An aircraft is cruising at a speed of 500 km.hr-1 at an altitude where the atmospheric density is 0.25 kg.m-3  and the absolute viscosity is 1.45 x 10-5 Pa.s.  Determine the Reynolds number based on the wing chord, which for this aircraft is 4.2 m.

To determine the Reynolds number for the aircraft based on the wing chord, we use the following formula for Reynolds number (\(Re\)):

\[ Re = \frac{\rho v L}{\mu} \]

where:
- \(\rho\) is the atmospheric density (\(0.25 \, \text{kg/m}^3\))
- \(v\) is the velocity of the aircraft (\(500 \, \text{km/hr}\))
- \(L\) is the characteristic length, in this case, the wing chord (\(4.2 \, \text{m}\))
- \(\mu\) is the dynamic viscosity (\(1.45 \times 10^{-5} \, \text{Pa} \cdot \text{s}\))

First, we need to convert the velocity from \(\text{km/hr}\) to \(\text{m/s}\):

\[ v = 500 \, \text{km/hr} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{hr}}{3600 \, \text{s}} = \frac{500 \times 1000}{3600} \, \text{m/s} = 138.89 \, \text{m/s} \]

Now we can substitute the values into the Reynolds number formula:

\[ Re = \frac{0.25 \, \text{kg/m}^3 \times 138.89 \, \text{m/s} \times 4.2 \, \text{m}}{1.45 \times 10^{-5} \, \text{Pa} \cdot \text{s}} \]

Calculate the numerator:

\[ 0.25 \times 138.89 \times 4.2 = 145.8345 \, \text{kg} \cdot \text{m} / \text{s}^2 \]

Now, divide by the dynamic viscosity:

\[ Re = \frac{145.8345}{1.45 \times 10^{-5}} = 1.005755 \times 10^7 \]

So, the Reynolds number is:

\[ Re \approx 1.01 \times 10^7 \]

Would you like more details or have any questions?

Here are 5 questions you might want to ask next:
1. How does the Reynolds number affect the flow characteristics around the wing?
2. Can you explain the significance of the Reynolds number in fluid dynamics?
3. What are typical Reynolds numbers for different types of aircraft?
4. How would changes in altitude affect the Reynolds number for this aircraft?
5. What are the implications of a high Reynolds number for aircraft design?

Tip: When working with unit conversions, ensure all your units are consistent before substituting values into formulas.

Learn how to calculate the Reynolds number for an aircraft cruising at 500 km/hr with an atmospheric density of 0.25 kg/m^3 and dynamic viscosity of 1.45 x 10^-5 Pa.s. Understand the impact of Reynolds number on fluid dynamics around the wing chord. Get detailed steps and formulas.

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