Fluid Dynamics
Fluid dynamics studies the motion of liquids and gases, explaining phenomena like lift and flow.
Bernoulli’s Principle
For an inviscid fluid, energy is conserved along a streamline:
\[ P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant} \]
Where \(P\) is pressure, \(\rho\) is density, \(v\) is velocity, \(g\) is gravity, and \(h\) is height.
Example
Water (\(\rho = 1000 \, \text{kg/m}^3\)) flows at \(v = 2 \, \text{m/s}\), \(h = 0\), \(P = 101325 \, \text{Pa}\):
\[ P + \frac{1}{2}(1000)(2)^2 = 101325 + 2000 = 103325 \, \text{Pa} \]
Applications
Fluid dynamics is key to aerodynamics (e.g., airplane wings), hydraulics, and weather prediction.