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14
Fluid Mechanics
CHAPTER OUTLINE
14.1
14.2
14.3
14.4
14.5
14.6
14.7

Pressure
Variation of Pressure with Depth
Pressure Measurements
Buoyant Forces and Archimedes’s
Principle
Fluid Dynamics
Bernoulli’s Equation
Other Applications of Fluid Dynamics

ANSWERS TO QUESTIONS
*Q14.1 Answer (c). Both must be built the same. The force on
the back of each dam is the average pressureof the water
times the area of the dam. If both reservoirs are equally
deep, the force is the same.

FIG. Q14.1

Q14.2

The weight depends upon the total volume of water in the glass. The pressure at the bottom
depends only on the depth. With a cylindrical glass, the water pushes only horizontally on the
side walls and does not contribute to an extra downward force above that felt bythe base. On
the other hand, if the glass is wide at the top with a conical shape, the water pushes outward and
downward on each bit of side wall. The downward components add up to an extra downward
force, more than that exerted on the small base area.

Q14.3

The air in your lungs, the blood in your arteries and veins, and the protoplasm in each cell exert
nearly the same pressure, so thatthe wall of your chest can be in equilibrium.

Q14.4

Yes. The propulsive force of the f ish on the water causes the scale reading to f luctuate. Its average value will still be equal to the total weight of bucket, water, and f ish.

Q14.5

Clap your shoe or wallet over the hole, or a seat cushion, or your hand. Anything that can sustain
a force on the order of 100 N is strong enough tocover the hole and greatly slow down the escape
of the cabin air. You need not worry about the air rushing out instantly, or about your body being
“sucked” through the hole, or about your blood boiling or your body exploding. If the cabin pressure drops a lot, your ears will pop and the saliva in your mouth may boil—at body temperature—
but you will still have a couple of minutes to plug thehole and put on your emergency oxygen
mask. Passengers who have been drinking carbonated beverages may f ind that the carbon dioxide
suddenly comes out of solution in their stomachs, distending their vests, making them belch, and
all but frothing from their ears; so you might warn them of this effect.

Q14.6

The boat f loats higher in the ocean than in the inland lake. According toArchimedes’s principle,
the magnitude of buoyant force on the ship is equal to the weight of the water displaced by the
ship. Because the density of salty ocean water is greater than fresh lake water, less ocean water
needs to be displaced to enable the ship to f loat.
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*Q14.7 Answer (b). The apple does not changevolume appreciably in a dunking bucket, and the water
also keeps constant density. Then the buoyant force is constant at all depths.
Q14.8

The horizontal force exerted by the outside f luid, on an area element of the object’s side wall, has
equal magnitude and opposite direction to the horizontal force the f luid exerts on another element
diametrically opposite the f irst.

Q14.9

No.The somewhat lighter barge will f loat higher in the water.

Q14.10 The metal is more dense than water. If the metal is sufficiently thin, it can float like a ship, with the
lip of the dish above the water line. Most of the volume below the water line is f illed with air.
The mass of the dish divided by the volume of the part below the water line is just equal to the
density of water. Placing abar of soap into this space to replace the air raises the average density
of the compound object and the density can become greater than that of water. The dish sinks
with its cargo.
*Q14.11 Answer (c). The water keeps nearly constant density as it increases in pressure with depth. The
beach ball is compressed to smaller volume as you take it deeper, so the buoyant force decreases....