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.

You can tell in a few ways. Probably the most canonical is to measure the time-varying velocity in the boundary layer at the point in question and look at the power spectrum. For a fully-developed, turbulent flow, there should be a very distinctive power spectrum for most flow classes. You can also determine this more qualitatively by comparing with the laminar regions of the same flow, e.g. if you had a sudden spike in heating rate or skin friction as you move downstream or the boundary layer abruptly rapidly grows in thickness, that can mean the flow has transitioned. Understanding some of the physics of a given flow helps immensely here, though, as sometimes you can be tricked by that approach.

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.

This is also not true, or at the very least highly misleading. For pipe flow and pipe flow only, there is a fairly strong correlation between the diameter Reynolds number and the development of turbulence. That said, having a given Reynolds number in a pipe only means that turbulence will develop, not that it has already. Otherwise, for any other geometry, there is no hard and fast rule relating the Reynolds number to the onset of turbulence. Finding such a rule would be a major discovery and possibly even the sort of things that could garner Nobel contention, though who really knows.