Power to Pipe Size Equation | Heat Geek Style

Thank you to Michael Paini, one of our amazing Heat Geeks Elites, for this video!
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[@RB-eg7mj]

Gents, great addition to the engineers tool box. Could I ask two favours, Q is energy or power (energy flow rate) using mass or mass flow rate respectively (no mix & match). This brings me to the second point, units. Pls stipulate units. As an example, pressure can be in many units, i.e. pa, bar, psi, mmHg, mmH2O to name a few. We don't want to be using l/s when we should be using kg/s by accident.

[@optionenergysolutionsltd6611]

Thanks for sharing guys 😅 I am definitely no maths teacher and this was a video to share with and help others who had gone through the Heat Geek training. We are all learning, and if there are any areas that are incorrect, I would be grateful to know where specifically. It certainly works in my calculations.

[@MartinPugh]

We've been looking at the various online resources relating to heating and heat pumps for a while now and a lot of times you watch an installer seemingly throw out a magic value for heat capacity but how they got to those values never made any sense until now. Things like "why are you multiplying by 4.2?" "Where does that 0.9" figure come from. I'm no heating engineer, as I'm sure you can tell, but I now think I have a reasonable understanding of the maths to have been able to recreate the formulas for our house so now having those conversations with a Heat Geek won't feel quite as daunting when we get to that stage of the process.

[@TL-xv9of]

4.2 is the specific heat capacity of water (it is more or less a constant). Units are kJ/kg*K. This is the amount of heat needed to rise the temperature of 1kg water by 1 Kelvin. Kelvin is absolute temperature but for temperature differential it is equal to 1°C. The 0.9 is the flow velocity inside the pipe in m/s (meter per second). To avoid high pressure losses and noise, you want to stay below 1m/s. In living spaces it is porbably better to stay below 0.5 -0.7m/s. Double velocity means increased pressure drop by 4 times. This converts into increased pump power consumption.

[@stevedeveaux3502]

Good stuff :) As an extension to this, which may help to simplify things further, I noted that a lot of the elements of that equation are constants so we can group all of these together and figure out a slightly simpler equation multiplying all the variables by a single constant (which is approximate/rounded due to pi etc). The result of the algebra gives in general: d = 17.4 * sqrt(P / (v * deltaT)) You could take this further by saying that for a boiler installation with deltaT = 20, d = 3.9 * sqrt(P / v) or for a heat pump installation with deltaT = 7, d = 6.6 * sqrt(P / v) Hopefully those equations make sense written down that way :) ...and to echo an earlier comment, you do have to make sure that the units are the same otherwise these constants won't work and the calculation for d will end up being ridiculous!!

[@TheBadoctopus]

Very nice 👌

[@markwhittam8744]

Very interesting, but does rule of thumb therefore say 1mm pipe diameter per kW?

[@lekanshanu5512]

Well done Micheal , Adam I managed to put the equation in a scientific calculator and got the same answers. But not sure how without a scientific calculator how would work it out.

[@tomjcarty]

My head is hurting after all that... Will make a spreadsheet out of it. Brill work!

[@davetaylor4741]

Like so many of the heat geek videos. I can follow the science. Or in this case the maths to work out the pipe size to use. At times I was filling in the equation before he wrote it. Once he started it off. He should have been a teacher. His explanation of how and why he was doing things was first class. Better than most maths teachers I had. The rest of the symbols and graphics no idea. The introduced example figures. One can only assume are written in the specs of the heat pump somewhere. Never going to fit one so doesn't really matter. But as an info nerd I enjoyed the video. Most of your videos are food for thought which makes them interesting.

[@tapplumbandheat]

Brilliant! Written this one down in the awakening course notes

[@roberthuntley1090]

A useful rule of thumb I discovered on a plumbing forum was "One kWhr will heat 1 tonne of water by 1 degree C", so delta T of 20C will deliver 2 kW if the flow is 0.1 tonnes per hour. From memory its only 92% accurate, but good enough to sanity check your calculations.

[@speedbird300]

Not very accurate, overestimated by about a third. Water has a specific heat capacity of 4.186 J/g°C, meaning that it requires 4.186 J of energy (1 calorie) to heat a gram by one degree. A joule is one watt for a second

[@erhanuygur8215]

thanks for the tips , really useful explanation

[@robhargreaves1472]

This is brilliant thanks for sharing, comes over really well mate cheers.

[@typxxilps]

good idea to add such input instead of just adding a link.

[@stevesteve6365]

Am I right in assuming that the formulas would be using the inside diameter of the pipe? 10mm OD copper is about 8mm ID which would reduce the capacity significantly.

[@stephenfarrell236]

Bloody brilliant. 👍

[@chinook9785]

How can Q/1000 = P/(c*dT) be equal to Q = P/(1000c*dT) it should be, because we have to multiply with 1000, Q = 1000*P/(c*dT)

[@danoneill8751]

Yup. I was thinking about mention this little glitch. Felt a bit mean as the chap is clearly trying his best.

[@thomasmcgillivray6191]

He divided Q by 1000 to go from kg/s to m³/s, so he had to divide the otherside of the equation by 1000. He's dividing both sides not balancing the equation 👍

[@rayclarke5367]

Thanks for this. Using this calculation a 6mm pipe would be good for 2Kw, (one big radiator). Yet micro-bore pipes seem to be frowned upon these days. I've seen 15mm recommended to each radiatior. Is there something else I'm missing?

[@matthieu8292]

nice one guys, thank you! regarding the velocity, is there a max speed not to be exceeded for the fluid in the radiator to be noiseless please?

[@ChrisfromLeedsinUK]

1m/s should be fine. 0.5 to 0.75 if you want it super quiet.

[@matthieu8292]

@@ChrisfromLeedsinUK thank you for responding

[@adrianred236]

If Q is the mas flow rate, where do you get the value for v from?

[@aerenewables]

how to do this on an iphone or can you ??

[@shep147]

I wish i could understand these formulas ??

[@pumpkinhead456]

Damn, could have went with 15 instead of 22s!

[@mikeroberts8412]

Thanks for sharing 👍

[@deanchapple1]

So how do you punch that equation in to a calculator??

[@oldblokeswhoshouldknowbett8108]

this is how youll get it into the calculator for the same answer 1000 x 4.2 x DT x pi x V divide by boiler kw invert (-1) square root multiply by 2000

[@optionenergysolutionsltd6611]

Get a decent calculator so you can enter brackets. Something like Calc HD Pro. Then enter the following: 2,000√(kW÷(1,000×SHC×DT×π×V))

[@deanchapple1]

@@optionenergysolutionsltd6611 thank you. 😁👍🏼

[@plumberdan5720]

Why the second close brackets at the end?

[@aerenewables]

help me out bro @@oldblokeswhoshouldknowbett8108

[@LeiChat]

Can you adjust the velocity (flow rate) and/or power to accommodate existing pipe diameter?

[@HeatGeek]

Yes bit may require hydraulic seperation

[@LeiChat]

@@HeatGeek Every time I think I'm a little closer to understanding what's involved in an ASHP system. haha 🤦‍♂

[@peterwalton1502]

Could someone just print some tables to use

[@JasonBeddoes]

Easy, im a lying bastard.