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Ph 111.01
December 1, 2008
PS 13a (33)
Problem 1 = Walker P. 1541.
To water the yard,
you use a hose with a diameter of
3.9
cm. Water
flows from the hose with a speed of
1.2
m/s. If you
partially block the end of the hose so the effective
diameter is now 0.55 cm, with what speed does
water spray from the hose?
m/s
d
1
d
2
v
1
v
2
A
1
A
2
Solution.
The equation of continuity, expressing the fact that the flow rate has to be the same
in both sections of the hose, says
11
2 2
Av
=
Using
2
4
A
d
π
=
and solving for
v
2
gives
()
( )
2
21
1
2
22
3.9 cm
1.2 m/s
60.3 m/s
0.55 cm
Ad
vv
v
===
=
Problem 2 = Walker P. 1543.
To fill a child's
inflatable wading pool you use a garden hose with
a diameter of 2.8 cm. Water flows from this hose
with a speed of 1.1 m/s. How long will it take to
fill the pool to a depth of
21
cm if it is circular and
has a diameter of
2.5
m?
min
d
v
A
D
Solution.
The flow rate from the hose is
h
V
2
4
d
FA
v
v
==
and the flow rate times the unknown time has
to equal the volume of the wading pool:
44
Dd
Vh
F
t
ππ
=
v
t
We set the second and fourth terms equal and cancel the factor of
4
:
Dh dv
t
=
and solve for
t
:
2
2
2.5 m
0.21 m
1 min
1521 s
25.4 min
0.028 m
1.1 m/s
60 s
Dh
t
dv
⎛⎞
⎛
⎞
=
=
⎜⎟
⎜
⎟
⎝⎠
⎝
⎠
Problem 3 = Walker P. 1553.
A garden hose is attached to a water faucet on one end and a spray
nozzle on the other end. The water faucet is turned on, but the nozzle is turned off so that no water
flows through the hose. The hose lies horizontally on the ground, and a stream of water sprays
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0.83
m.
What is the pressure inside the hose?
kPa
Solution.
We are going to apply
Bernoulli’s
law, which sets equal a total energy density,
including pressure, at different points along a
streamline of flow.
In the diagram we show a
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This note was uploaded on 05/13/2010 for the course PHYSICS 111 taught by Professor Staff during the Fall '08 term at S.F. State.
 Fall '08
 Staff

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