d4t_formulas/assets/formulas/fluids_and_pressure.d4rt

[
  {"name":"Density","description":r"""
Mass per unit volume of a substance.

$$\rho = \frac{m}{V}$$

Where:
- $\rho$: Density ($\mathrm{kg/m^3}$)
- $m$: Mass (kilograms)
- $V$: Volume (cubic meters)

Density is an intrinsic property of materials.

![Density illustration (Wikipedia)](https://upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Density_of_solids.svg/800px-Density_of_solids.svg.png)
""","input":[{"name":"m","unit":"kilogram"},{"name":"V","unit":"cubic meter"}],"output":{"name":"rho","unit":"kilogram per cubic meter"},"d4rtCode":"rho = m / V;","tags":["physics","mechanics","material"]},
  {"name":"Pressure","description":r"""
Force applied perpendicular to a surface per unit area.

$$P = \frac{F}{A}$$

Where:
- $P$: Pressure (Pascals)
- $F$: Force (Newtons)
- $A$: Area (square meters)

Pressure is transmitted equally in all directions in fluids.

![Pressure (diagram) (Wikipedia)](https://upload.wikimedia.org/wikipedia/commons/thumb/9/95/Pressure_in_fluid.svg/800px-Pressure_in_fluid.svg.png)
""","input":[{"name":"F","unit":"newton"},{"name":"A","unit":"square meter"}],"output":{"name":"P","unit":"pascal"},"d4rtCode":"P = F / A;","tags":["physics","mechanics","fluid"]},
  {"name":"Buoyant Force","description":r"""
Upward force exerted on an object immersed in a fluid (Archimedes' principle).

$$F_b = \rho g V$$

Where:
- $F_b$: Buoyant force (Newtons)
- $\rho$: Fluid density ($\mathrm{kg/m^3}$)
- $g$: Gravitational acceleration ($\mathrm{m/s^2}$)
- $V$: Displaced volume (cubic meters)

An object floats when buoyant force equals its weight.

![Archimedes principle (Wikipedia)](https://upload.wikimedia.org/wikipedia/commons/thumb/7/72/Archimedes-principle.svg/960px-Archimedes-principle.svg.png)

""","input":[{"name":"rho","unit":"kilogram per cubic meter"},{"name":"g","unit":"meters per square second"},{"name":"V","unit":"cubic meter"}],"output":{"name":"Fb","unit":"newton"},"d4rtCode":"Fb = rho * g * V;","tags":["physics","fluid","mechanics"]}
]