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Q & A: buoyant forces

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Most recent answer: 02/21/2013
Q:
Buoyant force concept and terminal velocity? My aerodynamics book(John Anderson Aerodynamics) say that whenever a body moves through a fluid, there are only two types of forces acting on the body. 1. Pressure force that acts perpendicular to the plane of the body and the other is the drag force that acts parallel to the objects velocity. Also i read an article that buoyant force is related to static fluids not moving fluids. Now, i was working on a concept of terminal velocity of an object moving through air in the Z direction. According to my concept, the air is continuously in motion and hence its a dynamic fluid. So, accordingly, the body falling through air will experience friction drag parallel to the velocity and pressure force perpendicular to the velocity. But as i was going through the derivation of the terminal velocity, they have counted the buoyant force in which is completely confusing me. If there is buoyant force when the body is moving through a moving fluid then when an aircraft is cruising at an altitude, why do they not mention the buoyant force? Rather they say that the vertical force is the pressure force which is also the lift force. I am really confused when to apply buoyancy and the concept of this pressure force which acts perpendicular to the plane of the body Please help me.
- surajit das (age 21)
Lawrence/Ks/US
A:
The buoyant forces don't go away when an object moves through a fluid. However, for airplanes in air the buoyant force is negligible, because the density of the airplane is enormous compared to the density of the air. For a balloon, the buoyant forces are worth keeping track of. The buoyant forces point up regardless of how the body is oriented, since the pressure in the fluid varies in the up-down direction.

Also, in general, frictional forces don't have to be exactly along the direction of relative motion. For non-spherical objects in general you get the frictional force vector by multiplying  the relative velocity vector by a tensor, not just a number. Sailors use this principle a lot- otherwise they'd not be able to control their direction.

Mike W.

(published on 02/20/2013)

Follow-Up #1: naming pressure and friction in fluids

Q:
According to my aerodynamics book, the only two way nature has to communicate the forces when an object moves through a fluid are:- 1. Pressure force acting normal to the plane of the body.2. Friction force between the air molecules and the aircraft body. I would like to know about the pressure force that acts normal to the plane of the body. How does this force originate? My intuition says that whenever a body moves a fluid such as air(say), the air molecules hit the body randomly at different angles. So, we can resolve each of this force in the X and Z direction. Is the X component of the net force called the friction/drag force and the Z component of the net force is called the pressure force/Normal force.
- surajit das (age 21)
ks
A:
Any force normal to the local surface plane is called pressure and any force along a direction in that local surface plane is called friction, locally.

There are several ways that the pressure can originate. In equilibrium any gas exerts a pressure because it "wants" to expand, meaning it can lower its free energy by expanding. That pressure gets smaller the farther up you go, so it provide some buoyant force- more pressure pushes up from the bottom than pushes down from the top. Additional pressure terms show up out of equilibrium because of the way the relative motion of the fluid and the object changes the distribution of gas molecules and their velocities.

As for the word "drag", I believe it is often used to describe the net force on an object resisting its motion through a fluid medium. Since at high speeds. part of the force comes from a build-up of pressure in front and a reduction of pressure behind, the categories "pressure" and "drag" aren't quite mutually exclusive.  I bet we'll hear more from some reader who knows more about fluid mechanics and can refine these definitions more.

Mike W.

(published on 02/21/2013)

Follow-up on this answer.