BUOYANCY

CE 3250

Joe Eckhardt, Mike Firestone, Christos Melistas, Meghan Vohs

What is Buoyancy?

• In simple terms, buoyancy is the ability of an object to float.

• Whether or not a given object will float is determined by the buoyant force on the object.

• This force is caused by the difference between the pressure at the top of the object, which pushes it downward and the pressure at the bottom of the object which pushes it upward. Because the pressure at the bottom of the object is always greater than the pressure at the top, every submerged object feels an upward buoyant force.

• The magnitude of this buoyant force is equal to the weight of the fluid that is displaced by the submerged object.

The weight of the water that is displaced by this block of wood is equal to the buoyant force acting on the block. (excerpt from http://www.pbs.org)

What is Buoyancy? (cont.)

• The difference between the buoyant force acting up on the object and the force due to gravity acting downward on the object will determine whether or not the object will float or sink.

• If the buoyant force is greater than the gravitational force, the object will float, but if the opposite is true, the object will sink.

Buoyancy kept the S.S. Edmund Fitzgerald afloat in the Great Lakes until water filled its hull causing the ships weight to exceed the buoyant force acting upward on it. The rest is history.

How to Calculate Buoyancy

• The buoyant force (FB) is equal to the weight of fluid the object displaces.– If an object is submerged it

displaces its total volume of fluid.

– If it is partially submerged it displaces the volume of fluid equal to its submerged volume.

– The weight of the fluid it displaces is the volume of fluid multiplied by the fluid’s specific weight.

How to Calculate BuoyancyTotally Submerged Object in Water

• Object’s Volume = 1ft3

• Specific Weight of Water (γWater) = 62.4lb/ft3

• FB = 1ft3 x 62.4lb/ft3 = 62.4lb

How to Calculate BuoyancyObject 50% Submerged in Water

• Object’s Volume = 1ft3

– Submerged volume = 0.5ft3

• Specific Weight of Water (γWater) = 62.4lb/ft3

• FB = 0.5ft3 x 62.4lb/ft3 = 31.2lb

Understanding Buoyancy

Q: An inverted spherical shell of diameter, d = 1m is used to cover a tank filled with water. What is the minimum weight the shell must be to hold itself in place?

Understanding Buoyancy (cont.)

A: Since only half the sphere is covering the tank, we only need to account for half the volume. So, V = 4/3 r3. Since only half the volume is to be accounted for, the volume that is to be used is V = 4/6 r3. So, the volume of the sphere will be 4/6 *(.5m)3 = .262m3. Then, the forces in the y-direction must be summed and set equal to zero. Our equation will be FB – W = 0. FB = Specific weight of water (W) * volume of sphere. So, our equation to solve for W will be (9,806 N/m3)*(.262m3) – W = 0. Solving for W, the minimum weight the shell must be to hold itself in place is 2,569.17N.

Who Needs Buoyancy?

• Everyone needs buoyancy!

• If you swim, boat, scuba dive, or float; you need buoyancy!!!

Buoyancy and Swimming

• Buoyancy is why most people float. Your body displaces water. When the weight of the water you displace is more than your weight you float.

• Because of buoyancy you weigh very little in water.

• You can put most of your energy into movement because you need very little to carry yourself