Calculating the Terminal Velocity of a Gold Particle in Water
Calculating the Terminal Velocity of a 10 µm Gold Particle in Water
When it comes to calculating the terminal velocity of a particle in a fluid, various properties such as density, viscosity, and size come into play. In this scenario, we are tasked with determining the terminal velocity of a 10 µm gold particle in water.
Final answer:
The terminal velocity of a 10 µm gold particle in water is calculated using the formula for terminal velocity taking into consideration the properties of both the particle and the fluid. Plugging in the given values, the terminal velocity comes out to be approximately 0.00036 m/s.
Explanation:
The terminal velocity is defined as the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration. This occurs when the force due to gravity equals the drag force. To calculate the terminal velocity of a 10 µm gold particle falling in water, we use the formula: v = (2/9) * (r^2) * g * (ρ - ρ') / µ.
Where:
v is the terminal velocity,
r is the radius of the particle,
g is the acceleration due to gravity,
ρ is the density of the particle,
ρ' is the density of the fluid, and
µ is the dynamic viscosity of the fluid.
Substituting the given values into the formula, we get: v = (2/9) * (5 * 10^-6 m)^2 * (9.81 m/s^2) * (15600 kg/m^3 - 1000 kg/m^3) / (0.01 kg/m.s). On performing the calculations, we get the value for terminal velocity as about 0.00036 m/s.