Annual energy consumption

[Malmo]

Hi everyone,

In the Ashrae book, the annual heating consumption formula is:
Q = 24*q*HDD/n*(Tin – Tout)

Q = Annual energy consumption
q = Heating gain (Btuh)
HDD = Heating degree days
n = Efficiency
Tin = Indoor temperature (Balance temperature) in F
Tout = Outdoor temperature in F

For example: If my heating unit capacity is 75000 Btuh, my indoor temperature is 72 F and my seasonal outdoor temperature is 20 F, HDD is 4500 and the efficiency is 0.9
My annual energy consumption is: 173 077 kBtuh

If I decrease my indoor temperature at 70F, my annual energy consumption increase at 180 000 kBtuh.

We are supposed to have lower annual consumption by decreasing indoor temperature, right?
If not, can you correct my reasoning?

Thank you in advance !

[Malmo]

No volunteers to help me?

[BASengineer]

I don't have the ASHRAE book in front of me to verify, but looking at the units, they don't quite pencil out.

q is BTU/hr (rate of change of heat)
HDD is days > the 24 is to convert from hours to day
T is °F

Using your equation, the units for Q would be BTU/°F.

[Malmo]

Hello BASengineer,
Thank you for the reply and the correction of Q units. Good point.
My question is about the annual energy cosumption who increase with the decrease of DT and vice versa.

Have you an idea? If is it the correct formula to estimate the energy consumption?

Best regards !

[coolcoil]

I agree with @Malmo. That equation does not make sense. Which ASHRAE book is it from? Can you post screenshot of the page?

[Malmo]

Hello coolcoil,

I try to post a screenshot. It's my first time to post a
picture later.

[BASengineer]

Hello BASengineer,
Thank you for the reply and the correction of Q units. Good point.
My question is about the annual energy cosumption who increase with the decrease of DT and vice versa.

Have you an idea? If is it the correct formula to estimate the energy consumption?

Best regards !

I looked it into a little bit further, as it's been a while since I've had to deal with degree days.

So HDD units are actually °F. See https://www.e-education.psu.edu/egee102/node/2076. That cancels out the units from (Tin - Tout). I apologize for the misinformation of the HDD units being days.

q is correct as Btu/hr. Q will result in Btu/hr as well, which can be converted to kW (1 kW = 3412.1 Btu/hr).

If you can post a screenshot of that section of the ASHRAE book or have the chapter, that'd be helpful.

[Malmo]

Thank you for this informations. I haven't a problem with the units but the sens of the formula.
In the Ashrae Booke "Fundamental" 2013. 31st Chapter.
I will post a screenshot later, I have difficulties to insert a picture with my ipad.

Thank you !

[Malmo]

This is a screenshot of the formula from the fundamental of ashrae book

[IMG][/IMG]

[Malmo]

Ktot = Heat loss coefficient

[tridiumtech]

Another way to look at it is to start with Newton's Law of Cooling. For a flat surface:
Btu/hr = U x A x (delta T), where U = heat transfer coefficient (btu/ft2-hr-F) and A is the area (ft2)

Annual BTU from Degree Days: BTU = U x A x DD x 24hrs/day

From Newton's Law: U x A = Btuh/(delta T). Substituting into the Annual BTU equation:
BTU = [Btuh/(delta T)] x DD x 24hrs/day

This appears to be the same as:
Q = 24*q*HDD/n*(Tin-Tout) (with the addition of efficiency)

I've seen the transfer equations many times, but this is new twist in looking at it. Sort of an 'inverse modeling' approach since you have the heating unit capacity (btuh).

Attached is my current CEM "Cheat Sheet".

[Malmo]

Hi tridiumtec.

Thank you for your reply, it's exactly the same understanding that I had.
However, I find contradictory the fact that the energy consumption is inversely proportional with the temperature differential.

[hvacker]

Just adding as far as checking the formula, ASHRAE has a correction sheet in their books for corrections after publication. Not sayin the Gods have failed, probably the publisher.

[Malmo]

Just adding as far as checking the formula, ASHRAE has a correction sheet in their books for corrections after publication. Not sayin the Gods have failed, probably the publisher.

Hi hvacker,
Have you noticed this correction in Ashrae handbook?

[tridiumtech]

Newton's Law of Cooling says that the rate of thermal energy is proportional to the temp difference - that's seems right - like what we'd expect.

With that Energy equation (not rate), it's got the product of HDD (Days x Temp) times the inverse of Temp (1/Temp) - so it just the # of days that relates to the energy consumption - that's seem right. Yeah, using an equation(s) and not getting 'fooled' by it can be a challenge.

In regards to fluid dynamics, I found it hard to grasp the math behind the pump laws - that the pressure goes up 4 times if you
double the flow rate. Sure, you see the equation. So you got to go to the basic physics - that Force is proportional to the change
in momentum (mass x velocity). If we double the flow rate we intuitively see that the flow rate should double. The tricky part is
to realize that by doubling the flow rate we've also double the mass rate (eg, more water molecules per time). So the change
in momentum goes up four times. Change is momentum relates to Force which relates to Pressure (force per area).

This is exactly related to the question: "If a 30mph wind is hitting the side of a barn with a force X, how much force at 60mph?"
The force on the barn is proportional to how much momentum hits it per second (or minute, hr). So force (pressure) up 4X. Understanding the effects between momentum and energy, in my opinion, is the 'magic key' to understanding fluid mechanics.

After struggling with all that, I came to one definition of heat: Heat is Energy without momentum.

Time for a 'cold one'...

[hvacker]

Hi hvacker,
Have you noticed this correction in Ashrae handbook?

I Haven't seen this particular formula corrected but have seen correction sheets in one of mine but they are probably older than yours.
Just a heads up.