Calculate Water Temperature in Pond Receiving Hot Water: Formula Included

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Discussion Overview

The discussion revolves around calculating the temperature of water leaving a pond that receives hot water at a continuous rate. Participants explore the impact of heat loss mechanisms, particularly evaporation, and the challenges of estimating temperature changes given various environmental factors. The context includes theoretical considerations and practical implications for a yet-to-be-built pond.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant suggests that if the pond were perfectly insulated, the water would leave at the same temperature as it entered, but acknowledges that real-life conditions will lead to heat loss primarily through evaporation.
  • Another participant proposes that to estimate heat loss, one could assume all heat loss is due to evaporation and suggests integrating the energy required for vaporization based on humidity and surface area.
  • A different viewpoint questions the practicality of measuring temperature at the pond's exit since the pond has not yet been constructed, and suggests using a rule of thumb for estimating cooling without specific humidity data.
  • One participant mentions that evaporation rates will depend on humidity and wind conditions, indicating that these factors are crucial for accurate calculations.
  • Another participant recommends looking into swimming pool heating calculators as a potential resource for similar calculations, noting that the situation is analogous to pool heating needs.
  • There is a suggestion to consider using copper pipes with water dripping over them to enhance cooling through evaporation, likening this to cooling towers.

Areas of Agreement / Disagreement

Participants express varying opinions on the primary factors affecting water temperature, particularly regarding the role of evaporation and the assumptions needed for calculations. No consensus is reached on a specific formula or method for estimating the temperature of the water leaving the pond.

Contextual Notes

Limitations include the lack of specific humidity data, the uncertainty of environmental conditions, and the dependence on assumptions regarding insulation and evaporation rates. The discussion also highlights the challenges in estimating temperature changes without empirical data.

mrhook
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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
 
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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.
 
mrhook said:
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...
 
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..
 
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?
 
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.
 
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