Final Answer:
The maximum diameter of spherical dust particles that can be separated by the 10 m/s air stream is approximately 0.1 millimeters.
Step-by-step explanation:
The separation of dust particles from a mixture relies on the balance between the upward air drag force and the downward gravitational force on the particles. For successful separation, the air drag force must overcome gravity. We can express this with the equation:
Drag force = 1/2 * C_d * ρ_air * A_particle * v_air^2
Gravity force = ρ_particle * g * Volume_particle
where:
C_d is the drag coefficient (assumed constant for simplicity)
ρ_air is the air density
A_particle is the particle's cross-sectional area (πr^2 for a sphere)
v_air is the air velocity
ρ_particle is the particle density (relative density * water density)
g is the acceleration due to gravity
Volume_particle is the particle's volume (4/3 πr^3 for a sphere)
Setting the forces equal and solving for the particle radius (r) allows us to estimate the maximum diameter:
r ≈ (9/4 * ρ_particle * g / C_d * ρ_air * v_air^2)^(1/3)
Plugging in the given values, we get a maximum diameter of around 0.1 millimeters.
Note: This calculation provides a simplified estimate and neglects factors like non-spherical particle shapes and varying air flow conditions.
Option:
This answer applies to option (B) in the original question.