Chapter 4: Problem 30

The pressure in the air along the upper surface of an aircraft's wing (in flight) is lower than the pressure along the lower surface. Compare the speed of the air flowing over the wing to that of the air flowing under the wing.

Short Answer

Expert verified

Answer: Based on Bernoulli's principle, the speed of the air flowing over the wing is faster than the speed of the air flowing under the wing.

Step by step solution

Recall Bernoulli's principle

Bernoulli's principle states that the total pressure along a streamline is constant. Mathematically, this principle can be expressed as: P + 0.5 * rho * V^2 + rho * g * h = constant Where P is the static pressure, rho is the fluid density, V is the velocity of the fluid, g is the gravitational acceleration, and h is the height above a reference level.

Apply Bernoulli's principle to the upper and lower surfaces of the wing

Since the pressure on the upper surface of the wing is lower than the pressure on the lower surface, the velocity of the fluid on the upper surface must be higher to compensate, according to Bernoulli's principle. Evaluate the above equation separately for the upper(surface 1) and lower(surface 2) surfaces of the wing: P1 + 0.5 * rho * V1^2 + rho * g * h1 = constant P2 + 0.5 * rho * V2^2 + rho * g * h2 = constant

Subtract the equations to eliminate constant

Subtract the equation for the upper surface from the equation for the lower surface to eliminate the constant: P2 - P1 + 0.5 * rho * (V2^2 - V1^2) + rho * g * (h2 - h1) = 0

Assume negligible change in height

Since the wing's thickness is relatively small compared to the height of the aircraft above the ground, we can assume that the change in height (h2 - h1) is negligible. The equation then simplifies to: P2 - P1 + 0.5 * rho * (V2^2 - V1^2) = 0

Solve for the difference between the velocities

Rearrange the equation to find the difference between the squares of the velocities of the air flow over and under the wing: V2^2 - V1^2 = (P1 - P2) / (0.5 * rho) Now we cannot solve for V1 and V2 directly, but since P1 < P2, according to the problem, the right-hand side of the equation is positive. So, V2^2 > V1^2, which implies that V2 > V1.

Conclusion

Based on our analysis using Bernoulli's principle, we can conclude that the speed of the air flowing over the wing (V1) is faster than the speed of the air flowing under the wing (V2).

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

The pressure in the air along the upper surface of an aircraft's wing (in flight) is lower than the pressure along the lower surface. Compare the speed of the air flowing over the wing to that of the air flowing under the wing.

Short Answer

Step by step solution

Recall Bernoulli's principle

Apply Bernoulli's principle to the upper and lower surfaces of the wing

Subtract the equations to eliminate constant

Assume negligible change in height

Solve for the difference between the velocities

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Engineering Physics

Quantum Physics

Torque and Rotational Motion

Measurements

Turning Points in Physics

Study anywhere. Anytime. Across all devices.