Fluids and Buoyancy

Buoyancy is the topic where a steel ship floating stops being a puzzle. The answer is density, and density is about the whole object rather than the material it is made of.

Density

Density = mass / volume.

Water is 1 gram per cubic centimeter, or about 62.4 pounds per cubic foot, and it is the reference everything is compared against.

Density belongs to the object, not just its material. A steel ship is mostly air by volume, so its average density is well below steel's - and that is why it floats while a steel bar sinks. The same steel, shaped differently, gives a different density.

Specific gravity is an object's density compared with water's. Above 1 sinks, below 1 floats, which is the same rule with the units removed.

Floating and sinking

Enlarge

Zoom in

Two forces act on anything in a fluid: its weight downward and the buoyant force upward.

A sinking object still has a buoyant force on it. It is simply not enough. That is why things weigh less in water than out of it, and why lifting something from a lake gets suddenly harder as it breaks the surface.

Archimedes' principle

The buoyant force on an object equals the weight of the fluid it displaces.

Two cases follow, and they are different:

A floating object displaces its own weight of fluid. A 2,000-pound boat pushes aside exactly 2,000 pounds of water, whatever its size.

A fully submerged object displaces its own volume, and the buoyant force is the weight of that volume of fluid, which is less than the object's weight or it would not have sunk.

A block displaces 3 cubic feet of water. What is the buoyant force on it?

Water weighs about 62.4 pounds per cubic foot, so 3 times 62.4 is about 187 pounds of upward force.

Denser fluids push harder. You float more easily in salt water than fresh, because salt water is denser, so a given volume displaced weighs more. That is asked directly.

Specific gravity and the hydrometer

Enlarge

Zoom in

Specific gravity compares a liquid's density with water's. Water is 1. A liquid with a specific gravity of 0.8 is less dense than water and floats on it.

A hydrometer measures specific gravity. It is a weighted float: it floats higher in a denser liquid, and the reading is taken where the surface meets its scale. It is how a battery's state of charge is checked - the electrolyte's density falls as the battery discharges - and how antifreeze strength is tested.

Flow

Flow rate is volume per unit time - gallons per minute, cubic feet per second.

In a pipe carrying a steady flow, the same volume passes every point each second. So if the pipe narrows, the fluid must speed up to get the same volume through a smaller opening.

Narrow means faster; wide means slower.

That is why a thumb over a hose end makes the water shoot further, and why a river runs fast through a gorge and slowly across a flood plain.

Flow rate = area x velocity, so halving the area doubles the velocity for the same flow.

Faster-moving fluid has lower pressure, which is the effect behind lift on a wing and behind a carburetor drawing fuel. At this level it is worth recognizing the relationship rather than calculating with it.

Viscosity

Viscosity is a fluid's resistance to flowing. Honey is viscous; water is not.

Viscosity falls as temperature rises for a liquid, which is why cold oil is thick and why an engine is hardest to turn over on a cold morning. That connects to the lubrication lesson in Auto and Shop.

What you can skip

Across the 42 questions on this topic in our bank:

• Bernoulli's principle never appears on this topic.
• Archimedes by name. Archimedes is named once; the questions apply the principle - an object is pushed up by the weight of the fluid it displaces - without naming it.

Where people lose points

Comparing the object's material density instead of its average density. A steel ship floats.

Thinking a sinking object has no buoyant force. It has one; it is just smaller than the weight.

Saying a floating object displaces its own volume. It displaces its own weight; a submerged one displaces its volume.

Thinking a narrower pipe slows the flow. It speeds it up.

Forgetting that fluid density matters, so the same object floats differently in salt and fresh water.

Work one in under a minute

A 500-pound raft floats on a lake. How much water does it displace, and what is the buoyant force on it?

It floats, so it displaces its own weight: 500 pounds of water.

The buoyant force equals the weight of that displaced water, so 500 pounds - which must be true anyway, because a floating object is in equilibrium and its weight has to be balanced exactly.

The raft's size, shape and material never entered the answer, and they did not need to.

Where this leads

Density and pressure together are what hydraulics and weather both rest on, and viscosity is where lubrication begins.