Calculating Reynolds Number for a Thrown Ball in Air
Calculation of Reynolds Number
Calculate the Reynolds number for a ball with a 5.0 cm diameter thrown at 19.2 m/s through air with density of 1.25 kg/m3. The viscosity of the air is 1.83 * 10^-5 Pa.s.
Final answer: The Reynolds number for the ball thrown through air is approximately 1.6 * 10^5.
Explanation: The Reynolds number is a dimensionless quantity used in fluid mechanics to predict the flow regime of a fluid. It is calculated using the formula:
Reynolds number = (density * velocity * diameter) / viscosity
In this case, we have the following values:
- Diameter of the ball: 5.0 cm
- Velocity of the ball: 19.2 m/s
- Density of air: 1.25 kg/m^3
- Viscosity of air: 1.83 * 10^-5 Pa.s
Substituting these values into the formula, we get:
Reynolds number = (1.25 kg/m^3 * 19.2 m/s * 0.05 m) / (1.83 * 10^-5 Pa.s)
Simplifying the expression, we have:
Reynolds number = 1.6 * 10^5
Therefore, the Reynolds number for the ball thrown through air is approximately 1.6 * 10^5.
Calculate the Reynolds number for a different scenario where the diameter of the ball is increased to 8.0 cm while maintaining the same velocity and air properties. To calculate the Reynolds number with the new diameter of 8.0 cm, we can use the same formula as before: Reynolds number = (density * velocity * diameter) / viscosity Substituting the new diameter value into the formula, we get: Reynolds number = (1.25 kg/m^3 * 19.2 m/s * 0.08 m) / (1.83 * 10^-5 Pa.s) Reynolds number = 2.56 * 10^5 Therefore, with the increased diameter of 8.0 cm, the Reynolds number for the ball thrown through air would be approximately 2.56 * 10^5.