hvac supply airflow calculation sample

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MET 465 – Supplement #4: Heating and Cooling Supply Airflow Determination

After the heating and cooling loads are calculated (refer to course supplements #2 and #3), the heating and coolingsystem supply airflow quantities must be calculated. Data from previous heating and cooling load calculationexamples will be utilized to illustrate this process for a multi-zone variable air volume (VAV) system with terminalreheat.

Figure 1: Example Building Floor Plan

Table 1: Cooling Load for Example Building:

Table 2: Heating Load for Example Building:

Room Sizes and Occupancy Levels

Room DimensionsDesignOccupancy#

Office 1 22’ x 22’ 2Office 2 22’ x 25’ 2Office 3 22’ x 25’ 2Office 4 22’ x 25’ 2ConferenceRoom

22’ x 50’ 20

Halls 6’ x 97’ 0

Note: The zone peak loads are shown inthe table above. The overall buildingpeak cooling load occurred at 2:00 pm,and that total will be utilized for systemcapacity sizing.

Conference 1

4 3 2

Zone Rooms1 12 2, 33 44 Conf, hall

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Cooling Load Parameters: Heating Load Parameters:Outdoor Air Temp. = 87 F Outdoor Air Temp. = -12 FOutdoor Relative Humidity = 26% Outdoor Relative Humidity = 0%Return Air Temp. = 76 F, 30%RH (space conditions) Return Air = 70 F, 30%RH (space conditions)

Air Flow Calculations for a VAV system with Terminal Reheat:

To maintain comfort and healthy air conditions with the HVAC system, the cooling coils must supply cooling at arate able to offset the heat gain to the space/zone being conditioned. Schematically, the conditioning process forcooling can be represented as shown in the figure below. Additionally, a pre-heat coil is included in the system withthe capability of heating 100% of the building air (at outdoor air conditions) to supply air conditions. This willguard against system shock when the temperature of outdoor air is very low.

Mixing Box

Space / Zone tobe Conditioned

OA

EA

RA

MA

SAat 55 F

Pre-heatCoil

CoolingCoil

SA at 90 FVAVTerminalUnit withReheat

Figure 1: Schematic of a VAV System with Terminal Reheat

Solution Method: (Air Flow requirements based upon cooling requirements)

To determine the amount of flow required in the VAV system, the following process is utilized:

1. Plot known conditions on the psychrometric chart.

See the psychrometric chart (page 7).

2. Compute the SHR for the cooling and dehumidification process.

SHR = Qsensible / Qtotal = 76912 BTU/hr / 85788 BTU/hr = 0.90

Refer to the psychrometric chart (page 7) for specifics.

Outdoor air enters the mixing box andmixes with return air. If necessary, themixed air will be heated sensibly to thesupply air temperature of 55 F.Generally, with a VAV system, themixed air will require cooling (suppliedby the cooling coil) to bring the supplyair to 55 F. The supply air temperatureof 55 F is a designer choice and is verycommon in HVAC applications.

HeatTotalHeatSensibleSHR

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3. Draw a line on the psychrometric chart protractor representing the calculated SHR.


4. Transfer a parallel line from the protractor to the room air conditions. This represents the “conditionline” for the space being conditioned. Conditioned air must be supplied to the space at conditionssomewhere on this line in order to offset the heat gain to the space.


5. Draw a vertical line representing the chosen supply air dry bulb temperature. The intersection of thesetwo lines represents the required supply air conditions needed to maintain the space at the desiredconditions.


6. List known psychrometric conditions of outdoor air, return air, mixed air, and supply air.

Condition mass DBT WBT RH TH AH SV cfm (lb/hr) ( F) ( F) % (BTU/lbda) (lbm/lbda) (ft3/lbda)

Outside Air 87 62 26.2 30.4 0.0086 16.8

Return Air 76 56 30 25.8 0.0069 16.43

Mixed Air

Supply Air 55 46.5 57 20 0.0048 15.7

7. Calculate the amount of supply air required to offset the load of the space (Energy Balance).

Qload= mSA(THRA-THSA)

mSA=( Qload / (THRA-THSA) ) = 85788 BTU/hr / (25.8-20) BTU/lb = 14,791 lb/hr

V = m * SV = 14,791 lb/hr * 15.7 ft3/lb * hr / 60 min = 3870 cfm

8. Calculate the supply air requirements (SAmax) for each zone and room at peak load

Example - For Zone 1:

Qload,z1 = mSA(THRA-THSA)

mSA=( Qload,z1/ (THRA-THSA) ) = 13778 BTU/hr / (25.8-20) BTU/lb = 2375 lb/hr

V = m * SV = 2375 lb/hr * 15.7 ft3/lb * hr / 60 min = 622 cfm

See attached summary sheet (page 7) for zone capacity requirements (SA max cfm column)

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9. Evaluate the required amount of outside ventilation air in each room and zone and calculate the outsideair fraction for that room and zone.

OA fraction = OA/SAmax

Example – For Zone 1:

Zone Room OA(cfm)

SAmax(cfm)

OAFraction

1 1 40 621 40/621 = 0.064

See attached summary sheet (page 7) for room OA fractions (OA fraction)

Note: The maximum OA fraction occurs in the conference room. Therefore, since all mixing happens at the mixingbox, the minimum outdoor air for the system must be set to accommodate the zone with the highest outdoor airquantity required. This is the case unless a dedicated outdoor air system (DOAS) is installed in the conference roomor the conference room air is filtered effectively. For this particular example the minimum outdoor air requirementis 24% of the total air. We will utilize that value.

10. Calculate the mixed air conditions.

SAMARAOA mmmm (for a constant mass system)

and mass of OA = .24 * mass of supply air = .24(14,791 lb/hr) = 3550 lb/hr

so: mass of RA = mass of SA – mass of OA = 14,791 – 3550 = 11,241 lb/hr

3550 lb/hr 87 F

14,791 lb/hr 14,791 lb/hr 3870 cfm

78.64 F 55 F

11,241 lb/hr76 F

DBMA = (3550/14,791) * (87 F) + (11,241/14,791) * (76 F) = 78.64 F

THMA = (3550/14,791) * (30.4 BTU/lb) + (11,241/14,791) * (25.8 BTU/lb) = 26.90 BTU/lb

11. Complete the psychrometric table values.

Condition m DBT WBT RH TH AH SV cfm (lb/hr) ( F) ( F) % (BTU/lbda) (lbm/lbda) (ft3/lbda)

Outside Air 3550 87 62 26.2 30.4 0.0086 16.8 994

Return Air 11,241 76 56 30 25.8 0.0069 16.43

Mixed Air 14,791 78.64 26.90 0.0073 16.49

Supply Air 14,791 55 46.5 57 20 0.0048 15.7 3870

MA SA

OA

RA

The amount of outside airrequired to maintain health inzone 1 is 6.4%.

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12. Calculate required Cooling Capacity.

QMA-SA = mSA(THMA-THSA) = 14,791 lb/hr * (26.90 – 20) BTU/hr = 102,058 BTU/hr

Tonnage of Cooling = 102,058 BTU/hr / 12,000 BTU/hr/ton = 8.5 Tons

Select cooling coils with 8.5 ton capacity capable of delivering 3870 cfm at 55 F.

13. Size the Reheat Coils in the terminal units.

Remember, the air temperature leaving the AHU is at 55 F and 56% RH (see psychrometric chart). Each reheat coil(RHC) supplies only sensible heat to this supply air in order to heat the zone. Humidity is not controlled in thiscase. Thus, the reheat process follows a SHF = 1.0 line on the psychrometric chart and only the sensible heat losswill be utilized to size the reheat coil.

Step 1: Draw a line with SHF = 1.0 from current supply air conditions on the psychrometric chart.


Step 2: Plot room air temperature on that line (desired temperature is 70 F)


Step 3: Make assumption about reheat air specific volume and temperature (DB between 90'F and 110'F)

Assume SVrhc = 17.4 ft3/lb @ DB = 109'F (See the psychrometric chart - page 7)

Step 4: Convert design volumetric flow rate (622 cfm) for the zone to a mass flow rate

mrhc = V/SVrhc = 622 ft3/min / 17.4 ft3/lb * 60 min/hr = 2144.8 lb/hr

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Step 5: Solve for the reheated air total heat required to maintain 70'F in zone 1.

Energy Balance Equation: Qload = mrhc(THrhc - THRA)

THrhc = (Qload / mrhc) + THRA = (21,213 BTU/hr / 2144.8 lb/hr) + 23.6 BTU/lb = 33.5 BTU/lb

Step 6: Intersect reheated air total heat with the SHF = 1.0 line to determine reheated air temperature.

DBrhc = 114'F (See the psychrometric chart - page 7)

Step 7: Solve for reheat coil capacity (reheat coil #1).

Qrhc1 = .91 * cfm * (DBrhc - DBSA)

= .91 * 622 * (114 – 55) = 33,373 BTU/hr

QRHC1 = 33,373 BTU/hr

See attached summary sheet (page 7) for zone reheat coil sizes.

14. Size the Pre-heat Coil (phc)

Qphc = System total air * .91 * (DBSA – DBOA)

= 3870 cfm * .91 * (55 - -12) F

Qphc = 151,433 BTU/hr Pre-heating capacity required at AHU (air-handling unit)

NOTE: The pre-heat coil is generally sized to heat 100% OA to SA conditions.

hvac supply airflow calculation sample

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