objectives learn about psychometrics psychometric chart equations

Objectives

Learn about Psychometrics

• Psychometric chart

• Equations

Humidity Ratio, W

• W = mw/ma

• Degree of saturation, µ = W/Ws

• Humidity ratio is hard to measure, but very useful in calculations

• What are units?

• Is W a function of temperature? What about Ws?

Ws = humidity ratio at saturationma = mass of dry airmw = mass of water vapor

Relative Humidity

• Φ = xw/xw,s = Pw/Pws

• Function of T

Easy to measure and useful in some contexts, but often need to know temperature as well

W

Ws

622.0

622.0

x = mole fractionP = pressureμ = degree of saturationW = humidity ratio

Dew-point temperature, td

• Temperature at which condensation will form• Under appropriate surface conditions

• Vapor is saturated

• Φ = ?

• Ws(P, td) = W

Wet-bulb temperature, VBT (t*)

• Temperature of wet surface or

• Temperature at which water, by evaporating into the air, will bring air to saturation adiabatically

• * superscript is designation that variable is evaluated at the wet-bulb temperature

• Note, distinct from that measured by a sling psychrometer• Section 9.5

Tables for Moist Air (P = 1 atm)

• Tables A.4 in your text

• Ability to get Ws for calculations

• Subscripts:• a = dry air, s = saturated air

v = va+µvas

h = ha+µhas

s = sa+µsas

Psychrometric Chart

• Need two quantities for a state point• Can get all other quantities from a state point

• Can do all calculations without a chart• Often require iteration• Many “digital” psychrometric charts available

• Can make your own

• Best source is ASHRAE fundamentals (Chapter 6)• Also in your text (back cover fold-out)

Ref: Tao and Janis (2001)

Ref: Tao and Janis (2001)

Ref: Tao and Janis (2001)

Ref: Tao and Janis (2001)

Examples

• What is enthalpy of air in the classroom right now?

• Condensation on windows when taking a shower

• How cold does it have to be outside for condensation to form on windows?

– Assumption is that windows are the same temperature as outside air

– 80 °F, RH = 80%

Alternate calculation for W

• PV = mRT (IGL)

• What do we know about R ratio?

• P = Pw + Pa

w

a

a

w

TRVP

TRVP

a

w

R

R

P

P

m

mW

a

a

w

w

w

w

PP

PW

622.0

R = gas constantP = pressureV = volumeT = absolute temperatureW = humidity ratio

Subscripts: w is water vapor, a is dry air

Calculation of psychometric quantities

• For an ideal gas,• hda = ∫cpadT, hw = ∫cpwdT

• So, hda = cp,dat which assumes a reference state of 0 °F or 0 °C – Tables A4• Note different reference

• hw = cpwt + hg0

• h = cp,dat + W(cpwt + hg0)Or you can use:• h = cpt + W∙hg0, cp = cp,da + Wcpw

cp = specific heath = enthalpyT = absolute temperaturet = temperature W = humidity ratio

Subscripts: w is water vapor, a is dry air, g is saturated water vapor

Adiabatic mixing

• Governing equation hmQhmoutin

External heat

Sensible heating

tcmQ p

Dehumidification by Cooling

Real Dehumidification Process

Mold in a duct

Transport of saturated air

tsurface < tdp Condensation

Humidification

hw Specific enthalpy of water added to system

hg Specific enthalpy of saturated water vapor

Summary

• Describe psychrometric quantities

• Given any two psychrometric quantities, calculate any other quantity

• Use Tables A4 or psychrometric charts to look up psychrometric quantities

• Calculate psychrometric quantities at non-standard conditions