`L,(L)/(2)` and `(L)/(3)` are connected in series. Their radii are r, `(r)/(2)` and `(r)/(3)` respectively. Then, if stream-line flow is to be maintained and the pressure across the first capillary is P, then:

Options

A. the pressure difference across the ends of second capillary is `8P`
B. the pressure difference across the third capillary is 43 P
C. the pressure difference across the ends of second capillary is 16 P
D. the pressure difference across the third capillary is 59 P

Answer

A

Explanation

`(dQ)/(dt)=(piPr^(4))/(8etaL)`
As capillaries are joined in series so `((dQ)/(dt))` will be same for each capillary.
Hence, `(piPr^(4))/(8muL) =(piP'(r//2)^(4))/(8eta(L//2)) = (piP''(r//3)^(4))/(8eta(L//3))`
So pressure difference across the ends of 2nd capillary `P^(')=8p` and across the ends of 3rd capillary `P^('')=27p`