Quiz1A
DL Sec
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1.
Consider two pipes shown in the diagrams below. For Pipe 1, the water enters from the left end ( labeled
a
on
the diagram) at a speed of
6 m/s
, and flows through a point
b
and to the rest of the fluid circuit (not shown).
Similarly for Pipe 2, the water enters from the left end ( labeled
c
on the diagram) at a speed of
6 m/s
, and flows
through a point
d
and to the rest of the fluid circuit (not shown). You can assume that the fatter sections of both
pipes have no dissipation, however, narrower sections have significant resistances given by
R
b
(for Pipe 1) and
R
d
(for Pipe 2).We know the pressures at point
a
and
c
are equal and given by
1.075 x 10
5
Pascals
. The areas of
the pipes are given on the diagram.
Pipe 1
Pipe 2
R
b
A
b
= 50 cm
2
v
a
= 6m/s
a
b
A
a
=100 cm
2
d
A
d
= 25 cm
2
v
c
= 6m/s
c
A
c
= 100 cm
2
R
d
(Note R
d
> R
b
)
(a) Current conservation (applied to Pipe 1) tells you that
I
a
= I
b
(
I
a
= A
a
v
a
: current that flows through point
a
).
(i)
Find the fluid velocity
v
b
at point
b
.
I
a
= A
a
v
a
= A
b
v
b
=
I
b
(100 cm
2
)(6 m/s) = (50 cm
2
)v
b
v
b
= (100 cm
2
)(6 m/s)/(50 cm
2
) = 12 m/s
(ii)
Apply current conservation to Pipe 2 and find
v
d
at point
d
.
I
c
=
A
c
v
c
= A
d
v
d
=
I
d
(100 cm
2
)(6 m/s) = (25 cm
2
)v
d
v
d
= (100 cm
2
)(6 m/s)/(25 cm
2
) = 24 m/s
I
10.0
Used current conservation correctly to obtain v
b
and v
d
A
9.5
Minor math error causing the wrong answer but otherwise correct application
V
9.0
Thought that the area given was either radius or diameter
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 Spring '08
 Taylor
 Energy, Kinetic Energy, pipe, Energy density

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