Air, temperature, humidity and dew point

On Jamal's second morning Roz hands him a small instrument the size of a phone: a digital psychrometer that reads air temperature, relative humidity and dew point at the press of a button. "Temperature is only half of what the air is telling you," she says. "The other half is water." Every cubic metre of air in the hall carries some water vapour, and how much it carries decides whether static builds up, whether coils sweat, and whether the hall can use outside air to cool itself. This lesson covers the properties of air a technician reads and records every day.

Air is a mixture

The air in a data hall is a mixture of dry air, mostly nitrogen and oxygen, and water vapour. The dry air part hardly changes. The water vapour part varies from almost nothing on a cold winter day to a few percent of the mass on a humid summer afternoon. That small amount of water matters a great deal, because it can change from vapour to liquid and back again, and when it does, it absorbs or releases a large amount of heat.

The study of moist air is called psychrometrics. Engineers use psychrometric charts and software to design cooling systems. Technicians do not need to design anything, but they do need to understand four or five measurements and what each one says about the hall.

Dry-bulb temperature

The ordinary air temperature, measured by a thermometer that is dry and shielded from radiation, is called the dry-bulb temperature. When a monitoring screen shows a rack inlet at 24 °C (75 °F), that is a dry-bulb reading. It is the number servers care about most, because it sets how hot their components run.

Dry-bulb temperature can be measured in degrees Celsius or Fahrenheit. A difference in temperature, such as the rise across a server, is often written in kelvins in Canada, because a difference of 1 K equals a difference of 1 °C. In the United States temperature differences are written in degrees Fahrenheit; a difference of 1 °C is a difference of 1.8 °F. Mixing up an absolute temperature and a temperature difference is a common error when converting: 20 °C (68 °F) is 68 °F, but a rise of 20 K is a rise of 36 °F, not 68.

Relative humidity

Warm air can hold more water vapour than cold air before it becomes saturated. Relative humidity, RH, compares the water vapour actually in the air with the most the air could hold at the same temperature, as a percentage. Air at 100 percent RH is saturated; any cooler surface it touches will collect condensation.

Relative humidity is easy to measure and easy to misread, because it changes with temperature even when the amount of water in the air does not. Take the same air from a cold aisle at 20 °C (68 °F) and 50 percent RH and heat it through a server to 32 °C (90 °F). No water has been added or removed, but the relative humidity in the hot aisle falls to about 25 percent, because the warmer air could hold more. A technician who compares an RH reading in the hot aisle with one in the cold aisle and concludes that the servers are drying the air has misread the instrument.

This is why modern guidelines prefer to control moisture by dew point, which does not change when air is heated or cooled without condensation.

Dew point

The dew point is the temperature at which air would become saturated if it were cooled without adding or removing water. Cool the air below its dew point and water condenses: on a cold drink can in summer, on a window in winter, or on a cooling coil. The dew point is a direct measure of how much water the air carries. Two air samples with the same dew point carry the same amount of water vapour, whatever their temperatures.

For a technician, the dew point answers two practical questions:

• Will this surface sweat? Any pipe, coil or cold plate colder than the dew point of the air around it will collect water. Chilled-water pipes are insulated for this reason, and liquid cooling loops are kept above the room's dew point.
• Is the air within the moisture limits of the thermal guidelines? The ASHRAE guidelines set limits on dew point as well as on relative humidity, as Lesson 3 explains.

The psychrometer calculates dew point from the temperature and relative humidity using a standard formula. The Magnus approximation, below, is accurate to within a few tenths of a degree in the range found in data halls.

Here T is the dry-bulb temperature in degrees Celsius and RH is in percent. Jamal does not need to work it by hand; the monitoring system and his instrument do it. But running it once in code helps him see how dew point behaves.

import math
# Dew point from dry-bulb temperature and relative humidity (Magnus approximation)
def dew_point_c(t_c, rh):
    g = math.log(rh / 100) + 17.62 * t_c / (243.12 + t_c)
    return 243.12 * g / (17.62 - g)

def rh_at(t_c, dp_c):
    """Relative humidity of air with dew point dp_c once it is at t_c."""
    es = lambda t: math.exp(17.62 * t / (243.12 + t))
    return 100 * es(dp_c) / es(t_c)

samples = [("Cold aisle", 20, 50), ("Hot aisle (same air)", 32, None),
           ("Summer, outside", 31, 65), ("Winter, outside", -15, 70)]
dp_cold = dew_point_c(20, 50)
print(f"{'Air':22s} {'T, C':>6s} {'RH %':>6s} {'dew point, C':>13s}")
for name, t, rh in samples:
    if rh is None:
        rh = rh_at(t, dp_cold)
    dp = dew_point_c(t, rh)
    print(f"{name:22s} {t:6.1f} {rh:6.1f} {dp:13.1f}")

Air                      T, C   RH %  dew point, C
Cold aisle               20.0   50.0           9.3
Hot aisle (same air)     32.0   24.6           9.3
Summer, outside          31.0   65.0          23.6
Winter, outside         -15.0   70.0         -19.3

The first two rows show the same air before and after it passes through a server: the temperature rises, the RH falls, and the dew point stays the same. The third row is a humid summer day at the cooling tower; the fourth is a cold winter day, when the outside air holds very little water.

Wet-bulb temperature

If a thermometer bulb is wrapped in a wet wick and air blows across it, water evaporates from the wick and cools the bulb. The temperature it settles at is the wet-bulb temperature. In dry air, more water evaporates and the wet bulb reads much lower than the dry bulb; in saturated air, nothing evaporates and the two readings are equal.

Wet-bulb temperature matters most outside the hall. A cooling tower or evaporative cooler can cool water only down to near the outdoor wet-bulb temperature, so the wet bulb sets how well that equipment works on a given day. Weather files for cooling design list both dry-bulb and wet-bulb temperatures. Inside the hall, technicians rarely use the wet bulb except when checking evaporative equipment.

Humidity ratio

Engineers often express moisture as the humidity ratio: the mass of water vapour per kilogram of dry air, usually in grams per kilogram (in the United States usually in grains per pound, where 7,000 grains make a pound). Air at a dew point of 10 °C (50 °F) carries about 7.6 g of water for every kilogram of dry air (53 grains of water for every pound of dry air). The humidity ratio, like the dew point, does not change when air is heated or cooled without condensation. It is the number used to calculate how much water a humidifier must add or a coil will remove.

import math
# Humidity ratio (grams of water per kilogram of dry air) from the dew point, at sea level
P = 101.325   # kPa
def vp_kpa(dp_c):
    return 0.61094 * math.exp(17.625 * dp_c / (dp_c + 243.04))
for dp in (-9, 0, 10, 15, 20):
    pw = vp_kpa(dp)
    w = 622 * pw / (P - pw)
    print(f"dew point {dp:4d} C  ->  {w:5.1f} g of water per kg of dry air")

dew point   -9 C  ->    1.9 g of water per kg of dry air
dew point    0 C  ->    3.8 g of water per kg of dry air
dew point   10 C  ->    7.6 g of water per kg of dry air
dew point   15 C  ->   10.6 g of water per kg of dry air
dew point   20 C  ->   14.7 g of water per kg of dry air

Why moisture matters in a data hall

Too little moisture and too much moisture both cause problems, and the limits in modern guidelines are a balance between them.

• Static electricity: very dry air lets static charges build up on people and surfaces. A discharge can damage sensitive components. The risk is controlled mainly by grounding and electrostatic discharge practice, which the DCT-120 safety course covers, rather than by humidifying the room.
• Condensation: air near saturation will condense on any surface cooler than its dew point, wetting equipment and floors.
• Corrosion: high humidity combined with gaseous pollutants, such as sulfur compounds from industry or nearby traffic, can corrode the copper and silver in circuit boards. The guidelines tighten the humidity limit where pollution is present.
• Energy: adding or removing moisture uses a lot of energy. Humidifiers that boil water to make steam are especially costly, so most modern halls allow a wide humidity range and humidify little or not at all.

At Beauharnois, the winter outside air is very dry, often with a dew point well below freezing, and the hall's humidity drifts low through January and February. Stonebridge decided years ago not to run humidifiers in Hall A and to rely on electrostatic discharge controls instead, a choice supported by research ASHRAE used when it widened its humidity limits.

Measuring humidity correctly

Humidity sensors drift more than temperature sensors and are easily fooled. Roz gives Jamal her rules:

• Compare like with like: compare dew points, not relative humidities, between places at different temperatures.
• Let the instrument settle: a handheld psychrometer brought from a warm office into a cold aisle needs a few minutes to reach the air temperature before its RH reading is meaningful.
• Do not breathe on the sensor or hold it in the exhaust of a server; read it in the free air stream.
• Check fixed sensors against a calibrated reference at the interval the maintenance program sets, often once a year, and record the offset.
• Report sensors that disagree with their neighbours by more than the site's tolerance; do not quietly adjust them.

Altitude and air density

Air at higher altitude is thinner. A cubic metre of air at Beauharnois or Ashburn, both near sea level, weighs about 1.2 kg (A cubic foot of air at Beauharnois or Ashburn, both near sea level, weighs about 0.075 lb); the same volume in a mountain city weighs noticeably less and carries less heat for the same temperature rise. Equipment ratings and the air-flow formulas in this course assume sea-level air. Technicians working at sites well above sea level will see derating tables on cooling equipment and IT equipment nameplates for this reason.