The air passes through a large-diameter glass tube, then through a small-diamete

Question

The air passes through a
large-diameter glass tube, then through a small-diameter
tube, and nally 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 .645m/s.
(a) Find the velocity of the air in the small-diameter
tube. (b) Find the dierence 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, as shown in the gure.

Explanation / Answer

from continuity eqn , a1v1= a2v2 where as a1= pi r1^2 and v1 =.645 a2=pi r2^2 and v2=? so after solving this v2=(a1v1)/a2 hence vel. in smaller section=1.943 m/s b)mass=density*a1v1 mass flow rate=5.531*10^-5 head diff=(v2-v1)^2/2g =85mmof air c)pressure diff= dens*g[(v1^2-v2^2)/2g +.085] pressre diff=3.242 n/m2

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