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 cooling system supply airflow quantities must be calculated. Data from previous heating and cooling load calculation examples will be utilized to illustrate this process for a multi-zone variable air volume (VAV) system with terminal reheat.

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 Dimensions Design Occupancy # Office 1 22’ x 22’ 2 Office 2 22’ x 25’ 2 Office 3 22’ x 25’ 2 Office 4 22’ x 25’ 2 Conference Room 22’ x 50’ 20 Halls 6’ x 97’ 0

Note: The zone peak loads are shown in the table above. The overall building peak cooling load occurred at 2:00 pm, and that total will be utilized for system capacity sizing. Conference 1 4 3 2 Zone Rooms 1 1 2 2, 3 3 4 4 Conf, hall

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Cooling Load Parameters: Heating Load Parameters:

Outdoor Air Temp. = 87 F Outdoor Air Temp. = -12 F

Outdoor 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 a rate able to offset the heat gain to the space/zone being conditioned. Schematically, the conditioning process for cooling can be represented as shown in the figure below. Additionally, a pre-heat coil is included in the system with the capability of heating 100% of the building air (at outdoor air conditions) to supply air conditions. This will guard against system shock when the temperature of outdoor air is very low.

Mixing Box Space / Zone to be Conditioned OA EA RA MA SA at 55 F Pre-heat Coil Cooling Coil SA at 90 F VAV Terminal Unit with Reheat

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 and mixes with return air. If necessary, the mixed air will be heated sensibly to the supply air temperature of 55 F. Generally, with a VAV system, the mixed air will require cooling (supplied by the cooling coil) to bring the supply air to 55 F. The supply air temperature of 55 F is a designer choice and is very common in HVAC applications.

Heat

Total

Heat

Sensible

SHR

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3. Draw a line on the psychrometric chart protractor representing the calculated SHR. See the psychrometric chart (page 7).

4. Transfer a parallel line from the protractor to the room air conditions. This represents the “condition line” for the space being conditioned. Conditioned air must be supplied to the space at conditions somewhere 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 these two lines represents the required supply air conditions needed to maintain the space at the desired conditions.

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

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

OA fraction = OA/SAmax Example – For Zone 1:

Zone Room OA (cfm) SAmax (cfm) OA Fraction 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 mixing box, the minimum outdoor air for the system must be set to accommodate the zone with the highest outdoor air quantity required. This is the case unless a dedicated outdoor air system (DOAS) is installed in the conference room or the conference room air is filtered effectively. For this particular example the minimum outdoor air requirement is 24% of the total air. We will utilize that value.

10. Calculate the mixed air conditions.

SA MA RA

OA

m

(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/hr 76 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 air required to maintain health in zone 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 this case. Thus, the reheat process follows a SHF = 1.0 line on the psychrometric chart and only the sensible heat loss will 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. See the psychrometric chart (page 7).

Step 2: Plot room air temperature on that line (desired temperature is 70 F) See the psychrometric chart (page 7).

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)

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