MECHANICS (SSCP 1143/SSCP 1103)
TUTORIAL 9: FLUID MECHANICS
Answer 6 questions only from all the given questions below.
1)
Figure 1 (a)
a) Figure 1 (a) shows three containers filled to the same height with the same fluid. Briefly
explain with the reason in which container is the pressure at the bottom greatest?
(Answer: All three containers have the same pressure at the bottom, any necessary explanation
related with height, h can be accepted)
Figure 1 (b)
b) Two liquids, 1 and 2, are in equilibrium in a U-tube that is open at both ends, as in the
drawing. The liquids do not mix, and liquid 1 rests on top of liquid 2. Explain how is the density
ρ1 of liquid 1 related to the density ρ2 of liquid 2? (Answer: ρ1 is less than ρ2. any necessary
explanation related with height, h can be accepted)
2) An antifreeze solution is made by mixing ethylene glycol (ρ = 1116 kg/m3) with water.
Suppose that the specific gravity of such a solution is 1.0730 and density of water is 1.000 x
10 3 kg/m3. Assuming that the total volume of the solution is the sum of its parts, determine the
volume percentage of ethylene glycol in the solution.
(Answer: 63 %)
3)
Figure 2
A water tower is a familiar sight in many towns. The purpose of such a tower is to provide
storage capacity and to provide sufficient pressure in the pipes that deliver the water to
customers. The drawing shows a spherical reservoir that contains 5.25 x 10 5 kg of water when
full. The reservoir is vented to the atmosphere at the top. Ignore the diameter of the delivery
pipes. For a full reservoir, find the gauge pressure that the water has at the faucet in :
(a) house A and, (Answer: 2.45 x 10 5 Pa)
(b) house B (Answer: 1.73 x 10 5 Pa)
4) The atmospheric pressure above a swimming pool changes from 755 to 765 mm of mercury.
The bottom of the pool is a rectangle (12 m x 24 m). By how much does the force on the bottom
of the pool increase?
(Answer: 3.8 x 10 5 N)
5) A barber’s chair with a person in it weighs 2100 N. The output plunger of a hydraulic system
begins to lift the chair when the barber’s foot applies a force of 55 N to the input piston. Neglect
any height difference between the plunger and the piston. What is the ratio of the radius of the
plunger to the radius of the piston?
(Answer: 6.2)
6) An 81-kg person puts on a life jacket, jumps into the water, and floats. The jacket has a
volume of 3.1 x 10 -2 m3 and is completely submerged under the water. The volume of the
person’s body that is under water is 6.2 x 10 -2 m3. What is the density of the life jacket?
(Answer: 390 kg/m 3)
7)
Figure 3
A solid cylinder (radius = 0.150 m, height = 0.120 m) has a mass of 7.00 kg. This cylinder is
floating in water. Then oil (ρ = 725 kg/m3) is poured on top of the water until the situation
shown in the drawing results. How much of the height of the cylinder is in the oil?
(Answer: 7.6 x 10 -2 m)
8) A room has a volume of 120 m 3. An air-conditioning system is to replace the air in this room
every twenty minutes, using ducts that have a square cross section. Assuming that air can be
treated as an incompressible fluid, find the length of a side of the square if the air speed within
the ducts is:
(a) 3.0 m/s and, (Answer: 0.18 m)
(b) 5.0 m/s (Answer: 0.14 m)
9) Water flowing out of a horizontal pipe emerges through a nozzle. The radius of the pipe is
1.9 cm, and the radius of the nozzle is 0.48 cm. The speed of the water in the pipe is 0.62 m/s.
Treat the water as an ideal fluid, and determine the absolute pressure of the water in the pipe.
(Answer: 1.48 x 10 5 Pa)
10)
Figure 4
A small crack occurs at the base of a 15.0-m-high dam. The effective crack area through which
water leaves is 1.30 x 10 -3 m2.
(a) Ignoring viscous losses, what is the speed of water flowing through the crack?
(Answer: 17.1 m/s)
(b) How many cubic meters of water per second leave the dam? (Answer: 2.22 10 -2 m3/s)
