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Question: Water is conveyed through a uniform tube of 8 cm in diameter and 3140 m in length at the rate \(= 10...

Water is conveyed through a uniform tube of 8 cm in diameter and 3140 m in length at the rate =10−3= 10 ^ { - 3 } SI units)

A

B

0.625 N m−20.625 \mathrm {~N} \mathrm {~m} ^ { - 2 }

C

0.0625 N m−20.0625 \mathrm {~N} \mathrm {~m} ^ { - 2 }

D

0.00625 N m−20.00625 \mathrm {~N} \mathrm {~m} ^ { - 2 }

Answer

Explanation

Solution

According to poiseuille formula,

Rate of flow,

Where the symbols have their usual meanings.

Here,

r=82 cm=4 cm=4×10−2 m\mathrm { r } = \frac { 8 } { 2 } \mathrm {~cm} = 4 \mathrm {~cm} = 4 \times 10 ^ { - 2 } \mathrm {~m}

Substituting the given values we get

P=(2×10−3 m3 s−1)(8)(10−3 Nsm−2)(3140 m)(3.14)(4×10−2 m)4\mathrm { P } = \frac { \left( 2 \times 10 ^ { - 3 } \mathrm {~m} ^ { 3 } \mathrm {~s} ^ { - 1 } \right) ( 8 ) \left( 10 ^ { - 3 } \mathrm {~N} \mathrm { sm } ^ { - 2 } \right) ( 3140 \mathrm {~m} ) } { ( 3.14 ) \left( 4 \times 10 ^ { - 2 } \mathrm {~m} \right) ^ { 4 } }

=6.25×103Nm−2= 6.25 \times 10 ^ { 3 } \mathrm { Nm } ^ { - 2 }