EGM 6812 Fluid Mechanics 1 - Fall 2010
5
th
Homework
Problem 1
Given:
For high-speed, oscillatory, compressible flow past a finite length cylinder, the drag
force,
D
F
, is known to be a function of cylinder diameter,
D
, cylinder length,
L
,
cylinder roughness,
e
, free stream flow velocity,
V
, fluid density,
the fluid
speed of sound,
c
, fluid viscosity
, and the cylinder vortex shedding frequency,
.
The functional form of the drag is
(
,
,
)
DD
FF
D
L
e
V
c
Find:
a)
Use dimensional analysis to determine the relevant non-dimensional
-groups that
will isolate the effects of drag forces, unsteady inertial forces, viscous forces,
cylinder roughness, cylinder length, and compressibility in this flow.
Problem 2:
Given:
In fully developed turbulent pipe flow, the pressure drop,
P
, is known to be a
function of pipe diameter,
D
, pipe length,
L
, pipe roughness,
e
, average flow
velocity,
V
, fluid density,
, and the fluid viscosity
.
The functional form of the pressure drop is
P=
P(D
,
L
,
e
,
V
,
,
Find:
a)
Use dimensional analysis to determine the relevant non-dimensional
-groups that
will isolate the effects of pressure-drop, viscous forces, pipe roughness, and pipe
length in this flow.
,,,
Vc
D
Le