Two capillary tubes of same length each of 50   cm but of different radii 4   mm and 2   mm…

Two capillary tubes of same length each of 50 cm but of different radii 4 mm and 2 mm are connected in series. When water flows, the pressure difference between the ends of the arrangement is P. Then the pressure difference between the ends of the first tube is
  1. P2
  2. P17
  3. P4
  4. P8

Solution

The figure below represents the capillary tubes of same
lengths but different radii.

From the Poiseuille's equation, the expression for the water
resistance,

R=8ηlπr4

R1r4

The ratio of water resistance in tube I and II,

RlRII=rII4rl4=16×10-1216×16×10-12

16RI=RII

Let RI=R,RII=16R

Thus, the pressure difference between ends of first tube is,

pR+16R×R=p17

Asked in: AP EAMCET 2019 (21 Apr Shift 2)

Practice more Mechanical Properties of Fluids questions on Aicharya