Find the dimensions of the quantity v in the equation,
`v=(pip(a^(2)-x^(2)))/(2etal)`
where a is the radius and l is he length of the tube in which the fluid of coefficient of viscosity `eta` is flowing , x is the distacne from the axis of the tube and p is the pressure differnece.

Find the dimensions of a//b in the relation P =(a-x^2)/(bt), where x is distance, t is time and P is pressure.

Find the dimensions of a//b in the relation P =(b-x^2)/(at) where P is pressure. X is distance and t is time.

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

Check the correctness of the relation : upsilon = (pi P(a^2 - x^2))/(2etaI), Where upsilon is velocity, p is pressure difference, a is radius of tube, x is distance from the axis of tube, eta is coeff. Of viscosity and I is length of the tube.

A physical quantity P=B^(2)l^(2)//m where B is the magnetic induction, l is the length and m is the mass. The dimensions of P is

The velocity distribution for the flow of a Newtonian fluid between two wide, parallel plates is given by the equation u=(3V)/2[1-(y/h)^(2)] where V is the mean velocity. The fluid has coefficient of viscosity eta Answer the following 3 questions for this situation. Shear stress acting on the bottom wall is

Stoke's law states that the viscous drag force F experienced by a sphere of radius a, moving with a speed v through a fluid with coefficient of viscosity eta , is given by F=6 pi eta If this fluid is flowing through a cylindrical pipe of radius r, length l and a pressure difference of P across its two ends, then the volume of water V which flows through the pipe in time t can be written as (V)/(t)=K ((p)/(l))^(a)eta^(b)r^(c ) where k is a dimensionless constant. Correct values of a, b and c are -

The velocity distribution for the flow of a Newtonian fluid between two wide, parallel plates is given by the equation u=(3V)/2[1-(y/h)^(2)] where V is the mean velocity. The fluid has coefficient of viscosity eta Answer the following 3 questions for this situation. Consider a rectangular cross section of dimensions l x 2h as shown. The side AB is parallel to the plates. Volume flow rate through this cross section is