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Falling Rate Drying Time from Initial to Final Moisture Formula

GoFalling Rate Drying Time from Critical to Final Moisture Formula

GoFalling Rate Drying Time from Critical to Final Weight of Moisture Formula

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

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

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

Falling Rate Drying Time from Initial to Final Moisture Example

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Here is how the Falling Rate Drying Time from Initial to Final Moisture equation looks like with Values.

Here is how the Falling Rate Drying Time from Initial to Final Moisture equation looks like with Units.

Here is how the Falling Rate Drying Time from Initial to Final Moisture equation looks like.

30.0993 = (\frac{100}{0.1}) \cdot (\frac{0.1 - 0.05}{2}) \cdot (\ln (\frac{0.1 - 0.05}{0.065 - 0.05}))

30.0993s = (\frac{100kg}{0.1m²}) \cdot (\frac{0.1 - 0.05}{2kg/s/m²}) \cdot (\ln (\frac{0.1 - 0.05}{0.065 - 0.05}))

30.0993 = (\frac{100}{0.1}) \cdot (\frac{0.1 - 0.05}{2}) \cdot (\ln (\frac{0.1 - 0.05}{0.065 - 0.05}))

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Falling Rate Drying Time from Initial to Final Moisture Solution

Follow our step by step solution on how to calculate Falling Rate Drying Time from Initial to Final Moisture?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

t f = (\frac{100kg}{0.1m²}) \cdot (\frac{0.1 - 0.05}{2kg/s/m²}) \cdot (\ln (\frac{0.1 - 0.05}{0.065 - 0.05}))

Next Step Prepare to Evaluate

∴

t f = (\frac{100}{0.1}) \cdot (\frac{0.1 - 0.05}{2}) \cdot (\ln (\frac{0.1 - 0.05}{0.065 - 0.05}))

Next Step Evaluate

∴

t f = 30.0993201081484s

LAST Step Rounding Answer

∴

t f = 30.0993s

Falling Rate Drying Time from Initial to Final Moisture Formula Elements

Variables

Functions

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.

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.

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.

Initial Moisture Content for Falling Rate Period

The Initial Moisture Content for Falling Rate Period is defined as the ratio of the weight of moisture to the weight of dry solid present initially in the wet solid for drying operation.

Symbol: X_i(Falling)

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

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.

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.

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.

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Credits

Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

Vaibhav Mishra has created this Formula and 300+ more formulas!

Verified by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

Prerana Bakli has verified this Formula and 1600+ more formulas!

Other Formulas to find Falling Rate Drying Time

Go Falling Rate Drying Time from Critical to Final Moisture

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

Go Falling Rate Drying Time from Critical to Final Weight of Moisture

t f = (\frac{M c - M Eq}{A \cdot N c}) \cdot (\ln (\frac{M c - M Eq}{M f(Falling) - M Eq}))

Other formulas in Drying from Initial 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 Falling Rate Drying Time from Initial to Final Moisture?

Falling Rate Drying Time from Initial to Final Moisture evaluator uses Falling Rate Drying Time = (Dry Weight of Solid/Drying Surface Area)*((Initial Moisture Content for Falling Rate Period-Equilibrium Moisture Content)/Rate of Constant Drying Period)*(ln((Initial Moisture Content for Falling Rate Period-Equilibrium Moisture Content)/(Final Moisture Content for Falling Rate Period-Equilibrium Moisture Content))) to evaluate the Falling Rate Drying Time, The Falling Rate Drying Time from Initial to Final Moisture formula is defined as the time taken for drying in falling rate period based on the drying from initial to final moisture content drying for the specified drying conditions. Falling Rate Drying Time is denoted by t_f symbol.

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

FAQs on Falling Rate Drying Time from Initial to Final Moisture

What is the formula to find Falling Rate Drying Time from Initial to Final Moisture?

The formula of Falling Rate Drying Time from Initial to Final Moisture is expressed as Falling Rate Drying Time = (Dry Weight of Solid/Drying Surface Area)*((Initial Moisture Content for Falling Rate Period-Equilibrium Moisture Content)/Rate of Constant Drying Period)*(ln((Initial Moisture Content for Falling Rate Period-Equilibrium Moisture Content)/(Final Moisture Content for Falling Rate Period-Equilibrium Moisture Content))). Here is an example- 30.09932 = (100/0.1)*((0.1-0.05)/2)*(ln((0.1-0.05)/(0.065-0.05))).

How to calculate Falling Rate Drying Time from Initial to Final Moisture?

With Dry Weight of Solid (W_S), Drying Surface Area (A), Initial Moisture Content for Falling Rate Period (X_i(Falling)), Equilibrium Moisture Content (X_Eq), Rate of Constant Drying Period (N_c) & Final Moisture Content for Falling Rate Period (X_f(Falling)) we can find Falling Rate Drying Time from Initial to Final Moisture using the formula - Falling Rate Drying Time = (Dry Weight of Solid/Drying Surface Area)*((Initial Moisture Content for Falling Rate Period-Equilibrium Moisture Content)/Rate of Constant Drying Period)*(ln((Initial Moisture Content for Falling Rate Period-Equilibrium Moisture Content)/(Final Moisture Content for Falling Rate Period-Equilibrium Moisture Content))). This formula also uses Natural Logarithm (ln) function(s).

What are the other ways to Calculate Falling Rate Drying Time?

Here are the different ways to Calculate Falling Rate Drying Time-

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

Can the Falling Rate Drying Time from Initial to Final Moisture be negative?

No, the Falling Rate Drying Time from Initial to Final Moisture, measured in Time cannot be negative.

Which unit is used to measure Falling Rate Drying Time from Initial to Final Moisture?

Falling Rate Drying Time from Initial to Final Moisture is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Falling Rate Drying Time from Initial to Final Moisture can be measured.

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Falling Rate Drying Time from Initial to Final Moisture Formula

​GoFalling Rate Drying Time from Critical to Final Moisture Formula

​GoFalling Rate Drying Time from Critical to Final Weight of Moisture Formula

Falling Rate Drying Time from Initial to Final Moisture Example

Falling Rate Drying Time from Initial to Final Moisture Solution

Falling Rate Drying Time from Initial to Final Moisture Formula Elements

Credits

Other Formulas to find Falling Rate Drying Time

Other formulas in Drying from Initial to Final Moisture category

How to Evaluate Falling Rate Drying Time from Initial to Final Moisture?

FAQs on Falling Rate Drying Time from Initial to Final Moisture

Variable Name

GoFalling Rate Drying Time from Critical to Final Moisture Formula

GoFalling Rate Drying Time from Critical to Final Weight of Moisture Formula