For objects that are completely submerged in fluid, the submerged volume will be equal to the volume of the object itself. For objects that are floating on the surface of a fluid, only the volume under the surface of the fluid is considered. As an example, let’s say that we want to find the buoyancy force acting on a rubber ball floating in water. If the ball is a perfect sphere with a diameter of 1 meter (3. 3 ft) and it’s floating exactly halfway submerged in the water, we can find the volume of the submerged portion by finding the volume of the entire ball and dividing it in half. Since the volume of a sphere is (4/3)π(radius)3 , we know our ball’s volume is (4/3)π(0. 5)3 = 0. 524 meters3. 0. 524/2 = 0. 262 meters3 submerged.
In our example, our ball is floating in water. By consulting an academic source, we can find that water has a density of about 1,000 kilograms/meter3. The densities of many other common fluids are listed in engineering resources. One such list can be found here.
In our example, if we’re dealing with an ordinary, stationary system, we can assume that the only downward force acting on the fluid and object is the standard force of gravity — 9. 81 Newtons/kilogram.
In our example, if we’re dealing with an ordinary, stationary system, we can assume that the only downward force acting on the fluid and object is the standard force of gravity — 9. 81 Newtons/kilogram.
Let’s solve our example problem by plugging our values into the equation Fb = Vs × D × g. Fb = 0. 262 meters3 × 1,000 kilograms/meter3 × 9. 81 newtons/kilogram = 2,570 Newtons. The other units cancel each other out and leave you with Newtons.
A neutrally buoyant object will not float up to the surface or sink down to the bottom when it is in water. It will just be suspended in the fluid somewhere between the top and bottom. [4] X Research source For example, let’s say we want to know if a 20 kilogram cylindrical wooden barrel with a diameter of . 75 meters (2. 5 ft) and a height of 1. 25 meters (4. 1 ft) will float in water. This will take several steps: We can find its volume with the cylindrical volume formula V = π(radius)2(height). V = π(. 375)2(1. 25) = 0. 55 meters3. Next, assuming ordinary gravity and water with ordinary density, we can solve for the force of buoyancy on the barrel. 0. 55 meters3 × 1000 kilograms/meter3 × 9. 81 newtons/kilogram = 5,395. 5 Newtons. Now, we’ll need to find the force of gravity on the barrel. G = (20 kg)(9. 81 meters/second2) = 196. 2 Newtons. This is much less than the buoyancy force, so the barrel will float.
For the purposes of this experiment, it’s safe to assume that water has a standard density of 1000 kilograms/meter3. Unless you’re using saltwater or a different liquid entirely, most types of water will have a density close enough to this reference value that any minor difference won’t alter our results. [6] X Research source If you have an eyedropper handy, this can be very helpful for precisely leveling off the water in the inner container.
For the purposes of our example, let’s say that we’re lowering a toy car with a mass of 0. 05 kilograms into the inner container. We don’t need to know the volume of this car to calculate its buoyancy, as we’ll see in the next step.
In other words, if your object floats, the volume of the water that spills over will be equal to the volume of the object submerged under the surface of the water. If your object sank, the volume of the water that spills over will be equal to the volume of the entire object.
In our example, let’ say that our toy car sunk into the inner container and displaced about two tablespoons (. 00003 meters3). To find the mass of our water, we’d multiply this by its density: 1,000 kilograms/meters3 × . 00003 meters3 = 0. 03 kilograms.
Thus, objects with low masses but big volumes are the most buoyant types of objects. This property means hollow objects are especially buoyant. Think of a canoe — it floats well because it’s hollow in the inside, so it’s able to displace a lot of water without having a very high mass. If canoes were solid, they wouldn’t float very well at all. In our example, the car has a higher mass (0. 05 kilograms) than the water it displaced (0. 03 kilograms). This lines up with what we observed: the car sank.
