Reynold number `N_R` a dimensionless quantity determines the condition of laminar flow of a viscous liquied through a pipe. `N_R` is a function of density `rho` of liquid, average speed `upsilon` and coeff. Of viscosity `eta.` Given that `N_R prop D,` diameter of pipe. Show by the method of dimensions that `N_R prop(rhoupsilonD)/(eta)`

The cirtical velocity (upsilon) of flow of a liquied through a pipe of radius (r ) is given by upsilon = (eta)/(rho r) where rho is density of liquid and eta is coefficient of visocity of the liquied. Check if the relaiton is correct dimensinally.

Using the method of dimensions, 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 (eta) of the liquied.

volume rate flow of a liquid of density rho and coefficient of viscosity eta through a cylindrical tube of diameter D is Q. Reynold's number of the flow is

Reynolds number for a liquid of density rho , viscosity eta and flowing through a pipe of diameter D, is given by

Derive by the method of dimensions, an expression for the volume of a liquid flowing out per second through a narrow pipe. Asssume that the rate of flow of liwquid depends on (i) the coeffeicient of viscosity eta of the liquid (ii) the radius 'r' of the pipe and (iii) the pressure gradient (P)/(l) along the pipte. Take K=(pi)/(8) .

The rate of flow Q (volume of liquid flowing per unit time) through a pipe depends on radius r , length L of pipe, pressure difference p across the ends of pipe and coefficient of viscosity of liquid eta as Q prop r^(a) p^(b) eta^(c ) L^(d) , then

A liquid drop of radius R breaks into N smaller droplets of radii r, If liquid has density rho, specific heat s and surface tension, T, than the drop in temeperature is given

Define terminal velocity. Show that the terminal velocity upsilon of a sphere of radius r, density rho falling vertically through a viscous fluid of density sigma and coefficient of viscosity eta is given by upsilon = 2 / 9 ((rho - sigma)r^2 g) / eta Use this formula to explain the observed rise of air bubbles in a liquid.

The rate flow (V) of a liquid through a pipe of radius (r ) under a pressure gradient (P//I) is given by V = (pi)/(8)(P R^4)/(I eta), Where eta is coefficient of visocity of the liquied. Check whether the formula is correct or not.

When a solid moves therough a liquid, the liquid opposes the miotioon with a force F. The magnitude of F depends on the coefficient of viscosity eta of the liquid, the radius r of the sphere aknd the speed v of the sphere. Assuming that F is proportional to different powers of these quantities, guess a formula for F using the method of dimension.