Question

Impinging air jets may be used to clean particles from surfaces. The kinetic energy per unit volume (J/m³) of an air jet at a surface, Er, may be written as:

[ E = 1/2 * (rho * v²) * k * d⁻¹·³ ]
Where:
rho = density of air (1.3 kg/m³)
v = air velocity
k = proportionality constant (0.4 mm¹·³)
d = distance from the jet nozzle (10 mm)

For a sphere (A₄ = 1 × 10⁻¹⁹ J) adhered to a flat surface (A₂ = 1 × 10⁻²⁰ J), find:

1. What size of particle (diameter) could a hurricane force wind (v = 118 km/h) remove from a surface?
A) 0.1 mm
B) 0.5 mm
C) 1.0 mm
D) 2.0 mm

Answer 1

The size of the particle that a hurricane force wind can remove from a surface is approximately 0.1 mm.

Step-by-step explanation:

To find the size of the particle that a hurricane force wind can remove from a surface, we can use the formula for kinetic energy per unit volume of an air jet, which is given as: E = 1/2 * (rho * v²) * k * d⁻¹·³. We know that rho (density of air) is 1.3 kg/m³, v (air velocity) is 118 km/h (converted to m/s), k (proportionality constant) is 0.4 mm¹·³, and d (distance from the jet nozzle) is 10 mm. We need to solve for d, so we rearrange the formula and substitute in the known values.

The formula becomes:
E = 0.5 * (1.3 * (118/3.6)²) * 0.4 * (10/1000)⁻¹·³

By solving this equation, we find that the kinetic energy per unit volume is approximately 2.68 × 10⁻⁹ J/m³. Now we can use this value to find the size of the particle that can be removed from the surface. We know that the kinetic energy per unit volume of the adhered sphere (A₄) is 1 × 10⁻¹⁹ J and the kinetic energy per unit volume of the flat surface (A₂) is 1 × 10⁻²⁰ J.

By rearranging the formula for kinetic energy per unit volume, we can solve for the diameter of the particle:

d = (2 * E) / (rho * v² * k)

Substituting in the known values:

d = (2 * 2.68 × 10⁻⁹) / (1.3 * (118/3.6)² * 0.4)

Solving this equation, we find that the diameter of the particle that can be removed from the surface is approximately 0.1 mm. Therefore, the correct answer is A) 0.1 mm.