Falling Rate Drying Time from Initial to Final Moisture Calculator

✖The Dry Weight of Solid is the weight of dry solid present in the system in the drying mass transfer operation.ⓘ Dry Weight of Solid [W_S]			+10% -10%
✖The Drying Surface Area is the total area in the drying mass transfer operation i.e. exposed in contact with the drying medium.ⓘ Drying Surface Area [A]			+10% -10%
✖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.ⓘ Initial Moisture Content for Falling Rate Period [X_i(Falling)]			+10% -10%
✖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.ⓘ Equilibrium Moisture Content [X_Eq]			+10% -10%
✖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.ⓘ Rate of Constant Drying Period [N_c]			+10% -10%
✖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.ⓘ Final Moisture Content for Falling Rate Period [X_f(Falling)]			+10% -10%

✖The Falling rate drying time is the time taken for drying operation in the falling rate period.ⓘ Falling Rate Drying Time from Initial to Final Moisture [t_f]

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Falling Rate Drying Time from Initial to Final Moisture Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
t_f = (W_S/A)*((X_i(Falling)-X_Eq)/N_c)*(ln((X_i(Falling)-X_Eq)/(X_f(Falling)-X_Eq)))
This formula uses 1 Functions, 7 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Falling Rate Drying Time - (Measured in Second) - The Falling rate drying time is the time taken for drying operation in the falling rate period.
Dry Weight of Solid - (Measured in Kilogram) - The Dry Weight of Solid is the weight of dry solid present in the system in the drying mass transfer operation.
Drying Surface Area - (Measured in Square Meter) - The Drying Surface Area is the total area in the drying mass transfer operation i.e. exposed in contact with the drying medium.
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.
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.
Rate of Constant Drying Period - (Measured in Kilogram per Second per Square Meter) - 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.
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.

STEP 1: Convert Input(s) to Base Unit

Dry Weight of Solid: 100 Kilogram --> 100 Kilogram No Conversion Required
Drying Surface Area: 0.1 Square Meter --> 0.1 Square Meter No Conversion Required
Initial Moisture Content for Falling Rate Period: 0.1 --> No Conversion Required
Equilibrium Moisture Content: 0.05 --> No Conversion Required
Rate of Constant Drying Period: 2 Kilogram per Second per Square Meter --> 2 Kilogram per Second per Square Meter No Conversion Required
Final Moisture Content for Falling Rate Period: 0.065 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_f = (W_S/A)*((X_i(Falling)-X_Eq)/N_c)*(ln((X_i(Falling)-X_Eq)/(X_f(Falling)-X_Eq))) --> (100/0.1)*((0.1-0.05)/2)*(ln((0.1-0.05)/(0.065-0.05)))

Evaluating ... ...

t_f = 30.0993201081484

STEP 3: Convert Result to Output's Unit

30.0993201081484 Second --> No Conversion Required

FINAL ANSWER

30.0993201081484 ≈ 30.09932 Second <-- Falling Rate Drying Time

(Calculation completed in 00.004 seconds)

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Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

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

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< Drying from Initial to Final Moisture Calculators

Drying Surface Area based on Initial to Final Moisture Content for Falling Rate Period

LaTeX Go Drying Surface Area = (Dry Weight of Solid/Falling Rate Drying Time)*((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)))

Falling Rate Drying Time from Initial to Final Moisture

LaTeX Go 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)))

Drying Surface Area based on Initial to Final Weight of Moisture for Falling Rate Period

LaTeX Go Drying Surface Area = ((Initial Weight of Moisture for Falling Rate Period-Equilibrium Weight of Moisture)/(Falling Rate Drying Time*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)))

Falling Rate Drying Time from Initial to Final Weight of Moisture

LaTeX Go 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)))

< Important Formulas in Drying Mass Transfer Operation Calculators

Constant Drying Time from Initial to Critical Moisture Content

LaTeX Go Constant Rate Drying Time = Dry Weight of Solid*((Initial Moisture Content for Constant Rate Period-Critical Moisture Content))/((Drying Surface Area*Rate of Constant Drying Period))

Critical Moisture Content based on Initial Moisture Content for Constant Rate Period

LaTeX Go Critical Moisture Content = Initial Moisture Content for Constant Rate Period-((Drying Surface Area*Constant Rate Drying Time*Rate of Constant Drying Period)/Dry Weight of Solid)

Constant Drying Time from Initial to Critical Weight of Moisture

LaTeX Go Constant Rate Drying Time = (Initial Weight of Moisture for Constant Rate-Critical Weight of Moisture)/(Drying Surface Area*Rate of Constant Drying Period)

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

LaTeX Go Total Drying Time = Constant Rate Drying Time+Falling Rate Drying Time

Falling Rate Drying Time from Initial to Final Moisture Formula

LaTeX Go

What is Falling Rate Period Drying?

The falling rate drying period is a stage in the drying process where the rate of moisture removal from the material decreases over time as the internal moisture content of the material is reduced. During this period, the drying rate is typically controlled by the rate of moisture diffusion within the material, which is slower than the rate of heat and mass transfer at the surface of the material.

In this stage, the moisture content of the material decreases more slowly than during the constant rate drying period, as the remaining moisture is located deeper within the material and must diffuse to the surface before it can be removed. The length of the falling rate period depends on the properties of the material being dried, such as its porosity, particle size, and moisture distribution.

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

Falling Rate Drying Time from Initial to Final Moisture calculator 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 calculate 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 calculate Falling Rate Drying Time from Initial to Final Moisture using this online calculator? To use this online calculator 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. Here is how the Falling Rate Drying Time from Initial to Final Moisture calculation can be explained with given input values -> 30.09932 = (100/0.1)*((0.1-0.05)/2)*(ln((0.1-0.05)/(0.065-0.05))).

FAQ

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

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 and is represented as t_f = (W_S/A)*((X_i(Falling)-X_Eq)/N_c)*(ln((X_i(Falling)-X_Eq)/(X_f(Falling)-X_Eq))) or 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))). The Dry Weight of Solid is the weight of dry solid present in the system in the drying mass transfer operation, The Drying Surface Area is the total area in the drying mass transfer operation i.e. exposed in contact with the drying medium, 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, 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, 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 & 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.

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

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 is calculated using 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 calculate Falling Rate Drying Time from Initial to Final Moisture, you need 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)). With our tool, you need to enter the respective value for Dry Weight of Solid, Drying Surface Area, Initial Moisture Content for Falling Rate Period, Equilibrium Moisture Content, Rate of Constant Drying Period & Final Moisture Content for Falling Rate Period and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Falling Rate Drying Time?

In this formula, Falling Rate Drying Time uses Dry Weight of Solid, Drying Surface Area, Initial Moisture Content for Falling Rate Period, Equilibrium Moisture Content, Rate of Constant Drying Period & Final Moisture Content for Falling Rate Period. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)))
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)))

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