The buoyancy is a force that acts in the opposite direction to gravity on all objects immersed in a fluid. The weight pushes the object onto the fluid (liquid or gas) while the buoyancy brings it up, counteracting gravity. In general terms, the hydrostatic force can be calculated by the formula F.b = Vs × D × g, where Fb is the hydrostatic force, V.s is the immersed volume, D is the density of the fluid in which the object is placed and g is the acceleration of gravity. To know how to calculate the buoyancy of an object, read this guide.
Steps
Method 1 of 2: Using the Hydrostatic Boost Formula
Step 1. Find the volume of the submerged portion of the object
The hydrostatic force is directly proportional to the submerged volume of the object: the more it is immersed in the liquid, the greater the hydrostatic force acting on it. This action is detected on any object placed in a fluid, so the first step to calculate this force should always be the evaluation of this volume which, for this formula, should be indicated in meters3.
- For completely immersed objects, this volume is equivalent to the volume of the object itself. For those that float on the surface, however, only the underlying part must be considered.
- As an example, suppose we want to consider the hydrostatic force of a rubber ball in water. If it is a perfect sphere with a diameter of 1 meter and if it is exactly half out and half under the water, we can find the immersed volume by calculating that of the whole ball and dividing it by half. Since the volume of a sphere is (4/3) π (radius)3, we know that that of our ball is (4/3) π (0, 5)3 = 0.524 meters3. 0, 524/2 = 0, 262 meters3 IN the liquid.
Step 2. Find the density of the fluid
The next step in the process of finding the hydrostatic force is to define the density (in kilograms / meters3) of the liquid in which the object is immersed. Density is a measure of the weight of an object or substance relative to its volume. Given two objects of equal volume, the one with the highest density will weigh more. As a general rule, the greater the density of the fluid in which an object is immersed, the greater the buoyancy. With fluids, it is usually easier to find the density by simply looking at the tables referring to the material.
- In our example, the ball is floating in water. Consulting any textbook, we find that the density of water is about 1,000 kilogram / meter3.
- The densities of many other common fluids are shown in the technical tables. A list of this kind can be found here.
Step 3. Find the force due to gravity, ie the weight force (or any other downward force)
Whether the object floats or is completely submerged in the fluid, it is always and in any case subject to gravity. In the real world, this constant is worth approx 9, 81 newtons / kilogram. Furthermore, in situations where another force acts, such as the centrifugal one, the force must be considered total which acts downwards for the entire system.
- In our example, if we are dealing with a simple static system, we can assume that the only force acting downward in the object placed in the fluid is standard gravity - 9, 81 newtons / kilogram.
- However, what would happen if our ball floated in a bucket of water that was rotated horizontally in a circle at great strength? In this case, assuming the bucket is rotated fast enough so that neither the water nor the ball come out, the force that pushes down in this situation would come from the centrifugal force used to rotate the bucket, not from Earth's gravity..
Step 4. Multiply volume × density × gravity
When you know the volume of the object (in meters3), the density of the fluid (in kilograms / meters3) and weight force (or that, in your system, that pushes down), finding buoyancy force is simple. Just multiply the three quantities to get a result in Newtons.
We solve our problem by inserting the values found in equation Fb = Vs × D × g. F.b = 0, 262 meters3 × 1,000 kilograms / meters3 × 9, 81 newtons / kilogram = 2,570 newtons.
Step 5. Find out if your object floats by comparing it with its weight strength
Using the equation just seen, it is easy to find the force with which the object is pushed out of the liquid in which it is immersed. Furthermore, with a little more effort, you can also determine whether the object will float or sink. Simply find the hydrostatic force for the entire object (in other words, use its entire volume as V.s), then find the weight force with the formula G = (mass of the object) (9.81 meters / second2). If the buoyancy is greater than the weight, the object will float. On the other hand, if it is lower, it will sink. If they are the same, the object is said to "float in a neutral way".
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For example, suppose we want to know if a 20kg cylindrical wooden barrel with a diameter of 75m and a height of 1.25m will float in water. This study will require several steps:
- We can find its volume with the cylinder formula V = π (radius)2(height). V = π (0, 375)2(1, 25) = 0, 55 meters3.
- After that, assuming we are under the action of common gravity and have water of the usual density, we can calculate the hydrostatic force on the barrel. 0, 55 meters3 × 1000 kilograms / meter3 × 9, 81 newtons / kilogram = 5,395.5 newtons.
- At this point, we will have to find the force of gravity acting on the barrel (its weight force). G = (20 kg) (9, 81 meters / second2) = 196, 2 newtons. The latter is far less than the buoyancy force, so the barrel will float.
Calculate Buoyancy Step 6 Step 6. Use the same approach when the fluid is a gas
When it comes to fluids, it's not necessarily a liquid. Gases are treated as fluids, and although their density is very low compared to that of other types of matter, they can still support certain objects floating within them. A helium filled balloon is a typical example. Since this gas is less dense than the fluid that surrounds it (air), it fluctuates!
Method 2 of 2: Perform a Simple Buoyancy Experiment
Calculate Buoyancy Step 7 Step 1. Put a small cup or cup into a larger one
With just a few household items, it's easy to see hydrostatic principles in action! In this simple experiment, we will demonstrate that an object on the surface is subjected to buoyancy because it displaces a volume of liquid equal to the volume of the submerged object. We will also be able to demonstrate with this experiment how to practically find the hydrostatic force of an object. To start, put a bowl or cup inside a larger container, such as a basin or bucket.
Calculate Buoyancy Step 8 Step 2. Fill the container to the brim
Next, fill the smaller internal container with water. The water level must reach to the brim without it coming out. Be very careful at this point! If you spill water, empty the larger container before trying again.
- For the purposes of this experiment, it is safe to assume that water has a standard density of 1,000 kilograms / meter3. Unless salt water or a completely different liquid is used, most types of water will have a density close enough to this reference value that any infinitesimal difference will not change our results.
- If you have a dropper handy, it can be very useful for precisely leveling the water in the inner container.
Calculate Buoyancy Step 9 Step 3. Immerse a small object
At this point, find a small object that can fit inside the inner container without being damaged by the water. Find the mass of this object in kilograms (it is best to use a scale or a barbell that can give you the grams that you will convert to kilos). Then, without letting your fingers get wet, immerse it in the water slowly and steadily until it starts to float or you can hold it, then let it go. You should notice some water leaking from the edge of the internal container falling outside.
For the purposes of our example, suppose we immerse a toy car weighing 0.05 kilos in the inner container. It is not necessary to know the volume of this toy car to calculate the buoyancy, as we will see in the next step
Calculate Buoyancy Step 10 Step 4. Collect and measure the water that pours out
When you immerse an object in water, liquid moves; if it does not happen, it means that there is no space to enter the water. When it pushes against the liquid, it responds by pushing in turn, causing it to float. Take the water overflowed from the internal container and pour it into a glass measuring cup. The volume of water in the cup must be equal to that of the portion of the submerged object.
In other words, if your object floats, the volume of the water that overflows will be equal to the volume of the object immersed under the surface of the water. If it sinks, the volume of water poured will be equal to the volume of the entire object
Calculate Buoyancy Step 11 Step 5. Calculate the weight of the spilled water
Since you know the density of the water and can measure the volume of the water you poured into the measuring cup, you can find its mass. Simply convert this volume to meters3 (an online conversion tool, like this one, can help) and multiply it by the density of the water (1,000 kilograms / meters3).
In our example, let's assume that our toy car sinks into the internal container and moves about two teaspoons of water (0.00003 meters3). To find the mass of water, we need to multiply it by its density: 1,000 kilograms / meters3 × 0.0003 meters3 = 0, 03 kilograms.
Calculate Buoyancy Step 12 Step 6. Compare the mass of the displaced water with that of the object
Now that you know the mass of the object immersed in water and that of the displaced water, make a comparison to see which is greater. If the mass of the object immersed in the internal container is greater than that moved, it should sink. On the other hand, if the mass of the displaced water is greater, the object should remain on the surface. This is the principle of buoyancy in action - in order for an object to float, it must move a volume of water with a mass greater than that of the object itself.
- Thus, objects with small masses but with large volumes are the ones that tend to stay on the surface the most. This property means that hollow objects tend to float. Think of a canoe: it floats well because it is hollow inside, so it is capable of moving a lot of water even without having a very high mass. If the canoes were solid, they certainly wouldn't float well!
- In our example, the car has a mass greater than (0.05 kilograms) than water (0.03 kilograms). This confirms what has been observed: the toy car sinks.
