Acceleration of a fluid particle is the rate of change of the velocity of that fluid particle. As acceleration is a function of time, the components its position vector can be written as-
u = u (x, y, z, t)
v = v (x, y, z, t)
w = w (x, y, z, t)
Where,
u, v and w are the velocities in the direction x, y and z respectively.
Thus,
Acceleration in x-direction can be given by,
ax = du/dt =∂u/∂x.dx/dt + ∂u/∂y.dy/dt+ ∂u/∂z.dz/dt + ∂u/∂t
Or,
ax = u ∂u/∂x +v∂u/∂y+ w ∂u/∂z + ∂u/∂t
Here,
u = dx/dt
v = dy/dt
w = dz/dt
Similarly,
Acceleration in y-direction is given by,
ay = u ∂v/∂x + v∂v/∂y+ w ∂v/∂z+ ∂v/∂t
And,
Acceleration in y-direction is given by,
az = u ∂w/∂x + v∂w/∂y+ w ∂w/∂z + ∂w/∂t
Note:
ax , ay and az are material or substantial accelerations
∂u/∂t ,∂v/∂tand∂w/∂tare temporal or local accelerations
u ∂u/∂x + v∂u/∂y + w ∂u/∂z , u ∂v/∂x + v∂v/∂y + w ∂v/∂zand u ∂w/∂x + v∂w/∂y + w ∂w/∂zare convective accelerations
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
- Eulerian method for describing fluid method
- Lagrangian relationship from eulerian equations
- Steady and unsteady flows
- Uniform and non uniform flows
- Stream line
- Path lines
Links of Next Mechanical Engineering Topics:-
