Question

The rate of flow of liquid through a tube depends upon 1.coefficient of viscosity, ETA
2. radius of tube,
3. pressure gradient (deduce by the method of dimension the formula rate of flow of liquid..

Answer 1

Using method of dimensions , derive an expression for rate of flow (V) of a liquid through a pipe of radius (r) under a pressure gradient (p/l) . Given that V also depends on coefficient of viscosity (n)

Volume per sec = L^3 T^-1

Now according to above equation

V= P r^4 / ( neta ) l

=( M L^-1 T^-2 ) ( L^4 )

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( M L^-1 T^-1 ) ( L )

= L^3 T^-1