The sphere of diameter 0.02 m falls in a fluid of kinematic viscosity of 10 stokes with the terminal velocity of 0.02 m/s. What is the value of the coefficient of drag on the falling sphere?

Concept:

Drag Force (F_d) is applied to the body when it moves through and liquid media.

Drag is defined as forceful pull experienced by the flat plate while the fluid flows over it.

Pressure drag comes from the eddying motions that are set up in the fluid by the passage of the body; This drag is associated with the formation of the wake in the flow.

Frictional drag comes from friction between the fluid and the surfaces over which it is flowing.

\({{\rm{F}}_{\rm{d}}} = \frac{{{{\rm{C}}_{\rm{d}}} \times {\rm{\rho }} \times {\rm{A}} \times {{\rm{V}}^2}}}{2}\)

\({\rm{Drag\;Coefficient}},{\rm{\;}}{{\rm{C}}_{\rm{d}}} = \frac{{24}}{{{{\rm{R}}_{\rm{e}}}}}\) when R_e < 0.2

Drag Coefficient, C_d = \({24\over R_e}({1+{3\over 16R_e}})\) when 0.2 < R_e < 5

Where C_d is the drag coefficient and R_e is Reynold’s Number.

Calculation:

\({{\rm{R}}_{\rm{e}}} = \frac{{{\rm{V}} \times {\rm{d}}}}{{\rm{\nu }}} = \frac{{0.02 \times 0.02}}{{10 \times {{10}^{ - 4}}}} = 0.4\)

\({{\rm{C}}_{\rm{d}}} = \frac{{24}}{{0.4}} = 60\)

Note:

the The given answer is as per official  exam of SSC JE.