Acceleration

Acceleration

The rate of change of velocity with respect to time $a=\frac{dV}{dt}=a_{x}i+a_{y}j+a_{z}k$

We need to compute the partial derivatives when computing acceleration from velocity which yields a local acceleration ($\frac{\partial u}{dt}$) and a convective term ($\frac{\partial u}{\partial x},\frac{\partial u}{\partial y},\frac{\partial u}{\partial z}$).

The local acceleration is the unsteady term in Fluids which is where the velocity changes due to time, whereas the convective term has to do with where you are in space.

Here is the general expression for acceleration in Fluids…

This is sometimes written as…
$\frac{D}{Dt}=\frac{\partial }{\partial t}+U\frac{\partial }{\partial x}+V\frac{\partial }{\partial y}+W\frac{\partial }{\partial z}$

Now that we have an expression for acceleration we can use Newtons 2nd Law