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Temperature Changes in 100 m³ Tank

11/05/2019 9:12 PM

Dear all

the water flowrate is 5L/s and 60ºC. this how water are flowing through into the 100m³ with 24ºC water tank and discharge out on another side. close circle system.

when that time, the water temperature in tank will reach 28.3ºC?

Best regards

NT

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#1

Re: temperature changes in 100m³ tank

11/05/2019 10:18 PM

You need to know the ambient temperature and btu loss/gain rate as well as the inlet and outlet position on the tank as well as discharge rate...

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#10
In reply to #1

Re: temperature changes in 100m³ tank

11/06/2019 10:40 PM

Hello Solar Eagle, thank you for your reply

Could I neglect to ambient temperature about this problem?

Could we calculate as sample and very generally to this problem by heat transfer from hot water to cold water on period?

Note:

this tank is swimming pool and water will be circulated from drain of pool to heat exchanger via filtration system and than reserve into pool by nozzles.

Country temperature is 38ºC at summer season and 25ºC at cold season.

Best regards

NT

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#2

Re: temperature changes in 100m³ tank

11/06/2019 3:39 AM

A simple energy balance calculation will give the answer under hypothetical perfect mixing arrangements.

In the real world it depends upon where in the tank the temperature is being measured and the degree of mixing that is taking place within the tank, as well as the heat transfer to and from the local environment, which is a function of shape of the tank, ambient temperature and a host of other factors. If stratification is taking place then homogeneity would be an assumption that is invalid.

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#11
In reply to #2

Re: temperature changes in 100m³ tank

11/06/2019 11:01 PM

plus the heat gain of the circulating pump, at least 20% of the power into the pump leaves as heat in the water.

OP is likely looking for the details of the 'simple' energy balance calculation.

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#16
In reply to #11

Re: temperature changes in 100m³ tank

11/07/2019 5:18 AM

Acknowledged, however that thermal contribution to the <...60oC water...> can be considered transparent. <...5L/sec...> from <...24oC...> to <...60oC...> is about 750kW, and that's a bit big for a <...swimming pool...> pump!

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#18
In reply to #16

Re: temperature changes in 100m³ tank

11/07/2019 6:14 AM

Hello PWSlack

if we use to heat pump on the pool services pipe by directly, your figure as 750kW is correct.

Q = 1000kg/m³ x 4.187kj/kg°C x 0.005m³/s x 35ºC

Q = 732.725kW

I will not provide to the heat pump on the pool services pipe by directly and the hot water come from hot water storage tank via heat exchanger.

So my require electrical power for heat pump is about 250kW. because recovery period for heat pump is 3 hr.

Best regards

NT

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#21
In reply to #16

Re: temperature changes in 100m³ tank

11/07/2019 6:01 PM

Just as you stated earlier, one of the (minor) unaccounted for factors in the energy balance...

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#25
In reply to #11

Re: temperature changes in 100m³ tank

11/12/2019 5:08 AM

That's allowed for in the 60 deg going into the tank.

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#3

Re: temperature changes in 100m³ tank

11/06/2019 4:19 AM

That sounds like the opposite of a "close circle" system.

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#5
In reply to #3

Re: temperature changes in 100m³ tank

11/06/2019 8:21 AM

This sounds just like a homework problem ... the kind of question that is banned on this site

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#6
In reply to #5

Re: temperature changes in 100m³ tank

11/06/2019 10:22 AM

Please excuse me, but what does that have to do with anything that I said?

Ill-posed questions may (and should) be discouraged, but there is nothing wrong with legitimate homework questions.

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#4

Re: temperature changes in 100m³ tank

11/06/2019 6:53 AM

Around 40min with no thermal loss and perfect mixing.

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#7

Re: Temperature Changes in 100 m³ Tank

11/06/2019 11:00 AM

Some time soon after the 5L/s 60°C in-flowing water begins to mix with the 100m3 of 24°C water in the tank, there will be a point where the water temperature will be 28.3°C. Finding this location can only be accomplished with a thermometer.

It is feasible that most of the water in the tank could approach 60°C, depending on undefined conditions.

The contents of the tank will probably NEVER reach equilibrium with constant inflowing/outflowing.

You give insufficient details for any useful response to come forward.

Your question leaves too much unanswered.

Redefine the system parameters, and more completely define the conditions.

Such as, the tank dimensions and flow paths if known. What is the outflow? Etc.

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#9
In reply to #7

Re: Temperature Changes in 100 m³ Tank

11/06/2019 10:31 PM

thank you LYN for your reply.

this tank is swimming pool (10 x 0.7 x 1.2(D)) outside of building and need to serve hot water system from nozzles. outflowing from overflow pipe of pool's drain and should be same inlet flowrate. But I can't guess to the outlet temperature. project requirement is 28.3ºC for pool water.

our country temperature is 38ºC @ summer season and 25ºC at cold season. But could I neglect this case and want to calculate by generally?

If the pool reached at 28.3ºC, will stop to the hot water serving and run only circulation water from filtration system.

But the hot water service time should not more than 2 hr. Because the heating time to pool is more than 2 hr, the system need to start run at 4:00 am for the swimmers can use at 6:00 am.

Best regards

NT

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#12
In reply to #9

Re: Temperature Changes in 100 m³ Tank

11/07/2019 4:20 AM

Ah. So it's not a <...tank...>; it's a <...swimming pool...> instead. Well, that sort of needs to be known about in the original post and #8⇓ becomes irrelevant with that additional information.

A <...swimming pool...> will have a forced circulation in it so as to remove unwanted substances and a make-up arrangement to replace water lost to overflow and evaporation. That forced circulation promotes a little mixing. Depending on where in the <...pool...> the <...60oC...water...> is added there may well be little stratification, in which case the temperature will be more-or-less the same everywhere and the location of the measurement becomes not mission-critical. Getting the temperature to within one tenth of a degree centigrade is therefore also not mission-critical in this application.

The answer in #4⇑ stands, however how a body of that size loses much heat in ambient conditions of <...25oC...> to <...38oC...> remains a mystery, and therefore the time to achieve <...28.3oC...> could be much less than that suggested. In any case the <...not more than 2 hr...> criterion looks achievable.

However, the dimensions of <...10 x 0.7 x 1.2(D)...> (assumed metres) suggest a volume of only 8.4m3 and not the <...100m3...> in the original post. Assuming the flowrate figures are correct then the heating time goes down by a factor of 8.4/100 in those circumstances. However, a width of only <...0.7...> metre is not wide enough to swim in.

So something more is wrong with the information in the original post and the supplementary information provided so far.

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#8

Re: Temperature Changes in 100 m³ Tank

11/06/2019 11:09 AM

If the outflow were the same as the inflow, then it is a wonder what the purpose of the <...tank...> is. Usually, the only purpose of a tank is to let the level go up and down. If the level stays the same, then the <...tank...> isn't doing anything useful. So get rid of it.

"What you don't have cannot leak" - with apologies to the late Dr. Trevor Kletz, a globally-recognised process safety guru and a champion of process intensification.

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#13
In reply to #8

Re: Temperature Changes in 100 m³ Tank

11/07/2019 4:24 AM

OK. See #12⇑.

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#14
In reply to #13

Re: Temperature Changes in 100 m³ Tank

11/07/2019 4:50 AM

Yes PWSlack,

I can acceptable your answer about 40 minutes as #4.

when I check by that formula ((m1.c1.t1)x(m2.c2.t2))/((m1.c1)x(m2.c2)), I have got 59 minutes.

But I can't satisfy this formula. because I felling that this formula is not detail and only generally.

So, I hope that do u and CR4 have the best and specific way to solve this.

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#15
In reply to #14

Re: Temperature Changes in 100 m³ Tank

11/07/2019 5:12 AM

There isn't a formula for absolutely everything because a formula expects all the input arrangements to be known. The flaws in the information presented in this thread more than adequately illustrate that concept.

A back-of-the-envelope calculation can yield more insight, often, than a myriad of computer programs.

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#22
In reply to #8

Re: Temperature Changes in 100 m³ Tank

11/08/2019 8:58 PM

"...Usually, the only purpose of a tank is to let the level go up and down...."

.

There are a few morer typical uses for tanks other than allowing mismatch between supply and demand for a limited time.

Tanks are used commonly to allow processes to occur to a larger volume of fluid over a longer time. An example is a hot water heater tank. By heating more water over a longer time (and not as needed for intermittent use) less power is required.

Tanks are also used to allow sufficient time for certain biological or chemical reactions. An example is a septic tank allowing sufficient loiter time for anaerobic digestion.

Tanks are also used to construct artificial environments for the transport or longer term habitation of aquatic life. An example is the Giant Ocean Tank or a home aquarium.

The above examples are quite typical and are not based on the level going up and down.

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#17

Re: Temperature Changes in 100 m³ Tank

11/07/2019 5:50 AM

If the temperature in the cold season is 25o and higher at all other times how did the water get down to 24o?

On the coldest day when target temperature is achieved 18,000litres/hr is being put in with a Δt of 31.7o and 100,000 litres is loosing heat to ambient at a Δt of 3.3o. 58% of the heat input is being lost to ambient so the heaters still have to run 58% of the time to maintain target heat (ignoring heat input from swimmers). During warm up this loss builds up from zero when the water is at ambient so there is no Δt to the 58% figure while at the same time the Δt of the input reduces from 35o to 31.7o. A couple of degrees rise in ambient temperature between 4.00am. and 6.00am. which is typical for the temperate region described in the case study will completely skew the calculations.

Conclusion. The answer is indeterminate but will be different every day and depends on both the average ambient temperature and any difference in the ambient between the heating start time and the time the target temperature is achieved.

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#20
In reply to #17

Re: Temperature Changes in 100 m³ Tank

11/07/2019 10:38 AM

".... If the temperature in the cold season is 25o and higher at all other times how did the water get down to 24o? ...."

There are several possibilities.

  • The temperature given (25°) could be the daily high.
  • Evaporation to leas than saturated atmosphere.
  • The pool might be utilized as a heat sink for a heat pump used to provide heat somewhere else during the 'cold' period.
  • Cold precipitation may have topped off the pool.
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#19

Re: Temperature Changes in 100 m³ Tank

11/07/2019 8:59 AM

The method as described so far overflows (i.e., wastes) quite a bit of water into which you have put energy. Even under ideal assumptions such as instant complete mixing, this will be a calculus problem.

Since you have to waste some water in any event, it will be best to empty the pool partially before adding any warm water. That will conserve heat, and it will also make the temp calculation be a simple average.

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#23

Re: Temperature Changes in 100 m³ Tank

11/11/2019 1:19 PM

Friends,

First, having the open pool temperature lower than the average ambient is easy to understand because daytime and nighttime temperatures will vary, as well as radiative cooling of the pool to the night sky allowing for subcooling of tank.

Second, assuming a closed-loop water flow with no input of heat energy from the pump, the total water exchange is 1/333 of the tank volume each minute.

Assuming the mixing is 100% efficient and the outflow temperature does not change during a minute, a simple spreadsheet calculation will show the temperature difference between tank and outflow as (60-24)=36-degC and a change in the first minute to be 0.108 degC. By using this as the new temperature and running the calculation repeatedly, the time it takes to change the tank temperature to 28.3-degC is 45 minutes.

Discussion: if the assumption of outflow temperature changing only at the boundary of each minute instead of incrementally during the minute, the time to reach the desired temperature would not change by more than 1 minute. If the assumption of 100% mixing efficiency is incorrect this will increase the time. However in my experience with swimming pool operation and maintenance a water exchange rate as low as given in the original question has a fairly high probability of being over 90%.

Regardless, with the target of 45 minutes to achieve the desired temperature one can move on to the experimental stage and run the actual water flow and input temperature for maybe an hour or more, and monitor the discharge temperature during that time. The whole purpose of the question is to get an estimate of the probable time needed to achieve the desired temperature increase, not to give an absolute definitive answer that is accurate beyond any reasonable doubt.

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#26
In reply to #23

Re: Temperature Changes in 100 m³ Tank

11/12/2019 11:37 AM

"... If the assumption of 100% mixing efficiency is incorrect this will increase the time. ..."

Not necessarily. Depending on how the incomplete mixing occurs and the outlet temperature, retarding mixing could decrease the time (though never to less than a little under 40 minutes for this particular scenario assuming initial temperature homogeneity and endpoint based on average temperature of the tank). The key, of course, would be having the incomplete mixing result in the lowest temperature fluid leaving the tank outlet so that no added heat was taken away.

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#27
In reply to #26

Re: Temperature Changes in 100 m³ Tank

11/13/2019 9:24 AM

That’s a good point. I estimate it needs < 14m3 water at 60°C to do the job. If it’s anything like plug flow most of the water leaving is at 24°. Of course, if uniform temperature in the tank is needed it would have to be mixed at that point.

Alternatively, if the heat input to the circulating water is constant, rather than the output temperature controlled to 60°, that also reduces the heating time, to just under 40 mins as you say.

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#24

Re: Temperature Changes in 100 m³ Tank

11/12/2019 5:06 AM

It's an exercise in calculus. Assuming mixed tank so the temp is uniform, and ignoring heat losses -

Rate of temp rise dT/dt = 0.005*(60 - T)/100 where T = instantaneous temp.

Integrating between 24 and 28.3 deg gives T = 10^5/5*ln{(60 - 24)/(60 - 28.3)} sec, about 43 minutes.

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