How to Calculate Buoyancy: 12 Steps (with Images)

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How to Calculate Buoyancy: 12 Steps (with Images)
How to Calculate Buoyancy: 12 Steps (with Images)

Video: How to Calculate Buoyancy: 12 Steps (with Images)

Video: How to Calculate Buoyancy: 12 Steps (with Images)
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Buoyancy is the force acting in the opposite direction to the direction of gravity that affects all objects submerged in a fluid. When an object is placed in a fluid, its weight pushes the fluid (liquid or gas), while the buoyant force pushes the object upward, acting against gravity. In general terms, this force can be calculated with the equation FB = Vs × D × g, where FB is the buoyant force, Vs is the submerged volume, D is the density of the fluid in which the object is submerged, and g is the force of gravity. To learn how to determine the object's buoyancy, see step 1 to get started.

Steps

Method 1 of 2: Using the buoyant force equation

Calculate Buoyancy Step 1
Calculate Buoyancy Step 1

Step 1. Find the volume of the submerged portion of the object

The buoyant force acting on an object is directly proportional to the volume of the object that is submerged. In other words, the more solid the object, the greater the buoyant force acting on it. This means that even objects that sink in a liquid have a force pushing them up. To start calculating this intensity, the first step is to determine the volume of the object that is submerged. For the equation, this value must be in meters3.

  • For objects that are completely submerged in the fluid, the submerged volume is the same as the object. For those floating on the surface of the fluid, only the volume below the surface is considered.
  • As an example, let's say we want to find the buoyant force acting on a rubber ball floating in water. If the ball is a perfect sphere, one meter in diameter, and is half-floating in the water, we can find the volume of the submerged portion by finding the total volume of the sphere and dividing by two. Since the volume of the sphere is given by (4/3)π(radius)3, it is known that we will have a result of (4/3)π(0, 5)3 = 0.524 meters3. 0, 524/2 = 0.262 meters3 submerged.
Calculate Buoyancy Step 2
Calculate Buoyancy Step 2

Step 2. Find the density of your fluid

The next step in the process of finding the buoyant force is to define the density (in kilograms/meter3) of which the object is submerged. Density is a measure of an object or substance's relative weight by volume. Given two objects of equal volume, the one with greater density weighs more. As a rule, the greater the density of the fluid, the greater the buoyant force it exerts. With fluids, it is generally easier to determine density by looking at reference materials.

  • In our example, the ball is floating on water. Consulting an academic force, we can find that the density of water is about 1000 kilos/meter3.
  • Densities of other common fluids are listed in engineering sources. A list of these can be found here.
Calculate Buoyancy Step 3
Calculate Buoyancy Step 3

Step 3. Find the gravity force (or other downward force)

Whether the object is floating or fully submerged, it is always subject to the force of gravity. In the real world, this constant force is equal to 9, 81 Newtons/kilo. However, in situations where another force, such as a centrifuge, is acting on a fluid and the submerged object, it must also be considered to determine the total downward force.

  • In our example, if we are dealing with an ordinary and stationary system, we can assume that the only force acting downward is the force of gravity mentioned above.
  • However, what if our ball were floating in a bucket of water, spinning at great speed in a horizontal circle? In this case, assuming that the bucket is spinning fast enough to ensure that both the water and the ball do not fall, the downward force in this situation would derive from the centrifugal force created by the bucket's motion, not the earth's gravity.
Calculate Buoyancy Step 4
Calculate Buoyancy Step 4

Step 4. Multiply volume × density × gravity

When you have values for the volume of your object (in meters 3), the density of your fluid (in kilograms/meter3) and the force of gravity (or the downward force of your system), finding the buoyant force is easy. Simply multiply these three quantities to find the force in newtons.

Let's solve our example by substituting our values in equation FB = Vs × D × g. FB = 0.262 meters3 × 1000 kilos/meter3 × 9, 81 newtons/kilo = 2570 Newtons.

Calculate Buoyancy Step 5
Calculate Buoyancy Step 5

Step 5. Find out if your object floats by comparing it to the force of gravity

Using the buoyant force equation, it is easy to find the force that is pushing an object out of the fluid in which it is submerged. However, with a little more work, it is also possible to determine whether the object will float or sink. Simply find the buoyant force for the object (in other words, use its entire volume as Vs), then find the force of gravity with the equation G = (object mass)(9,81 meters/second2). If the buoyant force is greater than gravity, the object will float. But if the force of gravity is greater, it will sink. If they are equal, the object is called “neutral”.

  • For example, let's say we want to know if a 20 kilogram cylindrical wooden barrel with a diameter of 0.75 meters and a height of 1.25 meters will float on water. This requires a few steps:

    • We can find its volume with the formula V = π(radius)2(height). V = π(0, 375)2(1, 25) = 0, 55 meters3.
    • After that, assuming the default values for gravity and water density, we can determine the buoyant force on the barrel. 0, 55 meters3 × 1000 kilos/meter3 × 9, 81 newtons/kilo = 5395, 5 Newtons.
    • Now we need to find the gravity force on the barrel. G = (20 kg) (9.81 meters/second2) = 196, 2 Newtons. It is much less than the buoyant force, so the barrel will float.
Calculate Buoyancy Step 6
Calculate Buoyancy Step 6

Step 6. Use the same technique when your fluid is a gas

When solving type problems, don't forget that the fluid doesn't have to be a liquid. Gases are also considered fluid and, despite having lower densities compared to other types of matter, can still support the weight of some objects. A simple helium balloon is proof of that. Since the balloon's gas is less dense than the surrounding fluid, it floats!

Method 2 of 2: Performing a Simple Buoyancy Experiment

Calculate Buoyancy Step 7
Calculate Buoyancy Step 7

Step 1. Place a small cup or bowl into a larger container

With a few items from home, it's easy to see the buoyancy principles in action! In this simple experiment, we will demonstrate that a submerged object experiences thrust because it displaces a volume of fluid equal to the volume of the submerged object. As we do this, we also demonstrate how to find the buoyancy force of an experiment. To start, place a small container, such as a bowl or cup, inside a larger container, such as a larger bowl or bucket.

Calculate Buoyancy Step 8
Calculate Buoyancy Step 8

Step 2. Fill the container from the inside to the brim

Then fill the larger container with water. You want the water level to be up to the edge without tipping over. Be careful! If water spills, empty the larger container before trying again.

  • For this experiment, it is safe to assume that water has the density of water has the default value of 1000 kg/meter3. Unless you are using salt water or a different liquid, most types of water have a density close to the reference value.
  • If you have a dropper, it can be very useful to check the water level in the inner container.
Calculate Buoyancy Step 9
Calculate Buoyancy Step 9

Step 3. Submerge a small object

Now find a small object that fits inside the inner container and won't be damaged by water. Find the mass of this object in kilograms (use a scale for this). Then, without getting your fingers wet, dip the object into the water until it starts to float or you can no longer hold it. You should notice water from the inner container spilling into the outer container.

For the purposes of our example, let's say we're putting a 0.05 kg mass toy car into the inner container. We don't need to know the car's volume to calculate thrust, as we'll see next

Calculate Buoyancy Step 10
Calculate Buoyancy Step 10

Step 4. Collect and measure spilled water

When you submerge an object in water, a displacement of water occurs; if it didn't, there would be no room for him to enter the water. When he pushes the liquid, the water pushes back, causing the buoyancy. Take the spilled water and place it in a measuring cup. The volume of water must be equal to the submerged volume.

In other words, if your object floats, the volume of water you spilled will be equal to the volume of the object submerged in the water. If your object sinks, the volume of water it spills is equal to the volume of the whole object

Calculate Buoyancy Step 11
Calculate Buoyancy Step 11

Step 5. Calculate the weight of the spilled water

Since you know the density of water and can measure the volume that has been spilled, you can find the mass. Simply convert volume to meters3 (an online conversion tool like this one can be useful) and multiply it by the density of the water (1000 kg/meter3).

In our example, let's say our cart sank and dislodged about two tablespoons (0, 00003 meters)3). To find the mass of water, we multiply by its density:: 1000 kilos/meters3 × 0,0003 meters3 = 0.03 kilos.

Calculate Buoyancy Step 12
Calculate Buoyancy Step 12

Step 6. Compare the displaced volume to the object's mass

Now that you know the submerged mass and the displaced mass, compare them to see which is larger. If the mass of the object submerged in the inner vessel is greater than the mass of water displaced, it must have sunk. But if the displaced mass of water is greater than that, the object must have floated. This is the buoyancy principle; for an object to float, it has to displace a mass of water larger than the object.

  • Also, objects with smaller masses but larger volumes are the objects that float the most. This property means that hollow objects float. Think of a canoe; it floats because it's hollow, so it can displace a lot of water without needing to have a large mass. If canoes were solid, they wouldn't float well.
  • In our example, the car has a mass of 0.05 kilos, greater than the displaced water, 0.03 kilos. This confirms our result: the car sinks.

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