AP Free Response Question
2007 B4
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The large container shown in the cross section above is filled with a liquid of density 1.1 x 10
3
kg/m
3
. A small hole of area 2.5 x 10
-6
m
2
is opened in the side of the container a distance
h
below the liquid surface, which allows a stream of liquid to flow through the hole and into a beaker placed to the right of the container. At the same time, liquid is also added to the container at an appropriate rate so that
h
remains constant. The amount of liquid collected in the beaker in 2.0 minutes is 7.2 x 10
-4
m
3
.
(a) Calculate the volume rate of flow of liquid from the hole in m
3
/sec.
(b) Calculate the speed of the liquid as it exits from the hole.
(c) Calculate the height
h
of liquid needed above the hole to cause the speed you determined in part (b).
(d) Suppose that there is now less liquid in the container so that the height
h
is reduced to
h/2
. In relation to the container, where will the liquid hit the tabletop?
Justify your answer.
Topic Formulas
Description
Published Formula
actual pressure in a fluid
Bernoulli's Equation
buoyancy
Continuity Equation
mass density
pressure
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