A reservoir manometer consists of a U-tube in which the two arms have different

Question

A reservoir manometer consists of a U-tube in which the two arms have different diameters, as shown in Fig. 13-1. The diameter on the narrow side is 10.0 mm and the diameter on the reservoir side is 25.0 mm. The liquid in the manometer is oil with a density of 830 kg/m3 and the fluids in contact with the oil are gases of negligible density. The dotted line indicates the level of the oil when the pressures p 1 andp 2 are equal. What is the value ofh whenP 1 -P 2 = 1000 Pa?

Answer:

10.6 cm

FIGURE 13-1 15) A reservoir manometer consists of a U-tube in which the two arms have different diameters, as shown in Fig. 13-1. The diameter on the narrow side is 10.0 mm and the diameter on the reservoir side is 25.0 mm. The liquid in the manometer is oil with a density of 830 kg/m3 and the fluids in contact with the oil are gases of negligible density. The dotted line indicates the level of the oil when the pressuresp 1 andp 2 are equal What is the value ofh whenP 1-P 2-1000 Pa?

Explanation / Answer

P1 - P2 = rho * g *h [1+(d/D)2] = 1000pa

where d ---- diameter of narrow side = 10mm

          D ---- diameter of reservior side = 25 mm

                   h = 1000/rho * g * 1.16

                rho = 830 kg/m3

                 h = 1000/(830*9.8*1.16)

                      h = 10.59 cm = 10.6 cm

                     

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