An airplane has a rectangular wing with a chord length of 8 ft. If the airplane is flying at 200 knots TAS
and at 20,000 ft density altitude, find the Reynolds number at the trailing edge of the wing.

To find the Reynolds number at the trailing edge of the wing, we can use the following formula for Reynolds number (\(Re\)):

\[
Re = \frac{{\rho \cdot V \cdot L}}{{\mu}}
\]

Where:
- \( \rho \) is the air density
- \( V \) is the velocity (true airspeed, TAS)
- \( L \) is the characteristic length (in this case, the chord length of the wing)
- \( \mu \) is the dynamic viscosity of air

### Step-by-Step Solution

1. **True Airspeed (TAS):**
   The airplane is flying at 200 knots TAS. We need to convert this to feet per second (ft/s).

   1 knot = 1.68781 ft/s, so:
   \[
   200 \, \text{knots} = 200 \times 1.68781 = 337.562 \, \text{ft/s}
   \]

2. **Air density (\( \rho \)):**
   At a density altitude of 20,000 feet, the air density \( \rho \) is approximately \( 0.001267 \, \text{slug/ft}^3 \).

3. **Chord length (L):**
   The chord length is given as 8 feet.

4. **Dynamic viscosity (\( \mu \)):**
   At an altitude of 20,000 feet, the dynamic viscosity of air is approximately \( 3.737 \times 10^{-7} \, \text{slug/ft} \cdot \text{s} \).

### Now, substitute the values into the Reynolds number formula:

\[
Re = \frac{{0.001267 \, \text{slug/ft}^3 \cdot 337.562 \, \text{ft/s} \cdot 8 \, \text{ft}}}{{3.737 \times 10^{-7} \, \text{slug/ft} \cdot \text{s

Learn how to calculate the Reynolds number at the trailing edge of an airplane wing flying at 200 knots TAS and 20,000 ft density altitude. This problem involves fluid mechanics and aerodynamics, using the Reynolds number formula with specific data points. Suitable for advanced learners and professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation