Question

For a subsonic flow over an airfoil, an increase in velocity leads to:

• A. Increase in pressure
• B. Decrease in pressure
• C. No change in pressure
• D. Zero pressure
• E. None of the above

Hint:

Always remember the inverse relationship in subsonic aerodynamics: High Velocity = Low Pressure. This is the fundamental building block for understanding lift generation.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The behavior of a fluid moving at subsonic speeds (Mach number < 1) over a solid body like an airfoil is governed by the principle of conservation of energy.
For an incompressible or low-subsonic flow, this is expressed through Bernoulli's Equation.
Step 2: Key Formula or Approach:
Bernoulli's principle for steady, inviscid, and incompressible flow states:
\[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} \]
Where \( P \) is the static pressure, \( \rho \) is the fluid density, and \( v \) is the flow velocity.
Step 3: Detailed Explanation:
In the context of flow over an airfoil, the change in height (\( h \)) is negligible, so the term \( \rho gh \) is considered constant.
The equation simplifies to: \( P + \text{Dynamic Pressure} = \text{Total Pressure} \).
As the air moves over the curved surface of an airfoil, the streamlines are compressed, causing the velocity (\( v \)) of the fluid to increase.
According to the equation, if the velocity (\( v \)) increases, the dynamic pressure term (\( \frac{1}{2} \rho v^2 \)) increases.
Since the total pressure must remain constant, the static pressure (\( P \)) must decrease to compensate for the increase in velocity.
This difference in pressure between the upper and lower surfaces of the airfoil is what generates lift.
Step 4: Final Answer:
Therefore, an increase in velocity in a subsonic flow leads to a decrease in pressure.