Explanation:

The critical velocity is the velocity at which the laminar flow of a fluid changes to turbulent flow. It is influenced by various factors such as the coefficient of viscosity, density, and radius of the drop.

Formula:

V = K(n * r) / D

where,
V = Critical velocity
K = Dimensionless constant
n = Coefficient of viscosity
r = Radius of the drop
D = Density of the fluid

Derivation:

The critical velocity can be determined by considering the Reynolds number, which is a dimensionless quantity that characterizes the flow of a fluid. It is given by the following formula:

Re = D * V * r / n

where,
Re = Reynolds number

If the Reynolds number is less than a critical value, the flow is laminar, while if it is greater than the critical value, the flow is turbulent. The critical value of the Reynolds number is typically around 2000.

For a spherical drop, the radius can be expressed in terms of the volume as follows:

r = (3V / 4π)^(1/3)

Substituting this expression into the Reynolds number formula and solving for V, we obtain:

V = (4/3) * (n / D) * (K * V)^(3/2)

Rearranging this equation, we get:

V = K(n * r) / D

Thus, the critical velocity can be expressed in terms of the coefficient of viscosity, density, and radius of the drop, as well as a dimensionless constant K. The value of K depends on the specific conditions of the flow, such as the shape of the object and the nature of the fluid.

Conclusion:

In conclusion, the critical velocity of a body can be calculated using the formula V = K(n * r) / D, where K is a dimensionless constant that depends on the specific conditions of the flow. This formula is derived from the Reynolds number formula and takes into account the coefficient of viscosity, density, and radius of the drop.