When a solid moves through a liquid, the liquid opposes the motion with a force F. The magnitude of F depends on the coefficient of viscosity `eta` of the liquid, the radius r of the sphere and 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.

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.

The viscous force on a spherical body, when it moves through a viscous liquid, depends on the radius of the body, the coefficient of viscosity of the liquid and the velocity of the body.Find an expression for the viscous force.

A small metal sphere of radius a is falling with a velocity upsilon through a vertical column of a viscous liquid. If the coefficient of viscosity of the liquid is eta , then the sphere encounters an opposing force of

When a metallic sphere is dropped in a long column of a liquid, the motion of the sphere is opposed by the viscous force of the liquid. If the apparent weight of the sphere equals to the retardation forces on it, the sphere moves down with a velocity called.

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) .

A liquid of density rho and coefficient of viscosity eta , flows with velocity upsilon through a tube of diameter D. A quantity R = (rho upsilon D)/(eta) determines whether the flow will be streamlined or turbulent. R has the dimension of

The volume of a liquid of density rho and viscosity eta flowing in time t through a capillary tube of length l and radius R, with a pressure difference P, across its ends is proportional to :

A dimensionally consistent relation for the volume V of a liquid of coefficiet of viscosity eta flowing per second through a tube of radius r and length l and having a pressure difference p across its end, is

A liquid of coefficient of viscosity eta is flowing steadily through a capillary tube of radius r and length I. If V is volume of liquid flowing per sec. the pressure difference P at the end of tube is given by

The contripetal force F acting on a particle moving uniformly in a circle may depend upon mass (m), velocity (v) and redio ( r) of the circle . Derive the formula for F using the method of dimensions.