DSC03085

30 Pressure Distriburion in a Fluid

I ■    •

■■■■■■■Mm

e

2.13 in Fig. P2.13 the 20°C water and gasoline surfaces are open to the atmosphere and at the same elevation. What is the height A of the third liąuid in the right leg?

P* r 2.14 The closed tank in Fig. P2.14 is at 20°C. If the pressure at

IjąuKł levels in ihc open piezometer tubes B and C.

2-12 \M»en open tubes called piezometers are connected to a tank .'t ikjuid under pressure. thc liąuid riscs to the piezometer hrud. ot pressure head. of the liąuid. If p_A is the pressure at point A, show that all three piezometers rise to the same ³    A = pjy.

- Fig. P2.12

point .4 is 93 kPa absolute. what is the absolute pressure at point B in kPa? What percent error do you make by neglect-ing the specific weight of the air?

2.15 The air-oil-water system in Fig. P2.15 is at 20°C. Knowing that gage .4 reads 13 lbf/in² absolute and gage B reads 1.23 lbf/in² less than gage C. compute (a) the specific weight of the oil in łbf/ft³ and (b) the actual reading of gage £ in lbf/in¹ absolute. J    ^

131bf/in²abs    /{l^

2.16    A closed inverted cone, 100 cm high with diameter 60 cm at the top. is filled with air at 20°C and l atm. Water at 20°C is introduced at the bonom (the vertex) to compress the air isothermally undl a gage at the top of the cone reads 30 kPa (gage). Estimate (a) the amount of water needed (cm³) and (A) the resulting absolute pressure at the bonom of the cone (kPa).

2.17    The system in Fig. P2.17 is at 20°C. If the pressure at point A is 1900 Ibf/ft². determine the pressures at points B, C, and D in Ibf/ft². •

2.18 The system in Fig. P2.18 is at 20°C. If atmospheric pressure is 101.33 kPa and the pressure at the bonom of the tank is 242 kPa, what is the specific gravity of fluid X?

2.19 The U-tube in Fig. P2.19 has a l-cra ID and contains mer-ciuy as shown. If 20 cm³ of water is poured into the right-hand leg, what will the free-surface height in each leg be after the sloshing has died down?

Fig. P2.19

2.20 The hydraulic jacie in Fig. P2.20 is filled with oil at 56 Ibf/ft³. Neglecting the weight of the two pistons. what force F on the handle is required to support the 2000-Ibf weight for this design?

3-in diameter

Fig. P2.20

221 At 20°C gage A reads 350 kPa absolute. What is the height h of the water in cm? What should gage B read in kPa absolute?

Fig. P2.21

2.22 The fiiel gage for a gasoline tank in a car reads proponional to the bottom gage pressure as in Fig. P2.22. If the tank is 30 cm deep and accidentally contains 2 cm of water plus gasoline, how many centimeters of air remain at the top when the gage erroneously reads “fuli”?

2.23    In Prób. 12 we madę a crude integradon of the density dis-tribution p(z) in Table A.6 and esdmated the mass of the earth’s atmosphere to be m "• 6 E18 kg. Can this result be used to estimate the sea-level pressure on earth? Conversely. can the actual sea-level pressure of 10135 kPa be used to make a morę accurate estimate of the atmospheric mass?

2.24    Venus bas a mass of 4.90 E24 kg and a radius of 6050 km. Its atmosphere is 96 percent C0₂, but let us assume it to be 100 percent. Its surface temperaturę averages 730 K, de-creasing to 250 K at an aldtude of 70 km. The average surface pressure is 9.1 MPa. Estimate the atmospheric pressure of Venus at an aldtude of 10 km.

2.25    Mars has a mass of 6.38 E23 kg and a radius of 3381 km. Its atmosphere is mosdy C0₂—let us assume it to be 100 percent. Its surface temperaturę is highly variable but aver-ages about 200 K. The average surface pressure is 800 Pa. Estimate the atmospheric pressure of Mars at an aldtude of 10 km.

2.26    Invesugate the effect of doubling the lapse ratę on atmospheric pressure. Compare the standard atmosphere (Table A.6) with a lapse ratę cwice as high of B₂ = 0.0130 K/m.

«!