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# How Objects Float in Fluids

by Ron Kurtus (revised 19 February 2015)

The * way that objects float* is that at any depth in a fluid there is an upward force due to the effect of gravity on the fluid. This results in a pressure applied over an area.

If the density of an object in the fluid is greater than the density of the fluid, the object will sink. If the density is less than that of the fluid, the object will float upward due to the buoyancy from the fluid.

An object of lower density will float to the top and only be submerged by an amount according to the ratio of the densities.

Questions you may have include:

- What is the role of pressure at a depth in a fluid?
- How does the density of the object determine whether it will float?
- How do things float on the surface?

This lesson will answer those questions. Useful tool: Units Conversion

## Pressure at a depth

The fluid pressure due to gravity at a given depth is caused by the weight of the column of fluid—such as water—above that depth level. It is the same in all directions.

Pressure at depth is from weight of column

An object submerged in a fluid displaces its volume of the fluid. The upward force, or buoyancy, depends on the difference in densities between the fluid and object. Density equals the mass divided by the volume.

### Container of water

The upward and downward forces acting on a container of water that is submerged in water are equal.

"Container" of water has equal up and down pressures

Obviously, the density of the "container" is the same as the density of the fluid.

## Density determines ability to float

Whether the density of an object is greater or less than the density of the fluid will determine if it will sink or float.

### Greater density

If you put an object in a fluid that has a density that is greater than that of the fluid, the weight of the column including the object will be greater than the weight of the column with only the fluid.

For example, iron has a greater density than water. Thus a block of iron will weigh more than an equal volume of water. This means that the downward force, due to its weight, is greater than the upward force of the water at that depth. Thus the iron sinks.

Gravity pulls object with greater density downward

### Smaller density

On the other hand, if an object that was less dense than the fluid is submerged, the total weight of the column above a given depth will be less than that of the fluid.

For example, a piece of wood is typically less dense than water. Submerging the wood in the water results in an upward force—or buoyancy—that is greater than the downward force. The piece of wood tends to float upward.

Less dense object is pushed upward

Another example concerns a balloon filled with helium. Since the density of helium is less than that of air, the buoyant force pushes the balloon upward. That is, the upward pressure on the bottom of the balloon is greater than the downward pressure due to the weight of the balloon and column of air above it.

## Floating on surface

An object with less density than the fluid will float upward until it reaches the surface of the fluid. At that position, only part of the object is submerged.

Pressure equilibrium when floating

How much is submerged depends on the density of the object, as compared to the fluid. The equation is:

ρ_{f}V_{s}= ρ_{o}V_{o}

where

**ρ**is the density of the fluid_{f}**V**is the volume submerged_{s}**ρ**is the density of the object_{o}**V**is the volume of the whole object_{o}**ρV**is**ρ**times**V**

### Floating wood

For example, consider a block of pine wood floating in water. Pine has a density of 0.53 gm/cm^{3}. Pure water has a density of 1.0 gm/cm^{3}. Thus 1.0***V _{s}** = 0.53*

**V**. The volume submerged would be 0.53 times the total volume of the object.

_{o}If the block of pine had a volume of 100 cm^{3}, then slightly over 1/2 of it would be below the waterline. You can find the percentage by multiplying by 100%. Thus, 53% would be below the waterline and 47% would be above the waterline (100% - 53% = 47%).

### Metal ship

Although the density of steel is 7.86, which is much greater than the density of water, a ship made of steel will float. The reason is because the boat is hollow and not made of solid steel. Measuring the weight of the steel and dividing by the total volume of the ship will result in a density less than 1.0, the density of water. In fact, often the density of a ship is about 0.3 gm/cm^{3} before it is loaded with goods.

Metal ship has density less than water

## Summary

There is an upward force due to the effect of gravity at any depth in a fluid. If the density of an object in the fluid is greater than the density of the fluid, the object will sink. If the density is less than the fluid, the object will float. An object will float to the top and only be submerged by an amount according to the ratio of the densities.

Use your knowledge to help others

## Resources and references

### Websites

**Why can heavy steel ships float?** - Science Niblets

**Buoyancy** - HyperPhysics

### Books

**Top-rated books on Physics of Fluids**

**Fluid Mechanics** by Ira M. Cohen and Pijush K. Kundu, Academic Press (2004) $74.95

**Fundamentals of Fluid Mechanics** by Bruce R. Munson, Donald F. Young, Theodore H. Okiishi; Wiley (2001) $37.95

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## How Objects Float in Fluids