[praveencyr]

Hello everyone,

I wasn't sure if this is the right place to ask this question, but I feel that someone could help me solve this problem!

I would like to calculate pressure drop manually/analytically/theoretically across a convergent T-joint as given in attached picture. Air flow from top side with specific flow rate and water from left side with specific flow rate. The air and water mixes in bend and exits the pipe downwards. I know the pressure at top (air) and left (water) entry, now I would like to know how much is the pressure at bottom end (Air + Water mixture).

I tried to get help from many people and many forums, but I can't find a exact solution to this problem. So, could some guide me to find a solution?

Kind regards
Praveen

T_joint.png

[LuckyTran]

If the water and air actually mix completely then you end up with a water-vapor mixture system at some mixture ratio (or vapor fraction).

You need a property tables or an equation of state for the water-vapor system. Something like NIST's REFPROP.

To get the thermodynamic limit:
Get the enthalpy the inlets, add them up. The enthalpy at the outlet is the same. Now you go back to your equation of state and lookup the pressure for the given enthalpy and vapor fraction. This gives you the pressure loss caused by mixing only. It doesn't include the head loss from the flow navigating the T-junction and viscous losses. To get those losses, you need handbooks with empirical correlations or do some CFD or make some measurements.

[praveencyr]

Thanks LuckyTran for your idea.

As you said, REFPROP is one of the solution, but I need to solve it manually without using any external software or coding.

The thermodynamic method of solving the system to find the pressure drop seems to be really interesting, but for that I need a specific system equation which I can't find it anywhere or formulate it on my own. So could you suggest me some relevant article or journals for reference?

[LuckyTran]

The thermodynamic limit is rather stupid. You won't measure this pressure drop in a realistic system as pictured because it doesn't mix that fast. The thermodynamic limit is approached when the pipe after the junction is very very long. It also accounts for only the pressure drop change due to the mixing process itself and not the pressure drop down a length of pipe.

You don't have to specifically use REFPROP, you just need an equation of state. Before the codes became accessible, we used these things clled property tables and you can still find them in the back of an engineering thermodynamics book.

Originally Posted by praveencyr

The thermodynamic method of solving the system to find the pressure drop seems to be really interesting, but for that I need a specific system equation which I can't find it anywhere or formulate it on my own. So could you suggest me some relevant article or journals for reference?

It's nothing special. It's not even an equation. It's a table lookup problem. You can find it in any thermodynamics book. Enthalpy is conserved (which is just a fancy wording on the principle of energy conservation). The exit mixture ratio is roughly prescribed by the flowrates. Depending on actual flow conditions the system will be at the saturation pressure or saturation temperature so it will be at the mixture ratio of the inlets or it'll be at the mixture ratio at the saturation pressure.

For wet air, these tables are otherwise popularly graphed on psychometric charts which you can just google. Again, this is strictly for the thermodynamic part.