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Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period Formula

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The Final Moisture Content for Falling Rate Period is defined as the ratio of the weight of moisture to the weight of dry solid present after the completion of the drying process. Check FAQs

X f(Falling) = (\frac{X c - X Eq}{\exp (\frac{A \cdot t f \cdot N c}{W S \cdot (X c - X Eq)})}) + X Eq

X_f(Falling) - Final Moisture Content for Falling Rate Period?X_c - Critical Moisture Content?X_Eq - Equilibrium Moisture Content?A - Drying Surface Area?t_f - Falling Rate Drying Time?N_c - Rate of Constant Drying Period?W_S - Dry Weight of Solid?

Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period Example

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Here is how the Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period equation looks like with Values.

Here is how the Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period equation looks like with Units.

Here is how the Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period equation looks like.

0.0675 = (\frac{0.11 - 0.05}{\exp (\frac{0.1 \cdot 37 \cdot 2}{100 \cdot (0.11 - 0.05)})}) + 0.05

0.0675 = (\frac{0.11 - 0.05}{\exp (\frac{0.1m² \cdot 37s \cdot 2kg/s/m²}{100kg \cdot (0.11 - 0.05)})}) + 0.05

0.0675 = (\frac{0.11 - 0.05}{\exp (\frac{0.1 \cdot 37 \cdot 2}{100 \cdot (0.11 - 0.05)})}) + 0.05

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Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period Solution

Follow our step by step solution on how to calculate Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period?

FIRST Step Consider the formula

X f(Falling) = (\frac{X c - X Eq}{\exp (\frac{A \cdot t f \cdot N c}{W S \cdot (X c - X Eq)})}) + X Eq

Next Step Substitute values of Variables

∴

X f(Falling) = (\frac{0.11 - 0.05}{\exp (\frac{0.1m² \cdot 37s \cdot 2kg/s/m²}{100kg \cdot (0.11 - 0.05)})}) + 0.05

Next Step Prepare to Evaluate

∴

X f(Falling) = (\frac{0.11 - 0.05}{\exp (\frac{0.1 \cdot 37 \cdot 2}{100 \cdot (0.11 - 0.05)})}) + 0.05

Next Step Evaluate

∴

X f(Falling) = 0.0674791934680083

LAST Step Rounding Answer

∴

X f(Falling) = 0.0675

Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period Formula Elements

Variables

Functions

Final Moisture Content for Falling Rate Period

The Final Moisture Content for Falling Rate Period is defined as the ratio of the weight of moisture to the weight of dry solid present after the completion of the drying process.

Symbol: X_f(Falling)

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Final Moisture Content for Falling Rate Period

Critical Moisture Content

The Critical Moisture Content is the ratio of amount of moisture present in the solids at the transition of constant and falling rate period to that of the weight of dry solid.

Symbol: X_c

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Critical Moisture Content

Equilibrium Moisture Content

The Equilibrium Moisture Content is defined as the ratio of the weight of moisture in equilibrium with the solid to the weight of dry solid.

Symbol: X_Eq

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Equilibrium Moisture Content

Drying Surface Area

The Drying Surface Area is the total area in the drying mass transfer operation i.e. exposed in contact with the drying medium.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Drying Surface Area

Falling Rate Drying Time

The Falling rate drying time is the time taken for drying operation in the falling rate period.

Symbol: t_f

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Falling Rate Drying Time

Rate of Constant Drying Period

The Rate of Constant Drying Period is the rate of drying that takes place for a given set of drying conditions in the constant rate period.

Symbol: N_c

Measurement: Mass FluxUnit: kg/s/m²

Note: Value should be greater than 0.

Formulas to find Rate of Constant Drying Period

Dry Weight of Solid

The Dry Weight of Solid is the weight of dry solid present in the system in the drying mass transfer operation.

Symbol: W_S

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Dry Weight of Solid

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

Other formulas in Drying from Critical to Final Moisture category

Go Total Drying Time based on Constant Drying Time and Falling Drying Time

t = t c + t f

Go Constant Drying Time from Initial to Critical Moisture Content

t c = W S \cdot \frac{(X i(Constant) - X c)}{(A \cdot N c)}

How to Evaluate Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period?

Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period evaluator uses Final Moisture Content for Falling Rate Period = ((Critical Moisture Content-Equilibrium Moisture Content)/(exp((Drying Surface Area*Falling Rate Drying Time*Rate of Constant Drying Period)/(Dry Weight of Solid*(Critical Moisture Content-Equilibrium Moisture Content)))))+Equilibrium Moisture Content to evaluate the Final Moisture Content for Falling Rate Period, The Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period formula is defined as the final moisture content that can be attained from the specified critical moisture content based on the drying conditions in falling rate period. Final Moisture Content for Falling Rate Period is denoted by X_f(Falling) symbol.

How to evaluate Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period using this online evaluator? To use this online evaluator for Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period, enter Critical Moisture Content (X_c), Equilibrium Moisture Content (X_Eq), Drying Surface Area (A), Falling Rate Drying Time (t_f), Rate of Constant Drying Period (N_c) & Dry Weight of Solid (W_S) and hit the calculate button.

FAQs on Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period

What is the formula to find Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period?

The formula of Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period is expressed as Final Moisture Content for Falling Rate Period = ((Critical Moisture Content-Equilibrium Moisture Content)/(exp((Drying Surface Area*Falling Rate Drying Time*Rate of Constant Drying Period)/(Dry Weight of Solid*(Critical Moisture Content-Equilibrium Moisture Content)))))+Equilibrium Moisture Content. Here is an example- 0.067479 = ((0.11-0.05)/(exp((0.1*37*2)/(100*(0.11-0.05)))))+0.05.

How to calculate Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period?

With Critical Moisture Content (X_c), Equilibrium Moisture Content (X_Eq), Drying Surface Area (A), Falling Rate Drying Time (t_f), Rate of Constant Drying Period (N_c) & Dry Weight of Solid (W_S) we can find Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period using the formula - Final Moisture Content for Falling Rate Period = ((Critical Moisture Content-Equilibrium Moisture Content)/(exp((Drying Surface Area*Falling Rate Drying Time*Rate of Constant Drying Period)/(Dry Weight of Solid*(Critical Moisture Content-Equilibrium Moisture Content)))))+Equilibrium Moisture Content. This formula also uses Exponential Growth (exp) function(s).

What are the other ways to Calculate Final Moisture Content for Falling Rate Period?

Here are the different ways to Calculate Final Moisture Content for Falling Rate Period-

Final Moisture Content for Falling Rate Period=((Initial Moisture Content for Falling Rate Period-Equilibrium Moisture Content)/(exp((Drying Surface Area*Falling Rate Drying Time*Rate of Constant Drying Period)/(Dry Weight of Solid*(Initial Moisture Content for Falling Rate Period-Equilibrium Moisture Content)))))+Equilibrium Moisture Content

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Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period Formula

​GoFinal Moisture Content based on Initial to Final Moisture Content for Falling Rate Period Formula

Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period Example

Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period Solution

Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period Formula Elements

Other Formulas to find Final Moisture Content for Falling Rate Period

Other formulas in Drying from Critical to Final Moisture category

How to Evaluate Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period?

FAQs on Final Moisture Content based on Critical to Final Moisture Content for Falling Rate Period

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GoFinal Moisture Content based on Initial to Final Moisture Content for Falling Rate Period Formula