1
For the two-dimensional stress field in Fig. P2.1, let xx yy σ σ = = 3000 psf 2000 psf
xy σ = 500 psf
Find the shear on plane AA cutting through at 30°.
2
For the two-dimensional stress field in Fig. P2.1, let xx yy σ σ = = 3000 psf 2000 psf
xy σ = 500 psf
Find the normal stresses on plane AA cutting through at 30°.
3
For the stress field of Fig. P2.1, change the known data to σxx = 2000 psf, σyy = 3000 psf,
and σn(AA) = 2500 psf. Compute σxy
4
For the stress field of Fig. P2.1, change the known data to σxx = 2000 psf, σyy = 3000 psf,
and σn(AA) = 2500 psf. Compute the shear stress on plane AA.
5
A vertical clean glass piezometer tube has an inside diameter of 1 mm. When a pressure is applied, water at 20°C rises into the tube to a height of 25 cm. After correcting for surface tension, estimate the applied pressure in Pa.
6
Atlanta, Georgia, has an average altitude of 1100 ft. On a U.S. standard day, pressure gage A reads 93 kPa and gage B reads 105 kPa. Express these readings in gage or vacuum pressure, whichever is appropriate.
7
Express standard atmospheric pressure as a head, h = p/ρg, in (a) feet of ethylene glycol
8
Express standard atmospheric pressure as a head, h = p/ρg, in (b) inches of mercury;
9
Express standard atmospheric pressure as a head, h = p/ρg, in (c) meters of water
10
Express standard atmospheric pressure as a head, h = p/ρg, in (d) mm of methanol.
11
The deepest point in the ocean is 11034 m in the Mariana Tranch in the Pacific. At this depth γseawater ≈ 10520 N/m3. Estimate the absolute pressure at this
depth.
12
A diamond mine is 2 miles below sea level. (a) Estimate the air pressure at this
depth.
13
A diamond mine is 2 miles below sea level. (b) If a barometer, accurate to 1 mm of mercury, is carried into this mine, how accurately can it estimate the depth of the mine?
14
A closed tank contains 1.5 m of SAE 30 oil, 1 m of water, 20 cm of mercury, and
an air space on top, all at 20°C. If pbottom = 60 kPa, what is the pressure in the air space?
15
In Fig. P2.11, sensor A reads 1.5 kPa (gage). All fluids are at 20°C. Determine
the elevations Z in meters of the liquid levels in the open piezometer tubes B
16
In Fig. P2.11, sensor A reads 1.5 kPa (gage). All fluids are at 20°C. Determine
the elevations Z in meters of the liquid levels in the open piezometer tube C.
17
In Fig. P2.12 the tank contains water and immiscible oil at 20°C. What is h in centimeters if the density of the oil is 898 kg/m3?
18
In Fig. P2.13 the 20°C water and gasoline are open to the atmosphere and are at the same elevation. What is the height h in the third liquid?
19
The closed tank in Fig. P2.14 is at 20°C. If the pressure at A is 95 kPa absolute, determine p at B (absolute). What percent error do you make by neglecting the specific weight of the air?
20
In Fig. P2.15 all fluids are at 20°C. Gage A reads 15 lbf/in2 absolute and gage B
reads 1.25 lbf/in2 less than gage C. Compute (a) the specific weight of the oil;
21
In Fig. P2.15 all fluids are at 20°C. Gage A reads 15 lbf/in2 absolute and gage B
reads 1.25 lbf/in2 less than gage C. Compute and (b) the actual reading of gage C in lbf/in2 absolute.
22
Suppose one wishes to construct a barometer using ethanol at 20°C (Table A-3) as
the working fluid. Account for the equilibrium vapor pressure in your calculations and
determine how high such a barometer should be. Compare this with the traditional
mercury barometer.
23
All fluids in Fig. P2.17 are at 20°C. If p = 1900 psf at point A, determine the
pressures at B.
24
All fluids in Fig. P2.17 are at 20°C. If p = 1900 psf at point A, determine the
pressures at C
25
All fluids in Fig. P2.17 are at 20°C. If p = 1900 psf at point A, determine the
pressures at D in psf.
26
All fluids in Fig. P2.18 are at 20°C. If atmospheric pressure = 101.33 kPa and the bottom pressure is 242 kPa absolute, what is the specific gravity of fluid X?
27
The U-tube at right has a 1-cm ID and contains mercury as shown. If 20 cm3 of water is poured into the right-hand leg, what will be the free surface height in each leg after the sloshing has died down?
28
The hydraulic jack in Fig. P2.20 is filled with oil at 56 lbf/ft3. Neglecting piston weights, what force F on the handle is required to support the 2000-lbf weight shown?
29
In Fig. P2.21 all fluids are at 20°C. Gage A reads 350 kPa absolute. Determine (a) the height h in cm; and (b) the reading of gage B in kPa absolute.
30
The fuel gage for an auto gas tank reads proportional to the bottom gage pressure as in Fig. P2.22. If the tank accidentally contains 2 cm of water plus gasoline, how many centimeters “h” of air remain when the gage reads “full” in error?
31
In Fig. P2.23 both fluids are at 20°C. If surface tension effects are negligible, what is the density of the oil, in kg/m3?
32
Venus has a mass of 4.90E24 kg and a radius of 6050 km. Assume that its atmo-
sphere is 100% CO2 (actually it is about 96%). Its surface temperature is 730 K, decreasing to 250 K at about z = 70 km. Average surface pressure is 9.1 MPa. Estimate the pressure on Venus at an altitude of 5 km.
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