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
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