5-to-1 Fluid flow

Classical Mechanics Level 2

Five pipes of equal radius carry air into a sixth pipe with a radius ten times larger. If the air moves with speed v v in the larger pipe. How many times larger than v v is the speed of air in one of the smaller pipes?


The answer is 20.

July Thomas by July Thomas , 30, USA

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1 solution

July Thomas
Apr 13, 2016

Since there are five pipes of equal radius initially, the continuity equation can be written

5 A 1 v 1 = A 2 v 2 . 5 A_1 v_1 = A_2 v_2.

The problem gives r 2 = 10 r 1 r_2 = 10r_1 , so

5 π r 1 2 v 1 = π ( 10 r 1 ) 2 v 5\pi r_1^2 v_1 = \pi (10r_1)^2 v

5 r 1 2 v 1 = 100 r 1 2 v 5 r_1^2 v_1 = 100 r_1^2 v

v 1 = 20 v . v_1 = 20v.

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