EE1427 Engineering Science – Dr. Daniel Nankoo
Tutorial 7
7. Fluids – Tutorial 7
7.1
You buy a “gold” ring at a pawn shop. The ring has a mass of 0.014 g and a volume of
0.0022 cm 3 . Is the ring solid gold?
7.2
A cube of metal has a mass of 0.347 kg and measures 3.21 cm on a side. Calculate the density
and identify the metal.
7.3
Some species of dinoflagellate (a type of unicellular plankton) can produce light as the result
of biochemical reactions within the cell. This light is an example of bioluminescence. It is found that
bioluminescence in dinoflagellates can be triggered by deformation of the cell surface with a pressure
as low as one dyne (10 −5 N) per square centimetre. What is this pressure in (a) pascals and (b)
atmospheres? (10-1Pa, 10-6 atm)
7.4
A 72-kg person sits on a 3.8-kg chair. Each leg of the chair makes contact with the floor in a
circle that is 1.3 cm in diameter. Find the pressure exerted on the floor by each leg of the chair,
assuming the weight is evenly distributed. (1.4×106 Pa)
7.5
To prevent damage to floors (and to increase friction), a walking stick will often have a rubber
tip attached to its end. If the end of the walking stick is a circle of radius 1.2 cm without the tip, and the
tip is a circle of radius 2.5 cm, by what factor does the tip reduce the pressure exerted by the walking
stick? (4.3)
7.6
Suppose that when you ride on your 7.70-kg bike the weight of you and the bike is supported
equally by the two tires. If the gauge pressure in the tires is 70.5 lb in 2 and the area of contact between
each tire and the road is 7.13 cm 2 . What is your weight? (615N)
The weight of your 1320-kg car is supported equally by its four tires, each inflated to a gauge
7.7
pressure of 35.0 lb in 2 . (a) What is the area of contact each tire makes with the road? (b) If the gauge
pressure is increased, does the area of contact increase, decrease, or stay the same? (c) What gauge
pressure is required to give an area of contact of 116 cm 2 for each tire? (0.0135m2, 2.79×105Pa)
7.8
In a classroom demonstration, the pressure inside a soft drink can is suddenly reduced to
essentially zero. Assuming the can to be a cylinder with a height of 12 cm and a diameter of 6.5 cm,
find the net inward force exerted on the vertical sides of the can due to atmospheric pressure. (2.5kN)
7.9
As a storm front moves in, you notice that the column of mercury in a barometer rises to only
736 mm. (a) What is the air pressure? (b) If the mercury in this barometer is replaced with water, to
what height does the column of water rise? Assume the same air pressure found in part (a). (97.8kPa,
9.97m)
7.10 In the hydraulic system shown in Figure 7.10, the piston on the left has a diameter of 4.5 cm
and a mass of 1.7 kg. The piston on the right has a diameter of 12 cm and a mass of 3.2 kg. If the
density of the fluid is 750 kg m 3 , what is the height difference h between the two pistons? (1.0m)
Figure 7.10
7. Fluids
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EE1427 Engineering Science – Dr. Daniel Nankoo
Tutorial 7
7.11 A circular wine barrel 75 cm in diameter will burst if the net upward force exerted on the top
of the barrel is 643 N. A tube 1.0 cm in diameter extends into the barrel through a hole in the top, as
indicated in Figure 7.11. Initially, the barrel is filled to the top and the tube is empty above that level.
What weight of water must be poured into the tube in order to burst the barrel? (0.11N)
Figure 7.11
A cylindrical container with a cross-sectional area of 65.2 cm 2 holds a fluid of density
806 kg m 3 . At the bottom of the container the pressure is 116 kPa. (a) What is the depth of the fluid?
7.12
(b) Find the pressure at the bottom of the container after an additional 2.05 × 10 −3 m 3 of this fluid is
added to the container. Assume that no fluid spills out of the container. (1.90m, 118kPa)
7.13
A submarine called the Deep View 66 is currently being developed to take 66 tourists at a time
on sightseeing trips to tropical coral reefs. According to guidelines of the American Society of
Mechanical Engineers (ASME), to be safe for human occupancy the Deep View 66 must be able to
withstand a pressure of 10.0 N per square millimetre. (a) To what depth can the Deep View 66 safely
descend in seawater? (b) If the submarine is used in freshwater instead, is its maximum safe depth
greater than, less than, or the same as in seawater? Explain. (995m)
7.14 A water storage tower is filled with fresh water to a depth of 6.4 m. What is the pressure at (a)
4.5 m and (b) 5.5 m below the surface of the water? (1.45×105Pa, 1.54×105Pa)
7.15 You step onto an elevator holding a glass of water filled to a depth of 6.5 cm. After a moment,
the elevator moves upward with constant acceleration, increasing its speed from zero to 2.2 m/s in 3.1
s. (a) During the period of acceleration, is the pressure exerted on the bottom of the glass greater than,
less than, or the same as before the elevator began to move? Explain. (b) Find the change in the
pressure exerted on the bottom of the glass as the elevator accelerates. (46Pa)
7.16 Suppose you pour water into a container until it reaches a depth of 12 cm. Next, you carefully
pour in a 7.2-cm thickness of olive oil so that it floats on top of the water. What is the pressure at the
bottom of the container? (1.03×105Pa)
7.17
As a stunt, you want to sip some water through a very long, vertical straw. (a) First, explain
why the liquid moves upward, against gravity, into your mouth when you sip. (b) What is the tallest
straw that you could, in principle, drink from in this way? (10.3m)
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EE1427 Engineering Science – Dr. Daniel Nankoo
Tutorial 7
7.18
The patient in Figure 7.18 is to receive an intravenous injection of medication. In order to
work properly, the pressure of fluid containing the medication must be 109 kPa at the injection point.
(a) If the fluid has a density of 1020 kg m 3 , find the height at which the bag of fluid must be
suspended above the patient. Assume that the pressure inside the bag is one atmosphere. (b) If a less
dense fluid is used instead, must the height of suspension be increased or decreased? Explain. (0.77m)
Figure 7.18
7.19 A cylindrical container 1.0 m tall contains mercury to a certain depth, d. The rest of the
cylinder is filled with water. If the pressure at the bottom of the cylinder is two atmospheres, what is
the depth d? (0.74m)
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