ME 3720
HOMEWORK SET1
DUE: 09/15/10
1.
Derive dimensions of the following quantities in
MLT
and
FLT
systems and mention
their
SI units
.
i.
Mass flow rate, Volume flow rate, Surface Tension, Torque, Pressure
ii.
Dynamics Viscosity, Kinematic viscosity, Gas constant (R), Kinetic energy
(
mv
2
/2
), Work (force
x
displacement)
2.
Show that
i.
Momentum
(mass
x
velocity) is dimensionally equivalent to
impulse
(force
x
time).
ii.
Power
(work done per unit time) is dimensionally equivalent to
velocity times a
force
.
iii.
Power
is dimensionally equivalent to
rate of change of energy per unit time
.
3.
Air at 15
°
C forms a boundary layer near a solid wall. The velocity profile in the
boundary layer is approximated by a sine wave:
δ
π
=
2
y
sin
U
u
max
where y is the distance from the wall,
δ
= 6mm is the local boundary layer
thickness, and U
max
= 10 m/s is the free stream velocity. Calculate the
shear stress
(N/m
2
)
in the fluid, at the following ylocations:
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 Fall '08
 CUI
 Fluid Dynamics, Force, Shear Stress, Fundamental physics concepts, free stream velocity

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