Check the dimensional consistency of the poiseuille's formula for the laminar flow in a tube:
`V=(piR^(4)(p_1-p_2))/(8etal)`

Check the dimensional consistency of the equation (mV^2)/(r )= (Gm_(1)m_(2))/(r^2) .

Check the dimensional consistency of the following equations. (ii) Escape velocity, v=sqrt((2GM)/(R ))

V is the volume of a liquid flowing per second through a capillary tube of length l and radius r, under a pressure difference (p). If the velocity (v), mass (M) and time (T) are taken as the fundamental quantities, then the dimensional formula for eta in the relation V=(pipr^(4))/(8etal)

Check the dimensional consistency of the relations : (i) S= ut+(1)/(2)at^(2) (ii) (1)/(2)mv^(2)= mgh .

Check the dimensional consistency of the relation upsilon = (1)/(I) sqrt((P)/(rho)) where I is length, upsilon is velocity, P is pressure and rho is density,

When a liquid moves steadily under some pressure through a horizontal tube, it moves in the form of cylindrical layers coaxial to the ends of the tube. The velocity of different layers is different. The velocity of the layer is maximum along the axis of the tube and it decreases as one moves towards the walls of the tube. According to Poiseuille, the rate of flow of liquid through a horizontal capillary tube varies as the relation V alpha (pr^(4))/(eta l) where l and r are the length and radius of the tube and p is the pressure different between the ends of the tube and is the constant of proportionality. (pi pr^(4))/(8 etal) is dimensionally equivalent to (R is the resistance)

The volume of a liquid flowing out per second of a pipe of length I and radius r is written by a student as V=(pi)/(8)(pr^(4))/(etal) where p is the pressure difference between the two ends of the pipe and eta is coefficent of viscosity of the liquid having dimensional formula (ML^(-1)T^(-1)) . Check whether the equation is dimensionally correct.

To study the laminar flow of a liquid through a narrow tube, the following formula is used V=(pi P r^(4))/(8 eta l) . Given P = 76 cm of Hg , r = 0.28 cm , V = 1.2 cm^(2)s^(-1) , l = 18.2 cm If these quantities are measured to the accuracy of 0.5 cm of Hg, 0.01 cm, 0.1 cm^(3) s^(-1) and 0.1 cm respectively, find maximum percentatge error in the value of eta .

To study the laminar flow of a liquid through a narrow tube, the following formula is used V=(pi P r^(4))/(8 eta l) . Given P = 76 cm of Hg , r = 0.28 cm , V = 1.2 cm^(2)s^(-1) , l = 18.2 cm If these quantities are measured to the accuracy of 0.5 cm of Hg, 0.01 cm, 0.1 cm^(3) s^(-1) and 0.1 cm respectively, find maximum percentatge error in the value of eta .