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Two tubes of radii r 1 and r 2 and lengths l 1 and l 2, respectively, are connected in series and a liquid flows through each of them in stream line conditions. P 1 and P 2 are pressure differences across the two tubes. If P 2 is 4 P 1 and l 2 is l 1 4 then the radius r 2 will be equal to :

Options

  1. A4 r 1
  2. Br 1
  3. C2 r 1
  4. Dr 1 2

Correct answer

D. r 1 2

Step-by-step solution

d V d t = π 8 p r 4 η L p 1 r 1 4 L 1 = p 2 r 2 4 L 2 p 1 r 1 4 l 1 = 4 p 1 r 2 4 l 1 4 ⇒ r 2 4 = r 1 4 16 ⇒ r 2 = r 1 2

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