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What should be the difference in pressur...

What should be the difference in pressure across the ends of a 4 km long horizontal pipe line of diameter 8 cm to make water flow at the rate 20 litre/s`eta_("water")=10^(-2)MKS`. Neglect all forces other than viscous force.
[Hint : `V=(piPr^(4))/(8hl)]`

Text Solution

Verified by Experts

`r=(d)/(2)=(8)/(2)=4cm=4xx10^(-2)m`
`l=4km=4xx10^(3)m`
`V=20(L)/(S)=20xx10^(-3)m^(3)//s`
`eta=10^(-2)MKS,P=?`
`V=(piPr^(4))/(8etal)`
`P=(8etalV)/(pir^(4))`
`P=(8xx10^(-2)xx4xx10^(3)xx20xx10^(-3))/(3.14xx(4xx10^(-2))^(4))=(50xx10^(5))/(6.28)`
`thereforeP=7.96xx10^(5)Pa`
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KUMAR PRAKASHAN-MECHANICAL PROPERTIES OF FLUIDS -SECTION - B Numerical From DARPAN Based On Textbook
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