# Buoyancy

on . Posted in Fluid Dynamics

Buoyancy, abbreviated as B, is the upward force that is exerted on an object when it is immersed in a fluid (liquid or gas) and displaces an amount of fluid with a weight equal to the weight of the object.  It is a result of the difference in pressure between the top and bottom of the object due to the weight of the fluid that is displaced.  The magnitude of the buoyant force is equal to the weight of the fluid that is displaced by the object, and it acts in the opposite direction of gravity, which is why it causes objects to float.

• Archimedes' Principle  -  This principle states that the buoyant force acting on an object submerged or partially submerged in a fluid is equal to the weight of the fluid displaced by the object.  In other words, an object will experience an upward force equal to the weight of the fluid it displaces.
• Buoyant Force  -  The upward force exerted by a fluid on an object that is partially or completely submerged or immersed in the fluid.  This force is the result of the differences in pressure that exist at different depths within the fluid due to the gravitational pull on the fluid's mass.  The concept of buoyant force is a fundamental principle in fluid mechanics and plays a significant role in explaining why objects either float or sink in fluids.
• Density  -  Buoyancy depends on the density of the fluid and the density of the object.  If the density of the object is less than the density of the fluid, the object will float.  If the density of the object is greater than the density of the fluid, the object will sink.
• Negative Buoyancy  -  If the object's density is greater than the density of the fluid, the buoyant force exerted by the displaced fluid is insufficient to counteract the downward force due to gravity.  This leads to the object sinking until it reaches a depth where the buoyant force and the gravitational force balance each other out.
• Neutral Buoyancy  -  It is when the density of the object is equal to the density of the surrounding fluid.  This means that the object's average density is the same as the density of the fluid it displaces.  In this state, the object will neither rise to the surface nor sink to the bottom of the fluid; it will remain suspended at a specific depth.
• Positive Buoyancy  -  If the object's density is lower than the density of the fluid, it displaces a larger volume of fluid than its own weight, and the buoyant force exerted by the displaced fluid is greater than the downward force due to gravity.  This leads to the object's upward movement until the buoyant force and the gravitational force reach a balance, causing the object to float at a specific depth.
• Volume Displacement  -  The more volume an object displaces when submerged, the greater the buoyant force it experiences. This is why larger objects tend to experience stronger buoyant forces compared to smaller ones.

Buoyancy is why objects made of materials with densities less than that of the surrounding fluid tend to rise, and objects with densities greater than the fluid tend to sink.  This principle is crucial in understanding the behavior of ships in water, the flotation of objects, and even the movement of air within the Earth's atmosphere.

## Buoyancy formula

$$\large{ B = \rho \; g \; V }$$     (Buoyancy)

$$\large{ \rho = \frac{ B }{ g \; V } }$$

$$\large{ g = \frac{ B }{ \rho \; V } }$$

$$\large{ V = \frac{ B }{ \rho \; g } }$$

### Solve for B

 fluid density, ρ gravitational constant, g volume of solid, V

### Solve for ρ

 buoyancy, B gravitational constant, g volume of solid, V

### Solve for g

 buoyancy, B fluid density, ρ volume of solid, V

### Solve for V

 buoyancy, B fluid density, ρ gravitational constant, g

Symbol English Metric
$$\large{ B }$$ = buoyancy $$\large{lbf}$$ $$\large{N}$$
$$\large{ \rho }$$  (Greek symbol rho) = fluid density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ g }$$ = gravitational constant $$\large{\frac{lbf-ft^2}{lbm^2}}$$  $$\large{\frac{N -m^2}{kg^2}}$$
$$\large{ V }$$ = volume of solid $$ft^3$$ $$m^3$$

## Buoyancy formula

$$\large{ B = \rho \;g \;h\; A }$$     (Buoyancy)

$$\large{ \rho = \frac{ B }{ g \; h \; A } }$$

$$\large{ g = \frac{ B }{ \rho \; h \; A } }$$

$$\large{ h = \frac{ B }{ \rho \; g \; A } }$$

$$\large{ A = \frac{ B }{ \rho \; g \; h } }$$

Symbol English Metric
$$\large{ B }$$ = buoyancy force $$\large{ lbf }$$  $$\large{N}$$
$$\large{ \rho }$$ (Greek symbol rho) = density of the fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ g }$$ = gravitational acceleration  $$\large{\frac{ft}{sec^2}}$$    $$\large{\frac{m}{s^2}}$$
$$\large{ h }$$ = height of liquid displaced by a floating object $$\large{ ft }$$  $$\large{ m }$$
$$\large{ A }$$ = surface area of object  $$\large{ ft^2 }$$ $$\large{ m^2 }$$

Tags: Liquid Buoyancy