Question

Bernoulli's equation is the reason for the upward force that permits airplane flight. Which statement best summarizes the equation's relationship to flight? A. The speed of airflow is equal on the top and bottom of a wing, resulting in nonturbulent flight. B. The speed of airflow is greater over the curved top of the wing, resulting in less pressure on the top of the wing and the production of a net upward force on the wing, in turn resulting in flight. C. The speed of airflow on the flat bottom of the wing is greater than over the curved top of the wing, resulting in more pressure below the wing and the production of a net upward force on the wing, in turn resulting in flight. D. The weight of the wing is directly proportional to the weight of the air it displaces.

Short answer

B

Step-by-step solution

Understand Bernoulli's Principle

Bernoulli's Principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or potential energy of the fluid.

Apply Bernoulli's Principle to Airplane Wings

In the context of an airplane wing, air flows faster over the curved top surface of the wing compared to the flat bottom surface.

Analyze the Pressure Differences

Due to Bernoulli’s Principle, the faster airflow over the top of the wing results in lower pressure, while the slower airflow beneath the wing results in higher pressure.

Determine the Force Produced

The difference in pressure between the top and bottom surfaces of the wing creates an upward force, known as lift.

Select the Correct Statement

Based on the explanation, the correct statement is: B. The speed of airflow is greater over the curved top of the wing, resulting in less pressure on the top of the wing and the production of a net upward force on the wing, in turn resulting in flight.

Key concepts

Bernoulli's Principle

Bernoulli's Principle is a fundamental concept in fluid dynamics. It states that an increase in the speed of a fluid results in a decrease in its pressure or potential energy. This principle is crucial to understanding why and how airplanes fly. It is named after Daniel Bernoulli, a Swiss mathematician and physicist. When applied to air flow over an airplane wing, Bernoulli's Principle helps explain the creation of lift, allowing airplanes to become airborne and stay in flight.

Aerodynamics

Aerodynamics is the study of how gases interact with moving objects. In aviation, it specifically refers to how air flows over the wings and body of an aircraft. Understanding aerodynamics is crucial for designing efficient aircraft that can generate the necessary lift to overcome gravity. Factors such as the shape of the wing (airfoil), drag, lift, and thrust play significant roles in aerodynamics. The airfoil shape, with its curved top and flatter bottom, is essential in manipulating air pressure differences according to Bernoulli's Principle.

Air Pressure Difference

Air pressure difference is at the heart of how lift is generated. Bernoulli's Principle tells us that where there is high speed, there is low pressure, and vice versa. On an airplane wing, air travels faster over the curved upper surface than the flat lower surface. This speed difference results in lower pressure on top of the wing and higher pressure underneath. The pressure difference creates an upward force, or lift, that allows the airplane to rise off the ground and remain airborne.

Without this pressure differential, airplanes would not be able to achieve lift, making flight impossible.

Fluid Dynamics

Fluid dynamics is the branch of physical science that deals with the flow of fluids. Both liquids and gases are considered fluids because they can change shapes and flow. In aviation, fluid dynamics helps us understand how air (a fluid) interacts with the aircraft surfaces. By applying the principles of fluid dynamics, engineers can predict the behavior of air over the wings and optimize the design for better performance.

Central concepts in fluid dynamics include the continuity equation, explaining how fluid mass remains constant in a flow, and Bernoulli’s equation, describing the behavior of fluid under varying conditions.

Lift Force

Lift force is the key force that allows an airplane to fly. It is the result of pressure differences described by Bernoulli’s Principle. Lift acts perpendicular to the oncoming airflow and works to counteract the weight of the airplane. By generating enough lift, an airplane can not only take off but also maintain steady flight.

Several factors influence lift force, including the airspeed, the wing's surface area, and the angle of attack. Lift can be increased by changing any of these factors, but must always be balanced with other forces such as drag and thrust to ensure stable flight.