what is the terminal velocity of 5 µm particle with a density of 8.90 grams/cm^3
To calculate the terminal velocity of a particle, we need to use the terminal velocity equation:
v = √((2 * m * g) / (ρ * A * Cd))
Where:
- v is the terminal velocity of the particle.
- m is the mass of the particle.
- g is the acceleration due to gravity (approximately 9.8 m/s²).
- ρ is the density of the fluid (air in this case).
- A is the cross-sectional area of the particle.
- Cd is the drag coefficient of the particle.
To calculate the terminal velocity of a 5 µm (micrometer) particle with a density of 8.90 grams/cm³, we need to convert the units and determine the cross-sectional area and drag coefficient.
1. Convert the particle's density:
Density = 8.90 grams/cm³ = 8900 kg/m³
2. Calculate the mass of the particle:
We need to know the volume and density of the particle to calculate its mass. Since the particle is spherical, we can use the volume formula for a sphere:
Volume = (4/3) * π * r³
Where r is the radius of the particle. The radius of a 5 µm particle is 2.5 µm (half of the diamater). Convert the radius to meters:
r = 2.5 µm = 2.5 * 10^-6 m
Calculate the volume of the particle:
Volume = (4/3) * π * (2.5 * 10^-6 m)³
3. Calculate the mass of the particle using the volume and density:
Mass = Density * Volume
4. Determine the cross-sectional area of the particle:
The cross-sectional area depends on the shape of the particle. Since the shape is not specified, we'll assume it to be a circular shape. The cross-sectional area of a circle is given by:
A = π * r²
Where r is the radius of the particle.
5. Find the drag coefficient:
The drag coefficient depends on the shape and size of the particle. Since the specifics of the particle are not mentioned, we'll need more information or make assumptions (e.g., assume a well-defined shape like a sphere or use an average value).
Once you have the values for the mass, density, cross-sectional area, and drag coefficient, you can substitute them into the terminal velocity equation to calculate the final answer.