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407
Fluid Mechanics
CHAPTER OUTLINE
15.1
Pressure
15.2
Variation of Pressure with
Depth
15.3
Pressure Measurements
15.4
Buoyant Forces and
Archimedes’s Principle
15.5
Fluid Dynamics
15.6
Streamlines and the
Continuity Equation for Fluids
15.7
Bernoulli’s Equation
15.8
Other Applications of Fluid
Dynamics
15.9
Context Connection
A
Near Miss Even Before
Leaving Southampton
ANSWERS TO QUESTIONS
Q15.1
The weight depends upon the total volume of glass. The pressure
depends only on the depth.
Q15.2
Both must be built the same. The force on the back of each dam is
the average pressure of the water times the area of the dam. If both
reservoirs are equally deep, the force is the same.
FIG. Q15.2
Q15.3
If the tube were to fill up to the height of several stories of the building, the pressure at the bottom of
the depth of the tube of fluid would be very large according to Equation 15.4. This pressure is much
larger than that originally exerted by inward elastic forces of the rubber on the water. As a result,
water is pushed into the bottle from the tube. As more water is added to the tube, more water
continues to enter the bottle, stretching it thin. For a typical bottle, the pressure at the bottom of the
tube can become greater than the pressure at which the rubber material will rupture, so the bottle
will simply fill with water and expand until it bursts. Blaise Pascal splintered strong barrels by this
method.
Q15.4
In the ocean, the ship floats due to the buoyant force from
salt water
. Salt water is denser than fresh
water. As the ship is pulled up the river, the buoyant force from the fresh water in the river is not
sufficient to support the weight of the ship, and it sinks.
Q15.5
Yes. The propulsive force of the fish on the water causes the scale reading to fluctuate. Its average
value will still be equal to the total weight of bucket, water, and fish.
Q15.6
Exactly the same. Buoyancy equals density of water times volume displaced.
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Fluid Mechanics
Q15.7
The buoyant force is a conservative force. It does positive work on an object displaced upward,
negative work on an object displaced downward, and zero work on an object displaced through a
closed path. Potential energy is associated with it and it is gravitational potential energy of the
objectfluidEarth system. This system possesses extra energy when you hold a tennis ball at the
bottom of a pool of water. As the tennis ball bobs up after it is released, the ball can do work in
pushing obstacles out of the way. This work is just the work that can be done by the water sinking
down to occupy the space vacated by the ball.
Q15.8
The rapidly moving air above the ball exerts less pressure than the atmospheric pressure below the
ball. This can give substantial lift to balance the weight of the ball.
Q15.9
At lower elevation the water pressure is greater because pressure increases with increasing depth
below the water surface in the reservoir (or water tower). The penthouse apartment is not so far
below the water surface. The pressure behind a closed faucet is weaker there and the flow weaker
from an open faucet. Your fire department likely has a record of the precise elevation of every fire
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This note was uploaded on 05/30/2011 for the course PHYS 150 taught by Professor Anzmeador during the Spring '08 term at EmbryRiddle FL/AZ.
 Spring '08
 AnzMeador
 Physics, Force

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