How To Calculate Buoyancy For A Pipe

When you dive into a swimming pool, your body will likely naturally float as long as you keep swimming. The way something like your body in a pool rises to the surface is in part dependent on the buoyant force. Objects underwater experience this upward force, a buoyant force. You can apply this to yourself and other objects like pipes and even use these principles for building rafts.

The buoyant force opposes an object as it enters water and, in this upward direction, allows objects like boats and buoys to float. This force results from the ​hydrostatic pressure​, the pressure that a fluid like water exerts on an object when the fluid is at rest. You can use a buoyancy calculator or equations to measure it.

You can measure the buoyant force as the result of hydrostatic pressure as

\(F=rgV\)

for the fluid density ​r​ in units of mass/volume (such as kg/m³), gravitational acceleration ​g​ (9.8 m/s²) and volume submerged in water ​V​ to calculate buoyant force F​.​

You can calculate the buoyant force that opposes the gravitational force as the mass of the water that surrounds the cube times the acceleration of the ​buoyant force​. The density of water is 1,000 kg/m³, and, because the cube is halfway submerged into water, the buoyant force acts on half of the cube's volume.

This means the mass of water around the cube is the density times the volume, or 1,000 kg/m³ x 4.5 m³, which is 4,500 kg. Multiplying this by 9.8 m/s² gives you 44,100 N of buoyant force. The opposition of buoyant force and gravitational force also means that an object floats or sinks depending on whether the buoyant force outweighs the gravitational force or not.

Polyvinyl chloride (PVC) pipes are an ideal candidate for use when building ​underwater pipelines​. If you know the diameter of a pipe that is fully submerged underwater, you can calculate the weight of water displaced per length of pipe (​Ww​).

This force-per-length ​Ww​ is given by

\(Ww=\pi d^2\times\frac{62.4}{4}\)

for diameter ​d​ of the pipe. The 62.4 value represents the weight of water in pounds-per-cubic-foot on the pipe, a handy measurement for determining the weight as a result of length.

You can obtain this equation as a result of a derivation of the buoyant force. If you know the weight of water in pounds-per-cubic-foot on the pipe, you can write the force it exerts on the pipe by multiplying it by the volume of the pipe as ​62.4 x V​ or ​62.4 x​ ​_πr²h​ for the radius ​r​ of the pipe's circular base and height ​h_​ as the length of the pipe.

You can re-write the radius as half of the diameter, or ​d/2​, so that this expression becomes ​_π(d/2)²h x 62.4​ or ​πd² h x 62.4/4.​ Finally, you can divide this expression by the length of the pipe h to get an expression for force-per-length ​Ww​ as ​πd² x 62.4/4._​

You can write a simplified version of the equation for ​Ww​ as ​Ww = 49.01 x d​² for an equation that only depends upon diameter. This method of finding a factor of the weight of water in pounds-per-cubic-foot on a pipe also lets you determine values for other types of pipes so that you may create equations that only change this factor (62.4) for whatever you need to submerge under water.

Keep in mind, as is the case with all buoyant forces, the force water or any fluid exerts on an object depends on the geometry of the object and how much of it is actually submerged in water. Floating dock plans can take advantage of these equations to determine which type of material is best for building them.

Building a PVC pipe raft can take advantage of the buoyant force exerted on PVC pipes partially submerged in water. You can build your own PVC pipe raft using base materials of about 84" of 6" of schedule 40 PVC, construction foam, caulking material and sheets of plywood.