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) .

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 following equations : (i) upsilon = u +at (ii) s = ut +(1)/(2) at^2 (iii) upsilon^2 - u^2 = 2as

Check the dimensional consistency of the following equations : (i) de-Broglie wavelength , lambda=(h)/(mv) (ii) Escape velocity , v=sqrt((2GM)/(R)) .

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,

Find the dimensions of a in the formula (p+a/V^2)(V-b)=RT

Walli's Formula || Properties For P-1 to P- 4

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 liquid flowing per second is called the volume flow rate Q and has the dimensions of [L]^(3)//[T] . The flow rate of a liquid through a hypodermic needle during an injection can be estimated with the following equation: Q=(piR^(n)(P_(2)-P_(1)))/(8etaL) The length and radius of the needle are L and R, respectively, both of which have the dimension [L]. The pressures at opposite ends of the needle are P_(2)andP_(1) , both of which have the dimensions of [M]//[L][T]^(2) . The symbol eta ' represents the viscosity of the liquid and has the dimensions of [M]//[L][T] . The symbol pi stands for pi and. like the number 8 and the exponent n, has no dimensions. Using dimensional analysis, determine the value of n in the expression for Q.