Fluid Mechanics: Buoyancy Buoyant Force The buoyant force is equal to the weight of the volume of fluid displaced by the object Pages 193-197 in book

Buoyancy and Fluids Buoyant forces act on all objects that are immersed in a fluid. Liquids and gasses but not solids are fluids. The buoyant force is the difference between the forces acting on the bottom and top of an object immersed in a fluid. (sans gravity) This is also known as Archimedes’ Principle. Buoyant force = weight of displaced fluid.

A Column of Cubes of Water mg 2 Fy2 Fy1 Fy = 0 Fy2 - Fy1– mg = 0 4 3 2 Air Water 1 mg Fy3 Fy2 3 Fy = 0 Fy3 - Fy2 – mg = 0 mg 1 No Force from above Fy1 Fy = 0 Fy1 – mg = 0

Buoyant force always acts up In a column of cubes of water, the buoyant force acting up balances out the weight of the cube acting down for all cubes in the column. This may not be the case if a cube of water is replaced with a cube of some other material. The cube of material will rise if its weight is less than the buoyant force. The cube of material will sink if its weight is greater than the buoyant force

Cube 3 is Now a Cube of Lead mg Fy3 Fy2 3 Fy < 0 Fy3 - Fy2 - mg < 0 4 3 2 Air Water Lead 1 The forces from the water (Fy3, - Fy2) remain the same, but mg increases because a cube of lead has more mass than a cube of water. This also makes sense, because the buoyant force is equal to the weight of the volume of water displaced, and if the cubes are the same volume, than the weight of water displaced will be the same.

Cube 3 is Now a Cube of Wood mg Fy3 Fy2 3 Fy > 0 Fy3 - Fy2 - mg > 0 4 3 2 Air Water Wood 1 The forces from the water (Fy3, - Fy2) remain the same, but mg will decrease because a cube of wood has less mass than that of water. This also makes sense, because the buoyant force is equal to the weight of the volume of water displaced, and if the cubes are the same volume, than the weight of water displaced will be the same.

Center of Buoyancy Every particle of fluid pushes on every square mm of an on object immersed in it. Just like the Center of Gravity of an object is the point where all of the weight can be considered to act, Center of Buoyancy is the point where all of the buoyant force can be considered to act. The Center of Buoyancy is located at the center of volume of an object. For a human this is closer to the lungs than the center of gravity.

Center of Buoyancy When a person lays out in the water, the force of gravity and the buoyant force are not lined up, so a net torque is produced and the legs rotate down, while the chest rotates up. mg Buoyant Force Hyper-extending at the hips brings the CG of body in line with center of buoyancy. In this position, zero net torque exists, and thus no rotation will be experienced Buoyant Force mg

Why a Hot Air Balloon Rises The air in the atmosphere produces a buoyant force on all objects. Hot air balloons use this to their advantage. Hot air doesn’t inherently rise because it is hot. Rather, it rises because it occupies more volume while maintaining the same mass. Thus the buoyant force overcomes the force of gravity pulling down on the balloon.

Helium in a Basketball If you pumped one basketball up with 5 lbs of air, and a second basketball up with 5 lbs of helium and both basketballs were the same volume, which one would be lighter? What if you pumped twice as many lbs of helium into the second ball as you did air into the first ball and they maintained the same volume?