Chapter14 PDF
Chapter14 PDF
Chapter14 PDF
CHAPTER
Fluids
14
Fluids at rest – pressure vs. depth
Pascal’s principle
Archimedes’s principle – Buoynat forces
Fluids in motion: Continuity & Bernoulli equations
1. How deep into a lake would you have to dive so that the increase in pressure you experience is one
atmosphere? (The density of water = 1000 kg/m3) (Ans: 10.2 m)
2. The open vertical tube in figure 1 contains two liquids of densities ρ1 = 1000 kg/m3 and ρ2 = 800 kg/m3,
which do not mix. Find the gauge pressure (pressure due to the liquids only) at the bottom of the tube.
(Ans: 9000 Pa)
3. The density of oil is 0.8 g/cm3. What is the height h of the column of oil shown in figure 2? (Ans: 10 cm)
4. A uniform U-tube is partially filled with water. Oil, of density 0.75 g/cm3, is poured into the left arm until
the water level in the right arm rises 3 cm (see figure 3). What is the length L of the oil column? (Ans: 8 cm)
5. An aluminum ball of volume 4.0 cm3 is dropped in water. Assume the density of water to be 1.0 g/cm3 and
the density of aluminum to be 2.7 g/cm3. Find the acceleration with which the ball sinks in the water (ignore
viscosity). (Ans: 6.2 m/s2)
6. Figure 5 shows a U-tube with cross-sectional area A and partially filled with oil of density ρ. A solid
cylinder, which fits the tube tightly but can slide without friction, is placed in the right arm. The system is in
equilibrium. What is the weight of the cylinder? (Ans: ALρg)
7. A pipe 16 cm in diameter is used to fill a tank of volume 5000 liters in 5 minutes. What is the speed at
which the water leaves the pipe? (Ans: 50 m/min)
8. A piston of radius R1 = 5.0 cm is used in a hydraulic press to exert a force F1 on the enclosed liquid to raise
a car of weight F2 = 13,500 N (see figure 7). If the radius of the larger piston is R2 = 15 cm, find F1.
(Ans: 1.5×103 N)
9. A block of wood floats in water with two-third of its volume submerged. Find the density of the wood.
(Ans: 667 kg/m3)
10. Water is pumped out of a swimming pool at a speed of 5.0 m/s through a uniform hose of radius 1.0 cm.
Find the mass of water pumped out of the pool in one minute. (Ans: 94 kg)
11. The dimensions of a boat (ρboat = 150 kg/m3) are 3.00 m × 3.00 m × 1.00 m. What maximum load can it
carry in sea water (ρsea water = 1020 kg/m3) without sinking? (Ans: 7830 kg)
12. A solid sphere of mass 5.0 kg is floating in water with half of its volume submerged. The density of water
is 1000 kg/m3. What is the buoyant force on the sphere? (Ans: 49 N)
B) v = v & P = P
1 2 1 2
E) v < v & P = P
1 2 1 2
5. Water is pumped through a hose of uniform cross-section, as shown in figure 11, from the lower level (1) to
the upper level (2). Which of the following expresses the correct relationship between velocity and pressure at
the two levels?
A. v1 = v2 and p2 < p1
B. v1 = v2 and p2 = p1
C. v1 < v2 and p2 < p1
D. v1 = v2 and p2 > p1
E. v1 > v2 and p2 > p1
10. Figure 19 shows a pipe of uniform cross section in which water is flowing. The directions of flow and the
volume flow rates (in cm3/s) are shown for various portions of the pipe. The direction of flow and the volume
flow rate in the portion marked A are:
A. ↓ and 15 cm3/s
B. ↑ and 11 cm3/s
C. ↓ and 9 cm3/s
D. ↑ and 7 cm3/s
E. ↓ and 3 cm3/s
B. F > F = F
a b c
C. F = F = F
a b c
D. F < F < F
b a c
E. F = F > F
c b a
14. Water pours into a very large open tank at a volume flow rate of Q (figure 32). The tank has an opening at
the bottom. The area of this opening for the water level in the tank to be maintained at a fixed level H is:
15. A U-tube has dissimilar arms, one having twice the diameter of the other (see figure 33. It contains an
incompressible fluid, and is fitted with a sliding piston in each arm, with each piston in contact with the fluid.
When the piston in the narrow arm is pushed down a distance d, the piston in the wide arm rises a distance:
A) d/4
B) d
C) 2d
D) d/2
E) 4d
Figure 27 Figure 28
Figure 29 Figure 30