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The critical velocity (v) depends on

1)coefficient of viscosity

2)density of liquid

3)radius

derive an expression of velocity

1
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1)coefficient of viscosity

2)density of liquid

3)radius

derive an expression of velocity

Log in to add a comment

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Let us dimension analysis.

Critical Velocity = Vc = K * coeff of viscocity^a * density^b * radius^c

L T^-1 = K * (M L^-1 T^-1)^a * (M L^-3)^b * L^c

= K * M^(a+b) L^(-a-3b+c) T^-c

So a+b =0 a = -b -a -3b +c = 1 a = 1 So b = -1 c = -1

* Vc = K . (coeff of visocity) / (density * radius)*

Critical Velocity = Vc = K * coeff of viscocity^a * density^b * radius^c

L T^-1 = K * (M L^-1 T^-1)^a * (M L^-3)^b * L^c

= K * M^(a+b) L^(-a-3b+c) T^-c

So a+b =0 a = -b -a -3b +c = 1 a = 1 So b = -1 c = -1