# Scaling law for static buoyancy

• farahtc
In summary, the scaling law for static buoyancy is a mathematical relationship that describes how the buoyant force acting on an object in a fluid changes with its size and density. It is based on Archimedes' principle and is given by the equation Fb = ρVg. This law differs from the scaling law for dynamic buoyancy in that it only considers size and density, while the dynamic law also factors in velocity and shape. It has practical applications in designing various objects and studying ocean currents and aquatic animals. However, it has limitations in situations with non-uniform gravitational fields and does not account for factors like surface tension and turbulence.
farahtc

## Homework Statement

Derive the scaling law for static buoyancy force of a solid sphere in a liquid with a density of γ.
Assume the sphere is made of a material with a density of γs (γs< γ).

## The Attempt at a Solution

I calculated the the buoyancy force of the sphere as

F=(pi/6)*d^3*γ*g, where F=buoyancy force, d=sphere diameter. NOw can anybody tell me what is scaling law?how to derive it?

Im doing this exact same problem in my MEMS class and i have the same issue

## 1. What is the scaling law for static buoyancy?

The scaling law for static buoyancy is a mathematical relationship that describes how the buoyant force acting on an object in a fluid changes with its size and density. It is given by the equation Fb = ρVg, where Fb is the buoyant force, ρ is the density of the fluid, V is the volume of the object, and g is the acceleration due to gravity. This law is based on Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces.

## 2. How is the scaling law for static buoyancy different from the scaling law for dynamic buoyancy?

The scaling law for static buoyancy only considers the size and density of the object and the fluid, while the scaling law for dynamic buoyancy also takes into account the velocity and shape of the object. In other words, the static scaling law only applies to objects that are completely submerged and not in motion, while the dynamic scaling law applies to objects that are partially or fully immersed and in motion.

## 3. Can the scaling law for static buoyancy be applied to all objects and fluids?

No, the scaling law for static buoyancy only applies to objects and fluids that have a constant density throughout. In reality, many fluids, such as air, have varying densities with altitude or temperature, and this can affect the buoyant force on an object. Similarly, objects with varying densities, such as a helium balloon, may not follow this law as accurately.

## 4. How does the scaling law for static buoyancy apply to real-life situations?

The scaling law for static buoyancy has numerous practical applications, such as in designing ships, submarines, and hot air balloons. It helps engineers determine the optimal size and shape for these objects to achieve the desired buoyant force and stability. It is also used in the study of ocean currents and the behavior of aquatic animals in different depths of water.

## 5. Are there any limitations to the scaling law for static buoyancy?

Yes, the scaling law for static buoyancy only applies to objects and fluids in a uniform gravitational field. This means that it may not accurately predict the buoyant force in situations where the gravitational field is not constant, such as near a black hole or in a space environment. Additionally, it does not take into account factors such as surface tension and turbulence, which can also affect the buoyant force on an object.

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