Fluid mechanics

1. May 3, 2014

varunika

how can we know whether the flow of liquid is steady or not from its velocity?

2. May 3, 2014

ZapperZ

Staff Emeritus
Check if dv/dt is zero?

Zz.

3. May 3, 2014

Qluq

In case of a laminar flow the flow would be steady when dv/dt=0. But how do you know it is laminar? In the real world v denotes a sort of average flow velocity, ignoring any turbulence. I think you should also check the Reynolds number. That will tell you something about the presence of turbulence. However, the Reynolds number depends also on the shape of the surroundings of the flow...

4. May 3, 2014

256bits

5. May 3, 2014

The only answer you need is that for a steady flow, $\frac{\partial \vec{v}}{\partial t} = 0$. In practice, there are no flows that are truly steady, as you will basically always find small fluctuations, but you can often approximate a flow as steady provided those fluctuations are small enough and random so as not to affect the mean flow in any way, which is not always the case.
This isn't true. In the real world, the $\vec{v}$ in the Navier-Stokes is the exact velocity at a given point in space and time and very well may be representative of a time-varying quantity. Now, if you make certain assumptions or models which involve averaging, then yes, it may well represent an average.