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When a body is acted upon by a constant force, its resulting acceleration is inversely proportional to the mass of the body and is directly proportional to the applied force. This takes into account the factors involved in overcoming Newton’s First Law. It covers both changes in direction and speed, including starting up from rest (positive acceleration) and coming to a stop (negative acceleration or deceleration). Newton’s Third Law: “For every action, there is an equal and opposite reaction.”
In an airplane, the propeller moves and pushes back the air; consequently, the air pushes the propeller (and thus the airplane) in the opposite direction—forward. In a jet airplane, the engine pushes a blast of hot gases backward; the force of equal and opposite reaction pushes against the engine and forces the airplane forward.
Magnus Effect
In 1852, the German physicist and chemist, Heinrich Gustav Magnus (1802–1870), made experimental studies of the aerodynamic forces on spinning spheres and cylinders. (The effect had already been mentioned by Newton in 1672, apparently in regard to spheres or tennis balls). These experiments led to the discovery of the Magnus Effect, which helps explain the theory of lift.
3-5
Flow of Air Against a Nonrotating Cylinder
If air flows against a cylinder that is not rotating, the flow of air above and below the cylinder is identical and the forces are the same. [Figure 3-3A]
A Rotating Cylinder in a Motionless Fluid
In Figure 3-3B, the cylinder is rotated clockwise and observed from the side while immersed in a fluid. The rotation of the cylinder affects the fluid surrounding the cylinder. The flow around the rotating cylinder differs from the flow around a stationary cylinder due to resistance caused by two factors: viscosity and friction.
Viscosity
Viscosity is the property of a fluid or semifluid that causes it to resist flowing. This resistance to flow is measurable due to the molecular tendency of fluids to adhere to each other to some extent. High-viscosity fluids resist flow; low-viscosity fluids flow easily.
Similar amounts of oil and water poured down two identical ramps demonstrate the difference in viscosity. The water seems to flow freely while the oil flows much more slowly. (An excellent website to demonstrate types of viscosity is found at the Cornell University website on viscosity, located at http://atlas.geo.cornell.edu/education/student/viscosity.html.)
Since molecular resistance to motion underlies viscosity, grease is very viscous because its molecules resist flow. Hot lava is another example of a viscous fluid. All fluids are viscous and have a resistance to flow whether this resistance is observed or not. Air is an example of a fluid whose viscosity can not be observed.
Since air has viscosity properties, it will resist flow to some extent. In the case of the rotating cylinder within an immersed fluid (oil, water, or air), the fluid (no matter what it is) resists flowing over the cylinder’s surface. Friction
Friction is the second factor at work when a fluid flows around a rotating cylinder. Friction is the resistance one surface or object encounters when moving over another and exists between a fluid and the surface over which it flows.
If identical fluids are poured down the ramp, they flow in the same manner and at the same speed. If one ramp’s surface is coated with small pebbles, the flow down the two ramps differs significantly. The rough surface ramp impedes the flow of the fluid due to resistance from the surface (friction). It is important to remember that all surfaces, no matter how smooth they appear, are not smooth and impede the flow of a fluid. Both the surface of a wing and the rotating cylinder have a certain roughness, albeit at a microscopic level, causing resistance for a fluid to flow. This reduction in velocity of the airflow about a surface is caused by skin friction or drag.
When passing over a surface, molecules actually adhere (stick, cling) to the surface, illustrated by the rotating cylinder in a fluid that is not moving. Thus,
1. In the case of the rotating cylinder, air particles near the surface that resist motion have a relative velocity near zero. The roughness of the surface impedes their motion.
2. Due to the viscosity of the fluid, the molecules on the surface entrain, or pull, the surrounding flow above it in the direction of rotation due to the adhesion of the fluid to itself.
There is also a difference in flow around the rotating cylinder and in flow around a nonrotating cylinder. The molecules at the surface of the rotating cylinder are not in motion relative to the cylinder; they are moving clockwise with the cylinder. Due to viscosity, these molecules entrain others above them resulting in an increase in fluid flow in the clockwise direction. Substituting air for other fluids results in a higher velocity of air movement above the cylinder simply because more molecules are moving in a clockwise direction.
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Pilot's Handbook of Aeronautical Knowledge飞行员航空知识手册(38)
