Air passes through a large-diameter glass tube, then through a small-diameter tu

Question

Air passes through a large-diameter glass tube, then through a small-diameter tube, and finally through a large-diameter tube again.

Suppose the diameters of the two sizes of tubes are 9.2 mm and 5.3 mm, and suppose that the velocity of the air in the large-diameter tube is 1.67 m/s.

(a) Find the velocity of the air in the small-diameter tube.

(b) Find the difference in pressure of the air in the large- and small-diameter tubes. The density of air is 1.29 kg/m3.

(c) The vertical tubes contain colored water. Find the dierence in height of the water in the middle tube and the two outer tubes. neglect viscosity of air. This means that in this problem, the water in the two outer tubes are at the same height, contrary to what

really happens.

Explanation / Answer

using equation of continuity we have

A1 V1 = A2 V2

V2 = A1 V1 / A2

= d1^2 / d2^2 *V1

= (9.2/5.3)^2 * 1.67

area in small cross section =5.03 m/s

pressure difference = density of air * (v2^2 - v1^2) *0.5

= 1.29 * (5.03^2 - 1.67^2)

=14.533 pascal

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