The volume flowrate of the liquid through the tube A of length l and radius r connected across a pressure had h be V. If two tubes B and C of same length but of radius r and `r/2` are connected in series across the same pressure head h, the rate of flow of liquid thrugh the combination is `V/x` find x.

Answer

`17.00`

Explanation

For any pressure head, pressure difference between two ends
`=P=h p g`
Rate of flow of liquid through tube A of radius r is
`V=(piPr^(4))/(4 etal)=(pi h rho g r^(4))/(8 etaI)`
When tubes B and C of radii r and `r/2` are
connected in series let h. bet the pressure head at the comon points of tubes B and C. The the rate of flow of liquid through each tube will be same and it is
`V_(B)=(pi(h-h.)rho gr^(4))/(8eta I)`..........i
`:.V_(c)=(pi h.rho g(r//2)^(4))/(8etaI)`........ii
Now `V_(B)=V_(C)=V.`
`h-h.=(h.)/16`........[From i and ii]
`:.h.=16/17h`.........iii
`:.V_(B)=V.=(pi(h-16/17h)rho g r^(4))/(8 etaI)`
.........[from i and ii]
`=1/17 ((pi h ro gr^(4))/(8 etaI))`
`:.V.=V/17`
`impliesx=17`