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:w;Tv Distribuiion in j Fluid

Find tr»c anilinie u' w huh the pressure deviation is (u) I tvrv*n: and <ó! 5 pcreent. What do you conclude?

Put ?n>b. 2.2t* on an analnie basis by assuming arbiirary B 1:1    |2.27). Show that. appro\immely. the deviution in

pressure is less than I percent of p_tł if ; < 0.14T_o/fl. Eanh”s atmosphcric corditions vary somewhat. On a certain G2> the sea-leve! temperaturę is 45°F. and the sea-level presje is 29.5 inHg. An airplane oserhcad register* an air temperaturę of 1S°F and a prcssure of 12 lbf/in^:. Estimate the plane's altitude. in ft.

Under some condirions the atmosphere is adiabatic, p ■* (constKp*). where k is the specific-heat ratio. Show that. for an adiabatic atmosphere. the prcssure variation is given by

it/tt-n ■

u - i)gz

P = Po

kRT,

o

Compare this formula for air at c = 10.000 m with the standard atmosphere in Table A.6.

In Fig. P2.30 fluid I is SAE 30 oil. and fluid 2 is carbon tetrachloride. If p_a - 99 kPa. determine the absolute pres-surc at point A.

H For the inverted manometer of Fig. P2.32, all fluids are at 20°C. If p_B — p_A = 97 kPa, what must the height H be in

L cm?

Meriam red oil.

SG-O.S27 N

Waler

18 cm

H

35 cm

Mercury

Fig. P2J2

233 In Fig. P2.33 the prcssure at point A is 25 lbf/in². All fluids are at 20°C. What is the air prcssure in the closed chambcr B. in Pa?

In Fig. P2.34 containers (a) and (b) are cylindrical and con-

nn

ditions arc such that p„ = p_h. Derive a formuła for the pressure difference p_a — p_b when the oil-water interface on the right rises a distance A/i < h. for (a) d < O and (b) d — 0.2D. What is the percentage change in the value of Ap?

235    For a specific application of Ptrob. 2.34, take D = 5 cm, L = 8 cm, and h = 10 cm. Both fluids are at 20°C. Evaluate Pa ~ Pb ^when A/i = 1 cm for (a) d 0 and (b) d = 1 cm.

236    For Fig. 2.9 in the texl. let fluid 1 be water and fluid 2 be mercury, at 20°C. The right leg is fined with a scalę to read p_A in kPa (gage). What should the length between scalę graduations be, in mm?

237    The inclined manometer in Fig. 2.37 contains Meriam red manometer oil, SG = 0.827. Assume that the reservoir is very larg^If the inclined arm is fltted with graduations 1 in apart, what should the angle 6 be if each graduation corre-sponds to 1 Ibf/ft² gage pressure for p/!

Fig. P237

238    Repeat Prób. 2.37 for a finite reservoir approximating a half-full hemisphere with a diameter of 6 in.

239    An 8-cm-diameter piston compresscs manometer oil into an inclined 7-mm-diameter tubę, as shown in Fig. P2.39. When a weight W is added to the top of the piston, the oil rises an additional distance of 10 cm up the tubę. as shown. How large is the weight, in N?

2.40 A pump slowly introduces mercury into the bottom of the closed tank in Fig. P2.40. At the instant shown. the air pressure p_B = 80 kPa. The pump stops when the air pressure

rises to 110 kPa. All fluids remain at 20°C. What will bc the manometer reading h at that urnę. in cm. if it is connected to standard sea-level ambient air p_nm?

2.41 The system in Fig. P2.41 is at 20°G. Compute the pressure at point A in lbf/ft² absolute.

Water

2.42 Very smali pressure differences p_A — p_B can be measured accurately by the two-fluid differential manometer in Fig. P2.42. Density pj is only slightly larger than that of the upper fluid p,. Derive an expression for the proportionality between h and p_A — p_B if the reservoirs are very large.