1. The formula described in
1. The formula described in the video is for sensible heat. If you apply that to air conditioning as you suggest, you’d be ignoring latent capacity and therefore CFM would be incorrect (understated). You would need to also measure the change in latent heat (delta-humidity ratio) across the evaporator coil. In practice, this could be done with a precision relative humidity probe and then convert the result to absolute humidity. Formulas for that can be found here: https://www.engineeringtoolbox.com/cooling-heating-equations-d_747.html

Keep in mind, it’s very difficult to measure cooling CFM in-situ (either directly or indirectly) with precision any better than about 10%, due to sensor error stacking.

2. It is impossible to use input power to calculate cooling output power. In particular, cooling COP varies significantly with conditions. If you were to back into output power using input power x rated COP, the result would only be ‘correct’ if site conditions exactly match rated conditions. In the test scenario from the video, this isn’t a problem since the test involves electric resistance heat, which by definition has a COP of exactly 1.

3. Compressor-based air conditioners (and heat pumps) have a COP greater than 1 because of the ‘magic’ of the refrigeration cycle. This requires more than a few words to explain… I believe Allison wrote an article about this?

thanks David
thanks David

yes, what was of common understanding to me. converting between the output power into different units of measure (BTU/h, or KW, or TON). but i have seen a YouTube video using the input power and convert it into BTU/h to eventully calculate the CFM using the sensible cooling formula (https://www.youtube.com/watch?v=aRJH-wJZ1Gs&feature=youtu.be)
i thought in beginning that would wrong,

1- what you think in the used formula?
2- how we can use the input power to calculate the output cooling power? (eventually after all, the input power was consumed in fever of producing only cooling output)
3- COP = output KW / input KW, and COP value always higher than 1 (ranging in 3 COP for most of the time), how can an output power be higher than input power?

There would be no reason to
There would be no reason to convert “input power” (KW) to BTU/H. The KW-BTU/H conversion formula is useful for converting “output power” from KW to BTU/H or vice versa. When we specify or measure an air conditioner’s output in BTU/H, we can calculate the EER (energy efficiency ratio) by dividing BTU/H output by KW input at a given operating point. OR, we can calculate COP (coefficient of performance) by dividing KW output by KW input. Hence, we can convert EER to COP by the following formula: COP = EER / 3.412.

we have two capacity element in the cooling BTU/h: sensible heat and latent heat.

the “Power input (KW)” to the HVAC unit (lets say RTU) are drawn by the unit to run the fan/compressor/other accessories.

as we know the conversion between Btu/h to KW ===> btu/h = 3.412 * KW (“conversion formula”)

the question:
the KW in the “conversion formula” is the same KW the “input power”

@Mohamamd, mass-flow
@Mohamamd, mass-flow properties determine how much heat is transferred between air and refrigerant. Essentially what happens is the more air (mass) you move across the coil, the warmer the coil becomes, thus increasing the delta-T between air and refrigerant. This allows more heat to be transferred. At first it seems counter-intuitive since the supply air is warmer, but the additional volume of air moved across the coil more than makes up for that. If you graph airflow vs total capacity at a given set of operating conditions, you’ll see the relationship is non-linear.

BTW, the same principal applies to heat pumps in heat mode except in that case, the exchange that occurs at the indoor coil is sensible heat only.

I derived the % increases/decreases from the expanded performance data for the Carrier 25HPB636-30 heat pump. See the table on page 13 of the Product Data PDF: https://www.carrier.com/residential/en/us/products/heat-pumps/25hpb6/ (scroll down to Documents section and select docs for Engineers, Architects and Contractors, then scroll down to Product Data).

thank you David and Allison.
thank you David and Allison.

i got your point, changing one parameter in the system will change all others and you can’t assume things will keep constant.

taking the numbers in your reply “”””Carrier 3-ton heat pump at 1200 CFM (400 CFM/ton, nominal), 63 entering wet bulb (75F dry bulb @ 50% RH) and 95F outdoor:
If airflow drops to 1050 CFM (350 CFM/ton), total capacity will drop by 2.1%, whereas sensible capacity will drop by 6.5% and latent capacity will increase by 18.5%! OTOH, if airflow increases to 1350 CFM (450 CFM/ton), total capacity will increase by 1.7%, whereas sensible capacity will increase by 6.2% and latent capacity will decreases by 19.6%!””””

1- what the reason behind the total capacity change? from engineering point view?
2- how you find and calculate the % of increases and decreases?

Expanding on Allison’s
Expanding on Allison’s comment, system airflow has a MUCH larger impact on sensible (and latent) capacity than total capacity. For example, referring to a Carrier 3-ton heat pump at 1200 CFM (400 CFM/ton, nominal), 63 entering wet bulb (75F dry bulb @ 50% RH) and 95F outdoor:
If airflow drops to 1050 CFM (350 CFM/ton), total capacity will drop by 2.1%, whereas sensible capacity will drop by 6.5% and latent capacity will increase by 18.5%! OTOH, if airflow increases to 1350 CFM (450 CFM/ton), total capacity will increase by 1.7%, whereas sensible capacity will increase by 6.2% and latent capacity will decreases by 19.6%!

Interestingly, rated kW input changes less 1.5% either way. This is why getting the airflow correct is so important. So, what is the correct airflow? It depends on how much latent capacity is needed. As we can see, dehumidification is a direct trade-off for sensible capacity and efficiency. In residential practice, designing a system to operate at less than 50% RH – ostensibly for improved comfort – is wasted energy in my opinion. But that’s another conversation.

Mohamamd, yes, the capacity

Mohamamd, yes, the capacity would be different if the air flow is different.  If you look up the expanded performance data for your system, it will show how the capacity changes with air flow rate, temperature (indoor and outdoor), and humidity.  In addition to changing the total capacity, changing the air flow also affects the balance of sensible and latent capacities.

a question:
considering we have a two HVAC units (same model) working on the same conditions (the same ambient temperature/same on-coil temperature).

with only one difference, the CFM not same for both machine.

does the total capacity change or would be the same for both HVAC units?