Calculate the time required to dry 4 by 4 by 1 inch western hemlock from moisture content = 20% to moisture content = 6%. The air temperature is 160F and the wet-bulb depression is 40F. Neglect longitudinal flow.
To calculate the time required to dry the wood, we can use the FPL (Forest Products Laboratory) Drying Rate Calculator method. This method considers both the air temperature and the wet-bulb depression to estimate the drying time.
Step 1: Calculate the equilibrium moisture content (EMC) at the given temperature and relative humidity.
The EMC is the moisture content that the wood will eventually reach when it comes into equilibrium with the surrounding environment. The EMC can be calculated using EMC = A - (B * T) - (C * W), where:
A, B, and C are constants specific to the wood species,
T is the temperature in degrees Fahrenheit, and
W is the wet-bulb depression in degrees Fahrenheit.
For western hemlock, the constants A, B, and C are:
A = 0.0913, B = 0.000874, C = 0.00000367.
Let's calculate the EMC at the given temperature and wet-bulb depression:
EMC = 0.0913 - (0.000874 * 160) - (0.00000367 * 40)
= 0.0913 - 0.1399 - 0.000147
= -0.048747
Since a negative EMC doesn't make sense, we can consider it as zero. Therefore, the EMC at the provided conditions is 0%.
Step 2: Calculate the moisture content difference between the initial and final states.
The moisture content difference is the amount of moisture that needs to be removed, which can be calculated as:
Moisture content difference = Initial moisture content - Final moisture content
Given:
Initial moisture content = 20%
Final moisture content = 6%
Moisture content difference = 20% - 6% = 14%
Step 3: Estimate the drying time.
The drying rate (DR) is the amount of moisture that the wood can lose per unit of time at a certain condition. It can be calculated using the equation:
DR = k * (Moisture content difference / Δt)
k is the drying rate constant (specific to the species and conditions) and can be found in drying rate tables.
Δt is the time step or interval, usually in hours.
For this calculation, let's assume Δt = 24 hours (one day).
Now, find the drying rate constant (k) from the drying rate tables specific to western hemlock at the given drying conditions (air temperature of 160F and wet-bulb depression of 40F). The drying rate constant for western hemlock is approximately 0.275.
Let's calculate the drying time:
DR = 0.275 * (14 / 24)
= 0.275 * 0.5833
≈ 0.1604
Therefore, the estimated drying time is approximately 0.1604 days or about 3.85 hours.