Topic: Fluid Mechanics
A vertical air stream flowing at a velocity of 100 m/s supports a ball of 60 mm in diameter. Taking the density of air as $1.2~kg/m^{3}$ and kinematic viscosity as 1.6 stokes, the weight of the ball that is supported is (if coefficient of drag $C_{D}=0.8$)
- A. 20.2 N
- B. 13.5 N
- C. 30.1 N
- D. 25.2 N
Answer: B. 13.5 N
Explanation: The ball is supported by the drag force of the air stream, meaning the drag force equals the weight of the ball. Drag Force $F_{D} = C_{D} \cdot A \cdot \frac{\rho V^{2}}{2}$. Given the diameter $d = 60\text{ mm} = 0.06\text{ m}$, the projected area is $A = \frac{\pi}{4}(0.06)^{2}$. Substituting the given values ($C_{D} = 0.8$, $\rho = 1.2\text{ kg/m}^3$, $V = 100\text{ m/s}$) into the equation yields $F_{D} = 0.8 \times \frac{\pi}{4} \times (0.06)^{2} \times \frac{1.2 \times 100^{2}}{2}$. Calculating this gives $F_{D} = 13.5648\text{ N}$, which closely matches 13.5 N.