Water is conveyed through a horizontal tube 8 cm in diameter and 4 kilometer in length at the rate of 20 litre/s Assuming only viscous resistance , calculate the pressure required to maintain the flow . Coefficient of viscosity of water is 0.001 pa s

Explanation

Here, 2r=8 cm =0.08 m or r=0.04 m, l=4 km =4000 m,
`V=20 "litre"//s=20xx10^(-3) m^(3)s^(-1), eta=0.001 Pa-s, p= ?`
As, `V=(pi p r^(4))/(8eta l) " or" p=(8V eta l)/(pi r^(4))`
`=(8xx(20xx10^(-3))xx0.001xx4000)/(((22)/(7))xx(0.04)^(4)) =7.954xx10^(4) Pa`
`therefore` Height of mercury column for pressure difference p will be,
`h=(p)/(rho g)=(7.954xx10^(4))/((13.6xx10^(3))xx9.8)=0.5968 m=59.68 cm`