Simplistic fluid heat loss - water in a concrete tank

[sanderr2]

Hi all,
I'm sorry if this is an inappropriate question. I have built a basement swimming pool for my wife. Unfortunately I neglected to insulate outside the concrete and insulating inside the concrete has caused some construction issues so I am trying to work out the heat loss if I go ahead without insulation.

I know the approximate ground temperature outside the concrete box.
I can establish an R value for the waterproof concrete.
I know the dimensions i.e. the surface area of the pool walls / bottom and the volume of water.
The heat loss from the pool surface will presumably be the same whether I insulate the pool or not so can be disregarded for the comparison.

Is there an equation that I can plug my values into so see how many BTU I will have to put in with and without insulation so I can establish how much not insulating is going to cost me in energy terms?

Humble thanks in anticipation,
Rob

 

[sanderr2]

Hi - no need for anyone to reply. I've realized that the thermal conductivity of insulated is about 10x lower so whatever the cost, the energy required will presumably be about 10x the amount so insulated. I think this equates to an annual cost of £3000 vs £300 so it's a no brainer. Insulated it has to be... Rob

 

[sanderr2]

PS Couldn't find a way to delete my thread!