# Energy Efficient Building Design College of Architecture Illinois Institute of Technology, Chicago. Relative Humidities RH%

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1 Psychrometrics Psychrometric Chart Relative Humidities RH% % 80% Enthalpies 70% H btu/lb Not to Scale Humidity Numbers and Values % Ratios are approximate W lbs/lb Grains/lb W * % Wet Bulb Temps 65 WB o F ,3 Dew Point Temps 40% DP o F % % % o F Dry Bulb Temps o F Psychrometric Parameters Dry Bulb Temp ( o F) H Enthalpy (btu/lb : btu per 1 lb of air) WB Wet Bulb Temp ( o F) W Humidity Ratio (lbs/lb : lbs per 1 lb of air) DP Dew Point Temp ( o F) V Specific Volume (ft3/lb : ft3 per 1 lb of air) RH Relative Humidity (%) D Density (lbs/ft3 : lbs per 1 ft3 of air) = 1/V Figure Dry Bulb () temperature is the temperature of air as registered by an ordinary (mercury) thermometer. temp is indicative of the sensible heat content of the air. Wet Bulb (WB) temperature is the temperature of air as registered by a thermometer whose temperature sensing bulb is covered by a material (cloth) soaked in water and exposed to a rapidly moving current of air. The evaporation of the moisture surrounding the bulb cools the air. WB temp is indicative of the total heat (sum of both sensible heat and latent heat) content of the air. Dew Point (DP) temperature is the temperature at which condensation of moisture begins when the air is cooled by removing sensible heat only. DP temp is indicative of the moisture content and latent heat in the air. It is the best indicator of comfort conditions. Humidity Ratio (W) is the weight (lbs) of water vapor per unit weight (1 lb) of dry air. It is the moisture content of the air and it is indicative of the latent heat content of the air. Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-1

2 Saturated Air contains the maximum possible moisture (water vapor or steam) that the air can hold at a given temp. This maximum moisture content increases with increasing temperature. Relative Humidity (RH) is the ratio of the actual water vapor pressure at a given temp to the water vapor pressure of the air if the air was saturated at the same temp. RH is a ratio of water vapor pressures and not a ratio of moisture contents. However, it is very close to the ratio of moisture contents and the difference is about 2%. Dry Bulb () Temp W Relative Humidity (RH) W 70 % RH 70 o WB All points on 70 o DP this line are at All points on 70 o Dry Bulb this line are at Temp 70% Relative Humidity 70 o Wet Bulb (WB) Temp All points on W Enthalpy (H) All points on W this line are at 34.2 this line are 70 o WB 70 o Wet Bulb at 34.2 btu/lb Temp 70 o WB Enthalpy Dew Point (DP) Temp W Humidity Ratio (H) W W 70 o DP 70 o DP All points on this line All points on this line are at 70 o Dew Point are at lbs/lb Temp Humidity Ratio Figure Degree of Saturation (DS) is the ratio of moisture content (or humidity ratio) of the air at a given temp to the moisture content (humidity ratio) of the saturated air at the same temp. For HVAC design and for all everyday practical purposes, Relative Humidity (RH) and Degree of Saturation (DS) can be considered to be almost the same. Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-2

3 Degree of Saturation (DS) 100% RH DS = W / Ws 80% RH W DS = Actual Humidity Ratio % RH = Ws = 100% Humidity Ratio at 100% RH 50% RH = W / Ws DS = / = 78.9% 20% RH DS = / = 49.3% DS = / = 18.8% DS = 0% Figure 80 o H RH WB DP W H DP WB RH W Outdoor Air DP = 67.0 W = Indoor Air DP = 55.5 W = = 95.0 RH = 40.0 H = 38.6 = 75.0 RH = 50.0 H = 28.3 WB = 75.0 V = D = WB = 62.5 V = D = Note: reduced from 95 o F to 75 o F, WB reduced from 75 o F to 62.5 o F and DP reduced from 67 o F to 55.5 o F H reduced from 38.6 btu/lb to 28.3 btu/lb (17%) and W reduced from lbs/lb to lbs/lb (35%) RH increased from 40% to 50% but both the heat content H and the moisture content were reduced RH is not a good indicator of comfort air conditions and most people cannot relate to WB, H and W So a good indicator of comfort weather conditions (weather forecasts) is Temp and DP Temp Summer indoor design DP temp is about 55 o F so conditions around or below 55 o F DP are comfortable Figure Figure? shows typical summer outdoor air conditions for a location such as Chicago and the desirable indoor air design conditions in summer. Note that the outdoor RH is 40% but the indoor RH is higher at 50%. All other psychrometric parameters (, WB, DP, W and H) of the indoor air is less than that of the outdoor air. Both the heat content (H) and moisture content (W) were removed by cooling the outdoor air. Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-3

4 Sensible Heat Gain (SHG) or Loss (SHL) is the heat gained or lost by a substance (solid, liquid or gas, in this case air and water vapor mixture) without a change in state from solid to liquid or liquid to gas. There is a change in temp only. Latent Heat Gain (LHG) or Loss (LHL) is the heat gained or lost that changes the state of a substance (in this case the water vapor part only of the air and water vapor mixture) from solid to liquid or liquid to gas (in this case the water vapor part of the air and water vapor mixture). Total Heat Gain (THG) or Loss (THL) is the sum of the sensible and latent heat gained or lost. Enthalpy (H) or heat content is the total heat contained in the air and water vapor mixture. In English (IP) units the heat content of the air is measured from 0 o F and the heat content of the water vapor is measured from 32 o F which is the freezing point of water at standard pressure. So the enthalpy of dry air below 0 o F is a negative value. The enthalpy of moisture below 32 o F is not a factor since most of it will have condensed and then frozen out as ice from the air. In metric (SI) units the enthalpy of both the dry air and water vapor is measured from 0 o C. Sensible Heat Gain (SHG) Latent Heat Gain (LHG) Total Heat Gain (THG) SHG = H2 - H1 LHG = H3 - H2 THG = H3 - H1 H3 H3 H2 W H2 W W H1 H1 Figure Sensible Heat Factor (SHF) is the ratio of Sensible Heat removed (applies mainly to cooling processes) to the Total Heat removed. SHF = SH/TH. Enthalpy Deviation. The enthalpy values shown on the psychrometric chart are at saturation (100% RH and = WB = DP). The constant enthalpy value lines are assumed to be along the constant WB temp lines. Theoretically there is a very slight deviation between the constant enthalpy and WB lines that can be ignored in HVAC process calculations. Figure? shows a heating and humidification process. The heating is by a heating coil which could be electric resistance or a coil of tubes with hot water or steam passing through it. In practice the humidification process includes some sensible heat gain of the dry air by the steam also. Dehumidification is usually done by a cooling coil with chilled water passing through it s tubes. The Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-4

5 sensible heat and latent heat removal occurs simultaneous as the air temperature approaches the saturation temperature of the. It does not occur separately as shown in the figure. Latent heat removal can also be done by passing the moist air through desiccant material substances that will absorb the moisture from the air. The desiccant material has to be replaced routinely after it has absorbed all it can and is completely soaked with water. The air passing through such a dehumidifier can pick up some of the desiccant material contaminating the supply air to the space. So for this reason desiccant dehumidification is used mainly in industrial air conditioning. Heating and Humidification W Sensible Heat Gain (SHG) Latent Heat Gain (LHG) 50% RH Heating Steam 3 Coil Humidifier SHG LHG LHG % RH = 20 o F 100 o F 100 o F 1 SHG 5% RH 2 RH = H = 100% 7 btu 5% % 47.5 btu 20 o 100 o W = lbs lbs lbs Cooling and De-Humidification W 1 3 Sensible Heat Loss (SHL) Latent Heat Loss (LHL) 50% RH Cooling 1 Coil LHL SHL & LHL % RH 3 SHG = RH = H = 100 o F 50% 47.5 btu 100 o F 50% 47.5 btu 50 o 100 o W = lbs lbs Figure Specific Volume (V) and Density (D) Specific Volume (V) ft3/lb Density (D) lbs/ft3 Specific Volume 13.5 Lines Specific Volume (V) is the volume of of unit mass of air. Ex. 14 ft3 per lb Density (D) is the mass of unit volume of air. Ex lbs/ft3 D = 1 / V and V = 1 / D The values of density are not shown on the psychrometric chart. It is 1 / V Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-5

6 Notes Given any two psychrometric conditions, all the other psychrometric conditions can be read off the chart or calculated with equations that relate them to each other. In practice outdoor air conditions are given as Dry Bulb () and Wet Bulb (WB) temperatures and the desired indoor air design conditions are given as Dry Bulb () temperature and Relative Humidity (RH). If the WB is known then the Enthalpy (H) is known (and vice versa) and a second condition is not required. The constant value WB and H lines on the psychrometric chart are the same. If the Dew Point (DP) is known then the Humidity Ratio (W) is known (and vice versa) and a second condition is not required. The constant value DP and W lines on the psychrometric chart are the same. At 100% RH, = WB = DP. DP is calculated from and WB. Weather data from the National Climatic Data Center show (measured with a normal mercury thermometer) and WB (measured with a sling thermometer) temperatures. RH measurement methods (using a hygrometer) are approximate. Barometric Pressure (BP or P) of the atmosphere is measured with a barometer. Evaporative cooling towers are selection is based on WB. DP together with is the best indication of weather and comfort air conditions. The terms and WB are used in HVAC applications. When the temperature is given without any qualifying indication such as, WB or, it is assumed to be. Gas Laws: Examples 1. A given mass of dry air occupies 2100 ft3 and it's temp is 45 F. What is the volume of the air after it is heated to 125 F. T1 = = 505 K, V1 = 2100 ft3, T2 = = 585 K P1V1/T1 = P2V2/T2. Since pressure is not given assume P1 = P2 (cancels out) V2 = V1T2/T1 = 2100*585/505 = ft3 2. What is the volume of 100 lbs of dry air at 120 F and 5.3 pounds per square inch gauge (psig). Only one set of conditions is given. However the properties of standard air are known and this can always be used as the second set of conditions. They are 70 F temperature, atmospheric pressure of 14.7 pounds per square inch absolute (psia) and volume of ft3/lb. T1 = = 530 K, P1 = 14.7, V1 = P1V1/T1 = T2 = = 580 K, P2 = 5.3 psig = 20 psia. PiV1/T1 = 0.37 = P2V2/T2 = 20V2/580. V2 = 580*0.37/20 = ft3 for 1 lb of air Volume of 100 lbs of air at 120 F and 5.3 psig = 1073 ft3. Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-6

7 Psychrometrics - Examples Dry Bulb Wet Bulb WB Dew Point DP Rel Hum RH Hum Rat W Enthalpy H Sp. Vol V Density D Room-1 is at 80 and 50 RH. Room-2 is at 70 and 90 RH. Which room has the higher heat content? 2. Air at 65 is saturated. What is the DP, WB, RH, H, and W Q1 H2 > H1 Q2 Saturated Moisture Line W 100% RH W H(2) = 32.4 At 65 & 100% RH H(1) = 31.6 (2) 70, 90% RH WB = DP = DP (1) 80, 50% RH 65 WB A room is at 80 and 50 RH. An air-conditioning unit starts to cool the air. At what temp will the moisture in the air start to condense? What is the initial and final enthalpies and humidity ratios? Q3 Q3 W Moisture starts to H(1) = 31.6 condense at 59 F H(2) = 26.4 W (2) 59, 100% RH (1) 80, 50% RH (2) 59, 100% RH (1) 80, 50% RH W(1) = W(2) = Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-7

8 lbs of air at 80 and 50 RH is cooled to 50. How much (1) heat was removed, and (2) moisture was removed? H1 at 80, 50% RH = 31.6, H2 at 50, 100% RH = 20.3, H1 H2 = 11.3 btu/lb Heat removed from 100 lbs = 100 * (H1 H2) = 1130 btu W1 at 80, 50% RH = 0.011, W2 at 50, 100% RH = , W1 W2 = lbs/lb Moisture removed from 100 lbs = 100 * (W1 W2) = 0.34 lbs ft3 of air (density lbs/ft3) at 80 and 50 RH was cooled to 50 WB. How much (1) sensible heat (2) latent heat (3) total heat, and (4) moisture was removed? Q5 H1 = 31.6 SH/lb removed = H2 - H3 = = 6 btu/lb W LH/lb removed = H1 - H2 = = 5.2 btu/lb H2 = 26.4 TH/lb removed = H1 - H3 = 11.2 btu/lb or TH = SH + LH = = 11.2 btu/lb H3 = 20.4 Moisture removed = W1 - W3 = = (2) 59, 100% RH (1) 80, 50% RH W1 = = W2 Mass of air = volume * density = LH (3) 50, 100% RH 1000 ft3 * lbs/ft3 = 75 lbs SH W3 = SH removed = 75 * 6 = 450 btu LH removed = 75 * 5.2 = 390 btu Total Heat removed = 75 * 11.2 = 840 btu Moisture removed = 75 * = lbs cfm of outside air (OA) at 100 and 85 WB is mixed with 8000 cfm of return air (RA) at 75 and 40 RH. Calculate mixed air (MA) weight,, WB, DP, RH, W, H? Air density = lbs/ft3. When different quantities of two identical fluids (liquids or gases) but at different conditions are mixed (added together) then the new quantity is the sum of the two quantities. Example, 10 lbs of water added to 5 lbs of water is 15 lbs of water cfm (cubic feet per minute or ft3/min) of OA when mixed with 8000 cfm of RA adds up to 10,000 cfm of MA. The mass of these volumes of air is volume x density. OA = 2000 * = 150 lbs, RA = 8000 * = 600 lbs, MA = * = 750 lbs = OA + RA. The mixed air condition is the weighted average of the conditions of the two fluids that were mixed. You can find the weighted average by using the weights or volumes of OA and RA since they are in the same proportion. Example, 2000 cfm of OA at 95 when mixed with 8000 cfm of RA at 75 produces MA = 100*(2000/10000) + 75*(8000/10000) = 80. OA: = 100 o F, WB = 85 o F. RH = 55%, H = 49.4 btu/lb, DP = 80.8 o F, W = lbs/lb. RA: = 75 o F, RH = 40%. WB = 60 o F, H = 26.4 btu/lb, DP = 49.5 o F, W = lbs/lb. Mixed Air (MA): = 0.2* *75 = 80 o F, WB = 0.2* *60 = 65 o F DP = 0.2* *50 = 56.2 o F, RH = 0.2* *40 = 43% H = 0.2* *26.4 = 31 btu/lb W = 0.2* * = Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-8

9 7. In Q6, the mixed air is cooled to 50 DP. How much (1) sensible heat (2) latent heat (3) total heat, and (4) moisture was removed? The dew point (DP) of the mixed air is 56.2 o F. So the mixed air reaches 100% RH (saturated) when it is cooled to 56.2 o F. Additional cooling occurs along the saturated line (100% RH line). At DP = 50 o F, = 50 o F, WB = 50 o F, RH = 100%, H = 20.3 btu/lb, W = lbs/lb. Using Equations MA mass = ft3 * lbs/ft3 = 750 lbs. Specific heat of air = btu/lb. o F. SH removed = Mair * sp.ht. * (T1 T2) = 750 * * (80 50) = 5422 btu Latent Heat of condensation or vaporization of water at 50 o F = 1065 btu/lb LH removed = Mair * (W1 W2) * 1065 = 750 * ( *) * 1065 = 2478 btu Moisture removed = Mair * (W1 W2) = lbs Total Heat removed = SH + LH = = = 7900 btu Using Psychrometric Chart Q7 H1 = 31 SH/lb removed = H2 - H3 = = 7 btu/lb W LH/lb removed = H1 - H2 = = 3.6 btu/lb H2 = 27.4 TH/lb removed = H1 - H3 = 10.6 btu/lb or TH = SH + LH = = 10.6 btu/lb H3 = 20.4 Mixed Air at Moisture removed = W1 - W3 = = (2) 56.2, 100% RH (1) 80, 65 WB, 43% RH W1 = = W2 Mass of air = volume * density = LH (3) 50, 100% RH ft3 * lbs/ft3 = 750 lbs SH W3 = SH removed = 750 * 7 = 5250 btu LH removed = 750 * 3.6 = 2700 btu Total Heat removed = 750 * 10.6 = 7950 btu Moisture removed = 750 * = lbs 8. In Q7 the cooed air at 50 DP is reheated to 55. How much (1) sensible heat (2) latent heat (3) total heat, and (4) moisture was added? (1) SH added = Mair * sp.ht * (T1 T2) = 750 lbs * * (55 50) = 903 btu (2) LH added = 0 (3) TH added = SH = 903 btu (4) Moisture added = 0 Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-9

10 cfm of outside air at 10 is mixed with 8000 cfm of return air at 75 and 40% RH. The mixed air is heated to 110 and then humidified to 45% RH. How much (1) heat, and (2) moisture was added? What is the final WB, DP, W, H? OA: = 10 o F, WB = 10 o F. RH = 100%, H = 3.8 btu/lb, DP = 10 o F, W = lbs/lb. RA: = 75 o F, RH = 40%. WB = 60 o F, H = 26.4 btu/lb, DP = 49 o F, W = lbs/lb. Mixed Air (MA): = 0.2* *75 = 62 o F, WB = 0.2* *60 = 50 o F DP = 0.2* *49 = 41 o F, RH (from chart at 60, 50 WB) = 50% H = 0.2* *26.4 = 21.9 btu/lb W = 0.2* * = Heat (sensible) added = 10,000 ft3/min * lbs/ft3 * * (110 62) = 8676 btu Moisture (latent) added: Mixed air = 62 o F and W = lbs/lb. MA is heated to 110 o F but no moisture added, so W = (RH goes down from 50% to 10%) Air at 110, 10% RH & W is humidified to 45% RH. W increased to Moisture (latent heat) added = 10,000 ft3 * lbs/ft3 * ( ) * 1030 = 1,514 btu/lb. Latent heat of vaporization or condensation at 110 o F is 1030 btu per lb of moisture. Note that at 50 o F it was 1065 btu/lb At 110 and 45% RH (from chart): DP = 84 o F. WB and H are off the chart. 10. In Q9, the heated and humidified mixed air is supplied into a room of volume 100' x 100' x 10' and at 75 and 40% RH. Wall-U = 0.2, Roof-U = 0.15, Glass-U = % of the gross wall area is glass window. Outside Air (OA) at 10 o F and 10 o F WB infiltration into the room is 0.6 Air Changes per Hour (ACH). Specific heat of air and water vapor are and Latent heat of condensation / evaporation at 110oF is 1030 btu/lb. What is the new room, WB, DP, RH, W, H at the end of one hour? H at 110 and 45% RH is not on the psychrometric chart so calculate it. Amount of moisture per lb of air = (from chart) Amount of dry air per lb of air = = H btu/lb of dry air (M*spht*DT) = lbs * * (110 0) = btu/lb H btu/lb of moisture = lbs * 0.45 * (110-32) * 1030 = = 27.3 btu/lb H btu/lb of air (dry & moisture) = = 53.1 btu/lb Total amount of Supply Air (SA) = 10,000 ft3/min * lbs/ft3 = 75 lbs/min = 4500 lbs/hr. = 110 o F, DP = 84 o F, W = lbs/lb, H = 53.1 btu/lb Room Air (RA) = 100 x 100 x 10 = 100,000 ft3 = 100,000 * lbs/ft3 * 60 = 450,000 lbs at = 75 o F, RH = 40%, WB = 60 o F, DP = 50 o F, H = 26.5 btu/lb, W = lbs/lb. Outside Air (OA) = 2000 ft3/min (9,500 /lbs/hr) at = 10 o F, H = 3.8 btu/lb, W = lbs/lb. Infiltration Air (IA) = 0.6 ACH = 0.6* 100,000 ft3 / 60 = 1,000 ft3/min = 4500 lbs/hr. CFM = ACH * VOL / 60 Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-10

11 Outside Air at RH = 100% Heating Coil Humidifier = WB = DP = 10 o F 10,000 ft3/min (45,000 lbs/hr) H = 3.8 btu/lb at 110 o F, 40% RH OA MA SA W = lbs/lb Displaced Air = 100 RH 50 WB 45 RH Infiltration 10, ,000 = IA 11,000 ft3/min = Infiltration = 6 ACH 49,500 lbs/hr RA 0.6*100000/60 = ROOM 1000 ft3 = 4500 lbs/hr 100,000 ft3 = 75oF ,000 lbs RH = 50% 50 RH = WB = 10 o F = 75, RH = 50 WB = 60oF ROOM H = 3.8 btu/lb H = 26.4 btu/lb W = lbs/lb Heat loss (HL) through W = lbs/lb envelope 1,201,500 btu/hr When air enters the a room, an equal amount is displaced from the room 1,000 ft3 of Infiltation Air mixes with 99,000 ft3 of Room Air, New RA = Heat Loss = 0.01* *75 = WB = 0.01* *60 = 59.5 Infiltration Heat Loss = 4500 lbs/hr * 0,241 * (75-10) = 70,500 btu/hr RH = 45 W = Roof-U = 0.15, Wall-U = 0.20, Glass-U = 1.0. Roof- A = 100*100 = 100,000. Wall+Glass-A = 100*10*4 = 4,000. Wall-A = 2,000, Glass-A = 2,000. Room at Σ A*U = * * *1.0 = 17,400 75, 40 RH DT = = 65 Conduction Heat Loss (HL) = 17,400 * 65 = 1,131,000 btu/hr Total = Conduction + Infiltration = 1,201,500 btu/hr W = The heat loss (sensible) from the room is 1,201,500 btu/hr. The drop in (DT) is: W = ,000 * * DT = 1,201,500, DT = 11. = = 64 o F. W = From Chart ( = 64 o F, W = lbs/lb), WB = 55 o F, RH = 55%, H = 23.2 btu/lb ,000 ft3 of SA 110, W is mixed with 90,000 ft3 of RA 64, W = 0.1* *64 = So 10,000 ft3/min at 110 is not enough. Increasing the Supply Air quantity (based on cooling load) will increase System and Duct Sizes and also Fan Energy consumption. Increasing the Supply Air Temperature above 110 o F will be uncomfortable when it reaches the occupants. Climates with winter design temperatures below 30 o F require a separate heating system. The heating source can be hot water, steam, electric resistance or gas. It could even be coal or wood fireplaces. The envelope of the building analyzed above had Wall-U = 0.2, Roof-U = 0.15 and Glass-U = 1.0 (1/8 single glass). ASHRAE Standard 90.1 for Chicago is Wall-U = 0.084, Roof-U = and Glass-U = 0.46 for 40% to 50% glass. The typical U-value for coated ¼ inch double glass is about Using these envelope U-values, the building may not require a supplemental heating system. The U-values of the envelope must be such that the inside surface temps are reasonably high. It is possible to have the space air temp maintained at 75 o F but the inside surface temp of the 1/8 inch single glass come close to the outside air temp. There is now radiant heat transfer from the occupants to the cold envelope inside surfaces. This is not comfort. So even with an efficient envelope, there has to be warm air supply (usually linear strip diffusers in the ceiling along the perimeter) to maintain the envelope surfaces, particularly the glass, at acceptable temps. To do this. baseboard radiation or radiant ceiling panels along the perimeter are used. Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-11

12 11. A classroom space is 100 x 100 x 10. Room Air (RA) must be maintained at 75 o F and 50% RH. Outdoor Air (OA) condition is 95 o F and 60% RH. Sensible Heat Gain (SHG) through the walls, windows and roof is 89,500 btu/hr. Summer infiltration through the envelope is 0.1 air changes per hour (ACH). Lighting density is 2.0 watts/ft2 Receptacle (equipment connected to wall sockets) density is 1.0 watts/ft2 ASHRAE-Standard occupancy density for a classroom is 20 ft2/person ASHRAE-Standard occupancy ventilation air is 15 cfm (ft3/min) per person. Sensibe Heat Gain (SHG) by each person is 250 btu/hr. Latent Heat Gain (LHG) by each person is 200 btu/hr. LHG (evaporation / condensation) at 95 o F is 1,040 btu/lb LHG (evaporation / condensation) at 55 o F is 1,060 btu/lb The air must be supplied at 55 o F so that air reaching occupants is close to 75 o F. Calculate: (1) Room Sensible Heat Gain (SHG) and Latent Heat Gain (LHG). (2) Supply Air (SA) quantity CFM (Cubic Feet per Minute or ft3/min) at 55 o F to offset the Room Sensible Heat Gain (SHG). (3) Supply Air (SA) moisture content to offset the Room Latent Heat Gain (LHG). (4) Total cooling (including ventilation) load across cooling coil in tons refrigeration. The heat and moisture content in the Supply Air must be less than the required Room Air heat and moisture content by the amount of the SHG and LHG in the room. Air density is lbs/ft3, air specific heat is btu/lb. o F and there are 60 minutes in an hour. To convert CFM * 4.5 = lbs/hr. (ft3/min * lbs/ft3 * 60 min/hr = lbs/hr). Heat gain or loss is Mass (lbs or lbs/hr) * spht * DT where DT is the change in temperature. The factor 1075 is latent heat of condensation for water vapor at 32 o F. This is a safe high value. Room SHG and LHG Room Area (A) = 100 * 100 = 10,000 ft2. Room Volume (V) = 10,000 ft2 * 10 = 100,000 ft3. Number of people = 10,000 ft2 / 20 ft2/person = 500 People SHG from People = 500 P * 250 btu/hr per person = 125,000 btu/hr. LHG from People = 500 P * 200 btu/hr per person = 100,000 btu/hr. SHG from Lights = 10,000 ft2 * 2.0 w/ft2 * 3.41 btu/watt = 68,200 btu/hr. SHG from Receptacles = 10,000 ft2 * 1.0 w/ft2 * 3.41 btu/watt = 34,100 btu/hr. SHG through envelope = 89,500 btu/hr. Infiltration = 0.1 ACH = 0.1 * Volume = 0.1 * 100,000 = 10,000 ft3/hour = 166 ft3/min (CFM). Infiltration mass = 10,000 ft3/hr * lbs/ft3 = 1,000 lbs/hr. OA: = 95 o F, RH = 60%, WB = 83 o F, DP = 79 o F, H = 47.1 btu/lb, W = lbs/lb. RA: = 75 o F, RH = 50%, WB = 63 o F, DP = 55 o F, H = 28.3 btu/lb, W = lbs/lb. SHG (infltr) = (166 ft3/min * 4.5) lbs/hr * (spht) * (95 75) = 7,223 btu/hr. LHG (infltr) = (166 ft3/min * 4.5) lbs/hr * 1040 * ( ) = 97,400 btuhr. Total Room SHG = 125, , , , ,200 = 324,000 btuhr Total Room LHG = 100, ,400 = 197,400 btu/hr. Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-12

13 Supply Air CFM * * 60) lbs/hr * * (T-room T-supply) = Room Sensible Heat Gain. Supply Air CFM = SHG / (1.08 * (Tr Ts) ) = 324,000 / (1.08 * (75 55) = 15,000 ft3/min. Supply Air CFM per square foot of floor area = 15,000 ft3/min / 10,000 ft2 = 1.5 CFM/ft2 Space Area (A) = 100 * 100 = 10,000 ft2. Volume = 10,000 ft2 * 10 ft = 100,000 ft3. Occupancy is 20 ft2/person. No. of People = 10,000 ft2 / 20 = 500 People. Outdoor Air CFM = 500 People * 15 cfm/person = 7,500 ft3/min. Ratio = 7500/15000 = 0.5. Return Air CFM = SA OA = 15,000 7,500 = 7,500. Ratio = 7500/15000 = 0.5. OA: = 95 o F, RH = 60%, WB = 83 o F, DP = 79 o F, H = 47.1 btu/lb, W = lbs/lb RA: = 75 o F, RH = 50%, WB = 63 o F, DP = 55 o F, H = 28.3 btu/lb, W = lbs/lb Mixed Air (MA) = 0.5 * * 75 = 85 o F. WB = 0. 5 * * 63 = 73 o F H = 0. 5 * * 28.3 = 37.7 btu/lb. W = 0.5 * * = lbs/lb. DP = 68 o F (from psychrometric chart). The Mixed Air (or Cooling Coil entering air) at 85 o F and 68 o F DP has to be cooled to 55 o F (Cooling Coil leaving Air). Since 55 o F leaving air is less than 68 o F DP entering air, the leaving air is saturated. So leaving air is saturated (RH = 100%) and WB = DP = = 55 o F. Cooling Coil leaving air H = 23.2 btu/lb and W = lbs/lb to offset Room Sensible Heat Gain (SHG). But the leaving air at DP = 55 o F and W = lbs may not be enough to offset the Room Latent Heat Gain (LHG). So determine the required W and to offset LHG. The Room Latent Heat Gain(LHG) is = 197,400 btu/hr (CFM * 4.5) * (W-room W-supply) * 1060 = Room Latent Heat Gain. W-supply is unknown. CFM has been calculated as 15,000 ft3. The factor 4.5 converts cfm to lbs/hr. The factor 1060 is the latent heat of condensation for water vapor at about 55 o F to 45 o F. 67,500 lbs/hr * ( Ws) * 1060 = 197,400 btu/hr * ( Ws) = *Ws = 1. Ws = 2.37/362.5 = lbs/lb. At Ws = and RH = 100%, the = WB = DP = 47 o F. So the mixed air has to be cooled to 47 o F and then reheated to 55 o F. Required cooling coil leaving air condition is: = WB = DP = 47 o F, RH = 100%, W = , H = 18.7 Cooling Coil Load = 15,000 ft3/min * 4.5 * (H-entg H-lvg) = * 4.5 * ( ) = 1,282,500 btu/hr. 1 Ton cooling = 12,000 btu/hr. Cooling Load Tons = 1,282,500 / 12,000 = 107 tons. SH cooling = 15,000 * 4.5 * * (85 47) = 615,600 LH cooling = 15,000 * 4.5 * 1060 * ( ) = 601,020. TH cooling = SH + LH = 1,216,620 The air leaving the cooling coil at 47 o F must be reheated to 55 o F. Re-Heat load = 15,000 ft3/min* 4.5 * spht * (55 47) = 67,500*0.241*8 = 130,140 btu/hr. Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-13

15 12. An office space is 100 x 100 x 10. Room Air (RA) must be maintained at 75 o F and 50% RH. Outdoor Air (OA) condition is 95 o F and 60% RH. Sensible Heat Gain (SHG) through the walls, windows and roof is 89,500 btu/hr. Summer infiltration is zero air changes per hour (building is pressurized) Lighting density is 2.0 watts/ft2 Receptacle (equipment connected to wall sockets) density is 1.0 watts/ft2 ASHRAE-Standard occupancy density for a classroom is 143 ft2/person ASHRAE-Standard occupancy ventilation air is 20 cfm (ft3/min) per person. Sensibe Heat Gain (SHG) by each person is 250 btu/hr. Latent Heat Gain (LHG) by each person is 200 btu/hr. Use LHG (evaporation / condensation) of 1075 btu/lb for all air temperatures The air must be supplied at 55 o F so that air reaching occupants is close to 75 o F. Calculate: (1) Room Sensible Heat Gain (SHG) and Latent Heat Gain (LHG). (2) Supply Air (SA) quantity CFM (Cubic Feet per Minute or ft3/min) at 55 o F to offset the Room Sensible Heat Gain (SHG). (3) Supply Air (SA) moisture content to offset the Room Latent Heat Gain (LHG). (4) Total cooling (including ventilation) load across cooling coil in tons refrigeration. (5) Apparatus Dew Point (ADP) given Bypass Factor (BF) = 0.2 Room Area (A) = 100 * 100 = 10,000 ft2. Room Volume (V) = 10,000 ft2 * 10 = 100,000 ft3. Number of people = 10,000 ft2 / 143 ft2/person = 70 People SHG from People = 70 P * 250 btu/hr per person = 17,500 btu/hr. LHG from People = 70 P * 200 btu/hr per person = 14,000 btu/hr. SHG from Lights = 10,000 ft2 * 2.0 w/ft2 * 3.41 btu/watt = 68,200 btu/hr. SHG from Receptacles = 10,000 ft2 * 1.0 w/ft2 * 3.41 btu/watt = 34,100 btu/hr. SHG through envelope = 89,500 btu/hr. Infiltration = 0. SHG (infltr) = 0. LHG (infltr) = 0 Total Room SHG = 17, , , ,500 = 209,300 btuhr Total Room LHG = 14,000 btu/hr. Supply Air CFM = SHG / (1.08 * (Tr Ts) ) = 209,300 / (1.08 * (75 55) = 9,690 ft3/min. Supply Air CFM per square foot of floor area = 9,700 ft3/min / 10,000 ft2 = 0.97 CFM/ft2 Outdoor Air CFM = 70 People * 20 cfm/person = 1,400 ft3/min. Ratio = 1400/9690 = Return Air CFM = SA OA = 9,690 1,400 = 8,290. Ratio = 8290/9690 = OA: = 95 o F, RH = 60%, WB = 83 o F, DP = 79 o F, H = 47.1 btu/lb, W = lbs/lb RA: = 75 o F, RH = 50%, WB = 63 o F, DP = 55 o F, H = 28.3 btu/lb, W = lbs/lb Mixed Air (MA) = 0.14 * * 75 = 77.8 o F. WB = * * 63 = 65.8 o F H = * * 28.3 = 30.9 btu/lb. DP = 61 o F (from psychrometric chart). W = 0.14 * * = lbs/lb. Instructor: Varkie C. Thomas, Ph.D., P.E. Skidmore, Owings & Merrill LLP ARCH-551 (Fall-2002) ARCH 552 (Spring-2003) F6-15

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