What is the terminal velocity of a small water droplet falling through still air? How is the terminal velocity calculated in this scenario?
The terminal velocity of a small water droplet falling through still air is approximately 4.65154 in/s. The calculation is based on the diameter of the water droplet, which is 1.25 mil (3.175 × 10^-5 m), and the viscosity of still air (1.83 × 10⁻⁵ Pa). The formula for drag force (Fd) includes the viscosity (η) and the velocity (v), and in order to reach terminal velocity, acceleration must be zero. By applying the formula and the given values, the terminal velocity of the water droplet is determined.
Understanding Terminal Velocity Calculation
Terminal Velocity Formula: $v = 2/9 \times ρgr³/ η$
Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration. In the case of a small water droplet falling through still air, the drag force acting against the motion of the droplet plays a crucial role in determining the terminal velocity.
The calculation of terminal velocity involves considering the drag force, viscosity of the air, density of the droplet, gravitational acceleration, and the radius of the droplet. By setting the drag force equal to the weight of the droplet to achieve zero acceleration, the terminal velocity can be derived using the appropriate formula.
In this scenario, the terminal velocity of the small water droplet is found to be approximately 4.65154 in/s. This calculation demonstrates the balance between gravitational force and air resistance that determines how fast the droplet falls through still air. For a more in-depth explanation of terminal velocity and its significance in fluid dynamics, you can explore further resources like the link provided.