dimensional analysis.
The rate of a flow. V a of liquid through a capillary under a constant pressure depends upon (i) the
pressure gradient (P/) (ii) coefficient of viscosity of the liquid n (iii) the radius of the capillary tube
r. Show that the rate of volume of liquid flowing per sec V « Prélni.
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Answer: V∝
ηL
PR
4
Explanation:
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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