Calculate the viscosity of air.
Understand the Problem
The question is asking for the calculation of the viscosity of air, which involves applying the appropriate formulas and considering factors such as temperature and pressure.
Answer
The viscosity of air at 20°C is approximately $\mu \approx 1.81 \times 10^{-5} \, \text{kg/(m·s)}$.
Answer for screen readers
The viscosity of air at 20°C (293.15 K) is approximately $\mu \approx 1.81 \times 10^{-5} , \text{kg/(m·s)}$.
Steps to Solve
- Identify the viscosity formula for air To calculate the viscosity of air, we can use the Sutherland's equation, which is given by: $$ \mu = \mu_0 \left( \frac{T}{T_0} \right)^{3/2} \left( \frac{T_0 + S}{T + S} \right) $$ where:
- $\mu$ is the dynamic viscosity at temperature $T$,
- $\mu_0$ is the reference viscosity at temperature $T_0$,
- $S$ is Sutherland's constant.
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Assign known values Typically, the reference viscosity of air $\mu_0$ at $T_0 = 273.15 , K$ (0°C) is approximately $1.716 \times 10^{-5} , \text{kg/(m·s)}$ and Sutherland's constant $S$ for air is about 110.4 K. You need to specify the temperature $T$ in Kelvin for your calculation.
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Plugging in the temperature values Insert the values into the Sutherland’s equation. Assume, for example, $T = 293.15 , K$ (20°C): $$ \mu = 1.716 \times 10^{-5} \left( \frac{293.15}{273.15} \right)^{3/2} \left( \frac{273.15 + 110.4}{293.15 + 110.4} \right) $$
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Calculating the viscosity Calculate the first part of the equation, then the second part and finally multiply them: Calculate $\left( \frac{293.15}{273.15} \right)^{3/2}$ and $\left( \frac{383.55}{403.55} \right)$, then combine the results to find $\mu$.
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Final result After performing the calculations, you will get the viscosity of air at the given temperature.
The viscosity of air at 20°C (293.15 K) is approximately $\mu \approx 1.81 \times 10^{-5} , \text{kg/(m·s)}$.
More Information
The viscosity of a fluid depends on temperature; as temperature increases, the viscosity usually decreases. This behavior can be particularly useful in applications like aerodynamics and meteorology.
Tips
- Not converting temperatures to Kelvin before using them in calculations. Always ensure temperatures are in Kelvin for consistent results.
- Forgetting to apply the entire Sutherland's equation, especially in a multi-step calculation can lead to errors.
