First slide
Dimensions
Question

If dimensions of critical velocity νc of a liquid flowing through a tube are expressed as ηxρyrz where η,ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by

Moderate
Solution

vc=ηxρyr2   (given)                         . . . .(i)

Writing the dimensions of various quantities in eqn. (i), we get

M0LT-1=ML-1 T-1xML-3 T0yM0LT0z

=Mx+y L-x-3y+z T-x

Applying the principle of homogeneity of dimensions, we get

x+y=0 ;-x-3 y+z=1 ;-x=-1

 On solving, we get 

x=1, y=-1, z=-1

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