derive an expression for rate of flow (v) of a liquied through a pipe of radius (r ) under a pressure gradient (P/I) Given that V also depends on coefficient of viscosity (η) of the liquied.
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Explanation:
ANSWER
V∝R
a
(
L
P
)
b
η
c
V=[L]
3
[T]
−1
R=[L]
L
P
=[M][T]
−2
[L]
−2
η=[M][T]
−1
[L]
−1
⇒[L]
3
[T]
−1
=[L]
a
[M]
b
[T]
−2b
[L]
−2b
[M]
c
[L]
−c
[T]
−c
a−2b−c=3
b+c=0
−2b−c=−1
a=4,b=1,c=−1
V∝
ηL
PR
4
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