# Equation to find the reduction in velocity during condensation

1. Apr 19, 2014

### ASR

Velocity of any flowing vapour reduces as it condenses. Can any of you please suggest the equation to find the reduction in velocity of a vapour as it condense. Thanks in advance.

2. Apr 19, 2014

### Baluncore

It will depend on how you interpret “velocity of a vapour”. If temperature is thought of as being the statistical average kinetic energy of a population of molecules, then the statistical velocity distribution during condensation will include molecules in both the vapour and the liquid phase.

Condensation of an individual molecule will occur when it's kinetic energy falls below that needed to break the bonds to other molecules within the same liquid droplet.

The problem here is that we have two statistical populations of molecules. As energy is removed from the system, members of the vapour population are being selectively removed to the condensate population. That is a complex statistical equilibrium problem.

It could be seen that during the process of condensation there are two populations of molecules. In one, the liquid, are the majority of low KE molecules. In the other, the vapour, are the majority of the high KE molecules. But, energy is being shared between all molecules, in all phases, all of the time. Some are evaporating again from the condensate, while others are again condensing and providing energy to evaporate others. On average, individual condensed molecules will be travelling at slightly lower velocities than free molecules, but the density of the liquid will be greater and the molecules mean free path will be less.

In a volume away from any walls, the temperature difference between a condensation droplet and the surrounding vapour will be very small. From that you can estimate the average KE of a molecule in the liquid and in the vapour phase. Knowing the molecular weight makes it possible to calculate the average velocity drop occurring on condensation.

When condensation occurs onto a cold surface there will be a significant difference between vapour and condensate temperature. That will have a higher average KE difference and so a higher velocity difference. So it also depends on how you extract the energy from the system to cause the condensation.

3. Apr 20, 2014

### ASR

That's fine. I understood the physics behind it. But I am in need of an equation which would provide me the velocity of the fluid after condensation. In my case, velocity of steam is 600 m/s , 4kPa (Ts = 303 K) and it undergoes condensation process. I am wondering what will happen to the velocity after condensation, of course it will decrease but I need how much it will decrease.

4. Apr 20, 2014

### Baluncore

What is the temperature immediately after condensation?

5. Apr 20, 2014

### ASR

Temperature after condensation is 304 K

6. Apr 20, 2014

### Baluncore

Then there is no change in temperature, so there is no change in average kinetic energy and no change in velocity.

7. Apr 20, 2014

### ASR

but the vapour is condensed , therefore there will be change in kinetic energy of molecules

8. Apr 20, 2014

### Baluncore

Consider a mix of vapour and condensate at a fixed temperature. If you follow one molecule it will jump back and forth between phases, but over time it will have the same average KE as the population.

When two molecules travel together there is no difference in their individual KE than when they are travelling alone.

As the number of molecules in a droplet increases the envelope of the droplet travels slower but the molecules statistically travel within the droplet at the same average velocity determined by the temperature.