Water flows through a capillary tube of radius `r` and length at a rate of 40 ml per second, when connected to a pressure difference of h cm of water. Another tube of the3 some length but radius. `(r)/(2)` is connected in series with this tube and the combination is connected to the same pressure head.[density of water is `rho`]

Options

A. the pressure difference across each tube is `p_(1)=(rhogh)/(17)` and `p_(2)=(16)/(17)rhogh`
B. The pressure difference across each tube is `p_(1)=(rhogh)/(16)` and `P_(2)=(17)/(16)rhogh`
C. The rate of flow of the water through the combination is `(40)/(17)(c.c)/(sec)`.
D. The rate of flow of water through the combination is `(17)/(40)(c.c)/(sec)`.

Answer

A, C

Explanation

According to Pissiulle's equation.
Rate of flow `=(P)/(((8etaL)/(pir^(4))))`
Making a analogy with current flow.
Let `R_(1)=(8etaL)/(pir^(4)),R_(2)=(8etaL)/(pi((g)/(2))^(4))=16R`
`P_(1)+P_(2)=P=rhogh` and `(P_(1))/(P_(2))=(R_(1))/(R_(2))=(1)/(16)`
Also rate of flow `=(P)/(P_(1)+P_(2))=(P)/(17R_(1))=(40)/(17)=(mL)/(s)`