Help me to solve my house swimming pool temperature problem please

[Djok1234]

What's up guys. Is there anyone who can challenge to solve this theoretical problem that can help to solve my house problem?

There's an empty outdoor swimming pool that has width a, length b, and depth c, such as its volume = abc. The temperature of outside is -3 C° and we are trying to fill the pool with water poured out from two hoses. Each hose pours water with rate 500mL/sec. Our goal is to fulfill the swimming pool with water temperature 35C°. What should be the temperature of the water from the hoses so that the pool can maintain its 35 C°, if we pour the water for 1 hr? 5 hrs? 10 hrs? 24 hrs? You can ignore the water exceeding volume of the pool as it just flows out anyways.

I know that Q=McT, this formula is very useful but I just do not know where to start. Any help from physics geeks? Peace!

 

[berkeman]

What's up guys. Is there anyone who can challenge to solve this theoretical problem that can help to solve my house problem?

There's an empty outdoor swimming pool that has width a, length b, and depth c, such as its volume = abc. The temperature of outside is -3 C° and we are trying to fill the pool with water poured out from two hoses. Each hose pours water with rate 500mL/sec. Our goal is to fulfill the swimming pool with water temperature 35C°. What should be the temperature of the water from the hoses so that the pool can maintain its 35 C°, if we pour the water for 1 hr? 5 hrs? 10 hrs? 24 hrs? You can ignore the water exceeding volume of the pool as it just flows out anyways.

I know that Q=McT, this formula is very useful but I just do not know where to start. Any help from physics geeks? Peace!

Welcome to the PF.

Who in the world wants to go swimming when it's -3C out?

 

[Khashishi]

Well, it's going to depend on a lot of things, like the insulation of your pool walls, pool covers, humidity, and wind. I don't think a first principles approach is going to be very fruitful. Better check with experts in heated pools.
By the way, it's going to take a ton of energy to do what you want.

 

[DaveC49]

You could start by making some simplifying assumptions. I.e. perfectly insulating walls, no heat loss through the surface to get a first order solution and then introduce heat losses as a second order problem. In this case since the flow rates from both hoses are the same.
Q=Q1 + Q2 = m c T1 + m c T2 = 2m c Tf => Tf = (T1 + T2)/2. Knowing Tf then T1 and T2 can be any combination which adds up to 2 x Tf
In practice there will be some heat loss to the walls and surface.

Using the thermal properties of the walls ( and the soil behind the walls) you could estimate the heat loss to the walls under steady state conditions. Similarly you will find treatments of the heat loss from the surfaces ( radiative, convection and conduction). It is unlikely you will be able to get a full dynamical solution as the pool fills unless you use numerical approximations and finite element methods. With an estimate of the heat losses Ql though ,you could then revise the final temperature calculation using Qf = Q1 + Q2 -Ql = 2m C Tf.