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47.
(a) We use the Bernoulli equation:
p
1
+
1
2
ρv
2
1
+
ρgh
1
=
p
2
+
1
2
ρv
2
2
+
ρgh
2
,whe
re
h
1
is the height of
the water in the tank,
p
1
is the pressure there, and
v
1
is the speed of the water there;
h
2
is the
altitude of the hole,
p
2
is the pressure there, and
v
2
is the speed of the water there.
ρ
is the density
of water. The pressure at the top of the tank and at the hole is atmospheric, so
p
1
=
p
2
.S
incethe
tank is large we may neglect the water speed at the top; it is much smaller than the speed at the
hole. The Bernoulli equation then becomes
ρgh
1
=
1
2
ρv
2
2
+
ρgh
2
and
v
2
=
p
2
g
(
h
1
−
h
2
)=
p
2(9
.
8m
/
s
2
)(0
.
30 m) = 2
.
42 m
/
s
.
The ﬂow rate is
A
2
v
2
=(6
.
5
×
10
−
4
m
2
)(2
.
42 m
/
s) = 1
.
6
×
10
−
3
m
3
/
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 Fall '08
 SPRUNGER
 Physics

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