Question

Narrow capillary tubes A and B are of length l and l/2 and of the same radius r. The rate of flow of water through the tube A under a constant pressure head 'P' is 3 cm3/sec. If A and B are connected in series and the same pressure difference 'P' is maintained between the ends of the composite tube, then the rate of flow of water is

• A. (A) 1.5 cm3/s
• B. (B) 3 cm3/s
• C. (C) 2 cm3/s
• D. (D) None of these

Answer 1

Answer: (C)

(C) 2 cm3/s

Answer 2

Explanation:
The volumetric flow is given by:Vt(πr48ηl)PThe resistance of the pipe is R=8ηlπr4For the first pipe, length is 1 and for the second pipe, length is t2The resistance of the combination in series is:Rs=R1+R2=8ηlπr4+8ηπr4(l2)Rs=32×8ηLπr4⇒Rs=32RThe new volumetric flow is VV′V=RRs=23V′=23V=23×3=2cm3/s