manufacturer advertises a line of centrifugal pumps of various sizes given by the radius of the impeller (the
rotating part) denoted by R. These can be run by a motor at any rotating speed, N (in ra
ME19a.
SOLUTIONS.
Oct. 20, 2009. Due Oct. 29
PROBLEM 13
The velocity, u, in the x direction for a planar incompressible shear ow near a wall as shown in the following
sketch,
y
Velocity
Profile
u(x,y)
x
and is given by the expression
u=U
2y
y2
22
ax a x
ME19a.
SOLUTIONS.
Oct. 13, 2009. Due Oct. 20
PROBLEM 9
Consider the ow of a uid in which the uid elements are traveling with velocity, u, in the x direction (this is
the only non-zero velocity of the uid which it is necessary to consider in this problem).
ME19a.
SOLUTIONS.
Oct. 6, 2009. Due Oct. 13
PROBLEM 5
The L-shaped gate shown in the gure can rotate about the hinge. As the water level rises the gate will
automatically open when the water level rises to a certain height, h. If the length of the lower a
ME19a.
SOLUTIONS.
Set 1. Due Oct. 6
PROBLEM 1
A shaft which is 2 cm in diameter and 20 cm long is concentrically located in a journal of the same length
and 2.02 cm in diameter. The gap between the shaft and the journal is lled with oil whose dynamic visc