3-Problems.pdf

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Problems

*A Preview Question ( 䉳䉴 ) can be assigned prior to inclass coverage of a topic.

Pressure and Related Concepts

3.1 *

a. If pressure is 8 inches of water (vacuum), what is gage pressure in kPa?

b. If the pressure is 120 kPa abs, what is the gage pressure in psi?

c. If gage pressure is 0.5 bar, what is absolute pressure in psi?

d. If a person's blood pressure is 120 mm Hg, what is their blood pressure in kPa abs?

3.2 * A 100 mm diameter sphere contains an ideal gas at 20°C. Apply the grid method (p. 9) to calculate

the density in units of kg/m 3 .

a. Gas is helium. Gage pressure is 20 in H 2 O.

b. Gas is methane. Vacuum pressure is 3 psi.

Answer:

a. ρ = 0.175 kg/m 3 ,

b. ρ = 0.531 kg/m 3

3.3 * Using Section 3.1 and other resources, answer the following questions. Strive for depth, clarity,

and accuracy while also combining sketches, words, and equations in ways that enhance the effectiveness of

your communication.

a. What are five important facts that engineers need to know about pressure?

b. What are five common instances in which people use gage pressure?

c. What are the most common units for pressure?

d. Why is pressure defined using a derivative?

e. How is pressure similar to shear stress? How does pressure differ from shear stress?

3.4 The Crosby gage tester shown in the figure is used to calibrate or to test pressure gages. When the weights

and the piston together weigh 140 N, the gage being tested indicates 200 kPa. If the piston diameter is

30 mm, what percentage of error exists in the gage?

PROBLEM 3.4

Answer:

% error = 1.01%

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Apply the grid method (p. 9) to each situation.

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3.5 As shown, a mouse can use the mechanical advantage provided by a hydraulic machine to lift up an

elephant.

a. Derive an algebraic equation that gives the mechanical advantge of the hydraulic machine shown.

Assume the pistons are frictionless and massless.

b. A mouse can have a mass of 25 g and an elephant a mass of 7500 kg. Determine a value of D 1 and D 2

so that the mouse can support the elephant.

PROBLEM 3.5

3.6 Find a parked automobile for which you have information on tire pressure and weight. Measure the area of

tire contact with the pavement. Next, using the weight information and tire pressure, use engineering

principles to calculate the contact area. Compare your measurement with your calculation and discuss.

Hydrostatic Equation

3.7 *

Apply the grid method (p. 9) with the hydrostatic equation ( p = γ z ) to each of the following

cases.

a. Predict the pressure change p in kPa for an elevation change z of 10 ft in a fluid with a density of

90 lbm/ft 3 .

b. Predict the pressure change in psf for a fluid with S = 0.8 and an elevation change of 22 m.

c. Predict pressure change in inches of water for a fluid with a density of 1.2 kg/m 3 and an elevation

change of 1000 ft.

d. Predict the elevation change in millimeters for a fluid with S = 13 that corresponds to a change in

pressure of 1/6 atm.

3.8 * Using Section 3.2 and other resources, answer the following questions. Strive for depth, clarity,

and accuracy while also combining sketches, words, and equations in ways that enhance the effectiveness of

your communication.

a. What does hydrostatic mean? How do engineers identify whether a fluid is hydrostatic?

b. What are the common forms on the hydrostatic equation? Are the forms equivalent or are they

different?

c. What is a datum? How do engineers establish a datum?

d. What are the main ideas of Eq. (3.5)? That is, what is the meaning of this equation?

e. What assumptions need to be satisfied to apply the hydrostatic equation?

3.9 Apply the grid method (p. 11) to each situation.

a. What is the change in air pressure in pascals between the floor and the ceiling of a room with walls

that are 8 ft tall.

b. A diver in the ocean (S = 1.03) records a pressure of 2 atm on her depth gage. How deep is she?

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c. A hiker starts a hike at an elevation where the air pressure is 940 mbar, and he ascends 1200 ft to a

mountain summit. Assuming the density of air is constant, what is the pressure in mbar at the

summit?

d. Lake Pend Oreille, in northern Idaho, is one of the deepest lakes in the world, with a depth of 350 m

in some locations. This lake is used as a test facility for submarines. What is the maximum pressure

that a submarine could experience in this lake?

e. A 60 m tall standpipe (a standpipe is vertical pipe that is filled with water and open to the

atmosphere) is used to supply water for fire fighting. What is the maximum pressure in the standpipe?

3.10 As shown, an air space above a long tube is pressurized to 50 kPa vacuum. Water (15°C) from a reservoir

fills the tube to a height h . If the pressure in the air space is changed to 25 kPa vacuum, will h increase or

descrease and by how much? Assume atmospheric pressure is 100 kPa.

PROBLEM 3.10

Answer:

The height decreases by 2.55 m.

3.11 For the closed tank with Bourdontube gages tapped into it, what is the specific gravity of the oil and the

pressure reading on gage C ?

PROBLEM 3.11

3.12 This manometer contains water at room temperature. The glass tube on the left has an inside diameter of

1 mm (d = 1.0 mm). The glass tube on the right is three times as large. For these conditions, the water

surface level in the left tube will be (a) higher than the water surface level in the right tube, (b) equal to the

water surface level in the right tube, or (c) less than the water surface level in the right tube. State your

main reason or assumption for making your choice.

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PROBLEM 3.12

Answer:

Selection (a) is correct.

3.13 If a 200 N force F 1 is applied to the piston with the 4 cm diameter, what is the magnitude of the force F 2

that can be resisted by the piston with the 10 cm diameter? Neglect the weights of the pistons.

PROBLEM 3.13

3.14 Some skin divers go as deep as 50 m. What is the gage pressure at this depth in fresh water, and what is

the ratio of the absolute pressure at this depth to normal atmospheric pressure? Assume T = 20°C.

Answer:

p = 490, p 50 / p atm = 5.83

3.15 Water occupies the bottom 1.0 m of a cylindrical tank. On top of the water is 0.75 m of kerosene, which is

open to the atmosphere. If the temperature is 20°C, what is the gage pressure at the bottom of the tank?

3.16 An engineer is designing a hydraulic lift with a capacity of 10 tons. The moving parts of this lift weigh

1000 lbf. The lift should raise the load to a height of 6 ft in 20 seconds. This will be accomplished with a

hydraulic pump that delivers fluid to a cylinder. Hydraulic cylinders with a stroke of 72 inches are

available with bore sizes from 2 to 8 inches. Hydraulic piston pumps with an operating pressure range

from 200 to 3000 psig are available with pumping capacities of 5, 10, and 15 gallons per minute. Select a

hydraulic pump size and a hydraulic cylinder size that can be used for this application.

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PROBLEM 3.16

3.17 A tank with an attached manometer contains water at 20°C. The atmospheric pressure is 100 kPa. There is

a stopcock located 1 m from the surface of the water in the manometer. The stopcock is closed, trapping

the air in the manometer, and water is added to the tank to the level of the stopcock. Find the increase in

elevation of the water in the manometer assuming the air in the manometer is compressed isothermally.

PROBLEM 3.17

3.18 A tank is fitted with a manometer on the side, as shown. The liquid in the bottom of the tank and in the

manometer has a specific gravity (S) of 3.0. The depth of this bottom liquid is 20 cm. A 15 cm layer of

water lies on top of the bottom liquid. Find the position of the liquid surface in the manometer.

PROBLEM 3.18

Answer:

h = 5.00 cm

3.19 As shown, a load acts on a piston of diameter D 1 . The piston rides on a reservoir of oil of depth h 1 and

specific gravity S. The reservoir is connected to a round tube of diameter D 2 and oil rises in the tube to

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