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

Options

A. 45 cm
B. 50 cm
C. 59.68cm
D. 49.68 cm

Answer

C

Explanation

Here , 2r=8cm = 0.08 m or r=004m, l=4km=4000m,
`V=20litre//s = 20xx10^(-3) m^3 s^(-1), eta=0.001Pa-s, p=?`
As `V=(pipr^4)/(8etal) " or " p=(8Vetal)/(pir^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/(rhog)=(7.954xx10^4)/((13.6xx10^3)xx9.8)`
=0.5968 m = 59.68 cm