Calculating Humidification of a Room

I had an application where a customer needed to have a room at 80% relative humidity (RH). They produced a nylon backing for carpet, and they needed the high RH to reduce the “stickiness” in the process. Currently he was at 40% RH in a room that was sized at 40ft long by 20ft wide by 20ft high (12.2m long X 6.1m wide X 6.1m high). He wondered if our Atomizing Nozzles could help him. I decided to put on my engineering hat to calculate the amount of water that he would need to increase the moisture content. Other markets that would require higher RH in their ambient air are wood working, dust control, laboratories, and High Voltage applications.

Relative humidity (RH) is the percentage of water vapor as compared to saturation at the same temperature. So, at 100% RH, the ambient air cannot hold any more water. With our atomizing nozzles, we can atomize the water droplets to a very small droplet to help increase the absorption rate into ambient air. This will increase the RH of a room, but I will have to determine what size and how many.

The equation that I use is as follows, Equation 1:

Imperial Units                                                                    S.I. Units

H = V * RAC * (Wf – Wi) / (v * 7000) Imperial         H = V * RAC * (Wf – Wi) / (v * 997.9) Metric

Where:

H – mass flow rate of water, Lbs/hr                        H – mass flow rate of water, Kg/hr

V – Volume of Section, ft^3                                     V – Volume of Section, m^3

RAC – Room Air Changes, No. per hour                RAC – Room Air Changes, No. per hour

Wf – Final Water Content, Grains/lb of dry air        Wf – Final Water Content, Grams/Kg of dry air

Wi – Initial Water Content, Grains/lb of dry air        Wi – Initial Water Content, Grams/Kg of dry air

v – Specific Volume of Air, ft^3/lb                            v – Specific Volume of Air, m^3/Kg

Conversion Constant – 7000 Grains/lb                   Conversion Constant – 997.9 Grams/Kg

The customer stated that the room is at 68 deg. F (20 deg C). The humidity sensor is +/- 5%; so, when the RH in the room gets to 75%, it will kick on their system. They also use a standard HVAC unit to heat and cool the room. From these factors, we can determine some of the variables above. With the water content, you can find a chart online to determine the amount of water vapor that is contained in air at a specific temperature and RH. At 68 deg. F (20 deg. C), I was able to find the following information:

Imperial Units                                                       S.I. Units

Wi = 43 Grains/lb of dry air at 40% RH               Wi = 6.1 Grams/Kg of dry air at 40% RH

Wi = 80.5 Grains/lb of dry air at 75% RH            Wi = 11.5 Grams/Kg of dry air at 75% RH

Wf = 85.5 Grains/lb of dry air at 80% RH            Wf = 12.2 Grams/Kg of dry air at 80% RH

v = 13.35 ft^3/lb @ 68 deg. F, 1 atm                   v = 0.8334 M^3/Kg at 20 deg. C, 1 bar (absolute)

V = 40ft X 20ft X 20ft = 16,000 ft^3                     V = 12.2m X 6.1m X 6.1m = 454 m^3

Another factor is the number of air changes in that room. With the HVAC system, it will turn on and off to heat and cool the air.  Some fresh air is brought in during this cycle.  With a typical system, the room air will change between 2 – 4 times an hour.  So, RAC = 4/hour (worse case).  (Other locations may have scrubber systems, continuous air flow systems, etc. and the RAC will be greater).

If we plug in the numbers that we have, we can determine how much water that we will need to spray into the air to increase the RH from 40% to 80%.

Imperial Units

H = V * RAC * (Wf – Wi) / (v * 7000)

H = 16,000 ft^3 * 4/hr * (85.5 – 43 Grains/lb)/(13.35 ft^3/lb * 7000 Grains/lb)

H = 29.1 lb./hr

S.I. Units

H = V * RAC * (Wf – Wi) / (v * 997.9)

H = 454m^3 * 4/hr * (12.2 – 6.1 Grams/Kg)/ (0.8334 m^3/Kg * 997.9 Grams/Kg)

H = 13.3 Kg/hr.

Now that we know the rate of water to put into the ambient air, we have to look at the set up. With the settling time of the water droplets and the location of the humidity sensor, we will have a lead/lag problem.  To help in this situation, I would recommend to turn on the Atomizing Nozzles for 10 – 15 seconds, and wait 2 minutes to re-measure the RH.  This will help to not over saturate the room.  As for the location of the Atomizing Nozzles, you have to make sure that the spray does not contact any structure or other atomizing spray patterns.  This will cause the water to condense and either coat a structure or create rain.  To help with the entire system, I suggested our No Drip External Mix Wide Angle Flat Fan Pattern Atomizing Nozzle. This will eliminate a water valve at each Atomizing Nozzle. When the air pressure is turned off to stop spraying, the No Drip Atomizing Nozzle will seal and not allow any water to drip. To also help with consistent RH in the room, the EB2030SS was my choice. The spray range helps to cover the area especially with multiple units operating.

No Drip Atomizing Nozzle
No Drip Atomizing Nozzle

To determine the number of Atomizing Nozzles, we want to look at the time determination with the controller and the intermittence of operation. With the RAC = 4/hour, the air in the room will change over every 15 minutes.  We want to have a balance between the new air and the existing air.  So, with the time measurement of 2 minutes off and 15 seconds on, we will have 6 humidity checks over 15 minutes.  We can divide the amount of water to be injected into the room by 6 to cover that time span.  Also, we have to factor in that we will not be running the Atomizing Nozzle for the continuous hour.  We will have to adjust the amount for only running for 15 seconds.  So, the intermittent factor will be 0.0042 (the 15 seconds portion of the hour).

In taking into consideration the flow rate required during operation time, we can calculate the amount of flow required for the Atomizing Nozzle as in Equation 2.

Imperial Units                                                               SI Units

Flow rate: Q = H / (D * T * f)                                     Flow rate: Q = H / (D * T * f)

Mass Flow Rate: H = 29.1 lbs/hr                              Mass Flow Rate: H = 13.3 Kg/hr

Density of Water: D = 8.34 lbs/gal                            Density of Water: D = 1 Kg/L

Span division of time: T = 6                                      Span division of time: T=6

Intermittent Factor: f = 0.0042                                  Intermittent Factor: f = 0.0042

Q = 29.1 lbs/hr / (8.34 lbs/gal * 6 * 0.0042)              Q = 13.3 Kg/hr / (1 Kg/L * 6 * 0.0042)

Q = 138.5 gal/hr (GPH)                                            Q = 527.8 L/hr (LPH)

In the catalog, the model EB2030SS will flow 14.0 GPH (53.0 LPH) at 40 PSIG (2.8 Bar) water pressure. This would be in the compressed air pressure range of 50 PSIG (3.4 Bar) to 95 PSIG (6.5 Bar).  If we divide these out, it will tell us how many atomizing nozzles that is needed to humidify the room.

Imperial: 138.5 GPH/14.0 GPH = 9.9 or 10 Atomizing Nozzles.

SI units: 527.8 LPH/53.0 LPH = 9.9 or 10 Atomizing Nozzles.

The last thing to determine is the amount of time that would be required to maintain the 80% RH when the controller calls for more humidification. At 75% RH, we can use Equation 1 to determine the amount required to reach 80%.  As we plug in the initial Water Content, Wi, at 75% RH as 80.5 Grains/lb of dry air (11.5 Grams/Kg of dry air), we will get an H value of 3.42 lb/hr (1.55 Kg/hr).  With each Atomizing Nozzle putting out 14.0 GPH (53.0 LPH) of water, we can determine the time to atomize the 3.42 lbs (1.53 Kg) of water during the operational time.  The control will be much better as the air is changing with the new incoming air and the existing air.  Thus, we have in Equation 3:

Imperial Units                                                                SI Units

Time (sec): T = 3600 * m/ (N * Qa * D)                        Time (sec): T = 3600 * m/ (N * Qa * D)

Mass of water: m = 3.42 lb                                          Mass of water: m= 1.53 Kg

No. of Nozzles: N = 10                                                 No. of Nozzles: N = 10

Atomizing Flow Rate: Qa = 14.0 GPH                          Atomizing Flow Rate: Qa = 53.0 LPH

Density of Water: D = 8.34 lb/gal                                  Density of Water: D = 1 Kg/L

T = 3600 * 3.42 lb / (10 * 14 GPH * 8.34 lb/gal)            T = 3600 * 1.55 Kg / (10 * 53 LPH * 1 Kg/L)

T = 10.5 seconds                                                          T = 10.5 seconds

With some other humidification devices like steam generators, companies have to capitalize the system. With the Atomizing Nozzles, my customer was able to keep the cost down and control the RH at a high level for his manufacturing process.  In turn, he was able to increase productivity and reduce downtime.  If you need to increase the level of moisture in an area, you can always contact one of the Application Engineers at EXAIR for help.

John Ball
Application Engineer
Email:
johnball@exair.com
Twitter: @EXAIR_jb

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