Calculate Water Temperature in Pond Receiving Hot Water: Formula Included

[mrhook]

I have an open water pond which will be receiving hot water (75oC) at a continuous steady rate. I want to know the temperature of the water leaving the pond at the other end. Is there a formula I can use to calculate this from the following information?

Volume of pond (1650m3) (25mx25mx2m at base, with sloping sides)
Volume of water entering/leaving (165 l/min)
Temp of water entering 75oC
Ambient temp (assume 50oC as maximum - its in a hot country!)

Thanks for any help

 

[mgb_phys]

You need to work out the heat loss from the pond.
If it was perfectly insulated the water would leave with the same temperature it entered once it had heated all the water in the pond to that temperature.
In real life the heat loss will mostly be by evaporation, especially in a hot country - it's not going to be easy to work out, it will depend on relative humidity, any wind and the degree of turbulence and mixing of the incoming water.

 

[olgranpappy]

I have an open water pond which will be receiving hot water (75oC) at a continuous steady rate. I want to know the temperature of the water leaving the pond at the other end. Is there a formula I can use to calculate this from the following information?

Volume of pond (1650m3) (25mx25mx2m at base, with sloping sides)
Volume of water entering/leaving (165 l/min)
Temp of water entering 75oC
Ambient temp (assume 50oC as maximum - its in a hot country!)

Thanks for any help

Put a thermometer "at the other end".

Out of curiosity, why are you pumping the water in the first place? It seems rather queer that you have just sort of happened upon a small pond whose volume is an exact multiple of the pumping rate (1650 versus 165)? Hmm...

 

[cesiumfrog]

I would have thought you could assume all heat loss is evaporation, assume a particular humidity above the pond (e.g. zero under dry weather and unrestricted ventilation), look up the vapour pressure and integrate the energy given to vaporisation over the surface area..

 

[mrhook]

Well, I may have mislead you when I said I have a pond, as technically it hasn't yet been built! So I can't just put a thermometer at the other end!

What I need to prove is that the water won't be too hot when it reaches the other end (as I want to use a certain type of pipe that won't withstand the upper temperature range). So I was wondering if there was some sort of rule of thumb I could use to estimate the cooling. Unfortunately I don't have data on humidity etc, and it would vary throughout the year. Turbulence would be minimised as the water is entering via a delivery chamber.

Any further thoughts?

 

[mgb_phys]

The temperature depends largely on the evaporation - assuming it is well insulated, ie in the ground. The evaporation depends on humidity and any wind, you will need to know the humidity.
Look at swimming pool heating calculators, losts of makers of swimming pools have programs or web sites to estimate the amount of heating a pool needs - you are just doing the same calculation!

Since you are not cooling the water very much and you are going to lose a lot of the pool water by evaporation it might be easier to just run the water through loops of copper pipe and have water dripping over the outside of the pipes and evaporating - google for cooling towers.