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1) a) [3 marks]
A tank in the form of a right circular cylinder having its axis vertical and having
cross-sectional area
A
1
has a contoured orifice of exit area
A
2
in its side near the bottom.
As
shown in the diagram, the tank is closed at the top, except that a large pipe having cross-
sectional area
A
3
extends vertically downward into the tank interior in such a way that it admits
atmospheric air at a height
H
above the orifice axis.
If the tank is filled with water to a height
h
above the pipe exit, assuming frictionless flow, calculate the volume flux out of the orifice.
b) [3 marks]
A clown is riding in an elevator, holding a large helium-filled balloon on the end of
a string.
The cable to the elevator snaps, allowing th elevator to fall freely.
Due to her surprise,
the clown lets go of the balloon string at exactly the instant the elevator cable breaks.
According to the clown, what happens to the balloon?
Explain.
c) [5 marks]
The pressure drop,
)
p
, for steady, incompressible viscous flow through a straight
horizontal pipe depends on the pipe length,
l
, the average velocity,
V
, the fluid viscosity,
:
, the
pipe diameter,
D
, the fluid density,
D
, and the average “roughness” height,
e
.
Using
,
V
and
D
as reference variables, determine a set of dimensionless groups that can be used to correlate
data.