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SOLUTIONS – Ch. 14: 46
14.34.
IDENTIFY:
The volume flow rate is
Av
.
SET UP:
.
.
3
0.750 m/s
Av
=
2
/4
AD
π
=
EXECUTE:
(a)
.
23
0.750 m/s
vD
=
3
22
4(0.750 m/s )
472 m/s
(4.50 10 m)
v
−
==
×
.
(b)
must be constant, so
.
2
vD
11
2 2
=
2
2
21
1
2
(472 m/s)
52.4 m/s
3
DD
vv
⎛⎞
=
⎜⎟
⎝⎠
.
EVALUATE:
The larger the hole, the smaller the speed of the fluid as it exits.
14.41.
IDENTIFY
and
SET UP:
Apply Bernoulli’s equation to points 1 and 2
as shown in Figure 14.41. Point 1 is in the
mains and point 2 is at the maximum height
reached by the stream, so
2
0.
v
=
Figure 14.41
Solve for
1
p
and then convert this absolute pressure to gauge pressure.
EXECUTE:
111
222
pg
y
v
y
v
ρ
ρρ
++
=
Let
The mains have large diameter, so
1
0,
y
=
2
15.0 m.
y
=
1
0.
v
≈
Thus
12
2
.
p
y
=+
But
2a
,
p
p
=
so
32
5
1a
2
(1000 kg/m )(9.80 m/s )(15.0 m)
1.47 10 Pa.
pp g
y
−=
=
= ×
EVALUATE:
This is the gauge pressure at the bottom of a column of water 15.0 m high.
14.89.
IDENTIFY:
Apply Bernoulli’s equation and the equation of continuity.
SET UP:
Example 14.8 says the speed of efflux is
2
gh
, where
h
is the distance of the hole below the surface of
the fluid.
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 Fall '07
 Evrard

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