Eulerian method determines the behavior of fluid particles in fluid flow. It describes the velocity, acceleration, density, pressure, etc. of the fluid particles.
Consider S be the position vector of one particle from a fixed reference point. The particle can travel from initial spatial coordinates at time 0 to reach certain point in time t0.
Velocity, V of fluid particles can be given by-
V ⃗ = V (S ⃗, t)
Where,
S ⃗ = xi ̂ + yj ̂ + zk ̂
V ⃗ = u i ̂+ v j ̂ + w k ̂
Thus,
To identify the position of the particle, we can write-
u = u (x, y, z, t) (For scalar components)
v = v (x, y, z, t) (For scalar components)
w = w (x, y, z, t) (For scalar components)
Similarly,
dx/dt = u (x, y, z, t) (For scalar components)
dy/dt= v (x, y, z, t) (For scalar components)
dz/dt = w (x, y, z, t) (For scalar components)
Links of Previous Main Topic:-
- Vapour compression refrigeration cycle introduction
- Basic fluid mechanics and properties of fluids introduction
- Fluid statics introduction
- Manometers measurement pressure
- Fluid kinematics
- Lagrangian method for describing fluid method
Links of Next Mechanical Engineering Topics:-
- Lagrangian relationship from eulerian equations
- Steady and unsteady flows
- Uniform and non uniform flows
- Stream line
- Path lines
- Streak lines
- Acceleration of a fluid particle
- Continuity equation
- Continuity equation in three dimensions in differential form
- Continuity equation in a cylindrical polar coordinate system
- Bernoullis equation
- Basics and statics of particles introduction
- Equilibrium of rigid bodies introduction
