Help with a formula

[cweed]

I am working to determine what the temperature loss (minimal at best) would be by mixing a stream of water flowing at 2,400 gph at 85 degree (f) into another stream of water flowing at 37,000 gph. Any help would be great

 

[Redbelly98]

Do you mean you just need the final temperature of the mixture? That would be a weighted average of the two stream temperatures.

 

[cweed]

Yes the final temperature of the two stream the one at flowing 2,400 gph is 85 (f) and the one flowing at 37,000 gph is 105 (F).

 

[stewartcs]

Yes the final temperature of the two stream the one at flowing 2,400 gph is 85 (f) and the one flowing at 37,000 gph is 105 (F).

This would be a typical mixing chamber type problem, but you'll need to know the pressure. The mass and energy balance yields:

$$h_3 = \frac{\dot{m_1}h_1 + \dot{m_2}h_2}{\dot{m_1} + \dot{m_2}}$$

The m_dots with subs 1 and 2 are the respective mass flow rates coming into the mixing chamber. The h's are the respective enthalpies. They can be looked up in a steam table based on the inlet temperatures. This assumes of course that the inlet temperatures are below the saturation temperature of water at the specified pressure (i.e. it is in the compressed liquid state). Assuming that criterion is satisfied, the enthalpy of a compressed liquid can be approximated as a saturated liquid at the given temperature.

Once you have the enthalpy at the exit (h_3) you can look up the corresponding temperature in a steam table (or REFPROP if you have that database). If the exact enthalpy doesn't appear in your table you can interpolate and get a reasonable answer (depending on what accuracy you want).

Hope that helps.

CS