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Water is conveyed throuh a uniform tube ...

Water is conveyed throuh a uniform tube of 8 cm in diameter and 3140 m in length at the rate `2 xx 10^(-3) m^(3)` per second. The pressure required to maintain the flow is ( viscosity of water =`10^(-3)` )

A

`6.25 xx 10^(3) Nm^(-2)`

B

`0.625 N m^(-2)`

C

`0.0625 Nm^(-2)`

D

`0.00625 N m^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
A
According to Poiseuille formula,
Rate of flow , `V=(piPr^(4))/(8etal)`
Where the symbols have their usual meanings.
`therefore P=(V8etal)/(pir^(4))`
Here, `V=xx10^(-3)m^(3) s^(-1)`
`r=(8)/(2)cm=4 cm =4xx10^(-2) m`
`l=3140 m, eta=10^(-3) N s m^(-2)`
Substituting the given values, we get
`P=((2xx10^(-3) m^(3) s^(-1))(8)(10^(-3) N sm^(-2))(3140m))/((3.14)(4xx10^(-2) m)^(4))`
`6.25xx10^(3) N m^(-2)`
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