# Latent Heat Flow

## Latent heat is the heat when supplied to or removed from air results in a change in moisture content - the temperature of the air is not changed.

### Latent Heat Flow - English (Imperial) units

The latent heat flow due to moisture in air can be expressed in English (Imperial) units as

Q_{l}= 60 h_{we}ρ q Δx (1)

where

Q_{l}= latent heat flow (Btu/hr)

h_{we}= 1060 - latent heat of vaporization of water (Btu/lb)

ρ =0.075 - air density at standard conditions (lb/ft^{3})

q = measured air flow (ft^{3}/min)

Δx = difference in humidity ratio (lb)_{h2o}/lb_{dry_air}

### Latent Heat Flow - SI-Units

The latent heat flow due to moisture in air can be expressed in SI-units (metric) as

Q_{l}= h_{we}ρ q Δx / 3600 (2)

where

Q_{l}= latent heat flow (kW)

h_{we}= latent heat of vaporization of water (2454kJ/kg - in air at atmospheric pressure and 20^{o}C)

ρ =air density at standard conditions (kg/m1.202*^{3})

q = air flow (m^{3}/hr)

Δx = difference in humidity ratio ()kg_{h2o}/kg_{dry_air}

*Note that properties of air changes with temperature. Interpolate values if necessary.

### Example - Latent Heat Flow

A ventilation system transports *10000 m ^{3}/h* of air through a building.

The state of the make-up (supply) air is *0 ^{o}C* and

*100%*relative humidity. From the Mollier diagram the humidity ratio -

*x*- can be estimated to

*0.0037 (*.

*)**kg*_{h2o}/kg_{dry_air}The state of the room air is *20 ^{o}C* and

*40%*relative humidity. From the Mollier diagram the humidity ratio can be estimated to

*0.0057 (*.

*)**kg*_{h2o}/kg_{dry_air}The latent heat flow can be calculated as

*Q _{l} = (2465.56 kJ/kg) (1.202 kg/m^{3}) (10000 m^{3}/h) ((0.0057 (kg_{h2o}/kg_{dry_air})) - (0.0037 (kg_{h2o}/kg_{dry_air}))) / 3600 *

* = 16.5 kW*