Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period Calculator

✖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 Falling rate drying time is the time taken for drying operation in the falling rate period.ⓘ Falling Rate Drying Time [t_f]			+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 Dry Weight of Solid is the weight of dry solid present in the system in the drying mass transfer operation.ⓘ Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period [W_S]

⎘ Copy

👎

Formula

✖

Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period

Formula

`"W"_{"S"} = ("A"*"t"_{"f"})/((("X"_{"i(Falling)"}-"X"_{"Eq"})/"N"_{"c"})*(ln(("X"_{"i(Falling)"}-"X"_{"Eq"})/("X"_{"f(Falling)"}-"X"_{"Eq"}))))`

Example

`"122.9264kg"=("0.1m²"*"37s")/((("0.10"-"0.05")/"2kg/s/m²")*(ln(("0.10"-"0.05")/("0.065"-"0.05"))))`

Calculator

LaTeX

Reset

👍

Download Drying Formula PDF PDF Image

Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Dry Weight of Solid = (Drying Surface Area*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))))
W_S = (A*t_f)/(((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

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.
Falling Rate Drying Time - (Measured in Second) - The Falling rate drying time is the time taken for drying operation in the falling rate period.
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

Drying Surface Area: 0.1 Square Meter --> 0.1 Square Meter No Conversion Required
Falling Rate Drying Time: 37 Second --> 37 Second 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

W_S = (A*t_f)/(((X_i(Falling)-X_Eq)/N_c)*(ln((X_i(Falling)-X_Eq)/(X_f(Falling)-X_Eq)))) --> (0.1*37)/(((0.1-0.05)/2)*(ln((0.1-0.05)/(0.065-0.05))))

Evaluating ... ...

W_S = 122.926364672216

STEP 3: Convert Result to Output's Unit

122.926364672216 Kilogram --> No Conversion Required

FINAL ANSWER

122.926364672216 ≈ 122.9264 Kilogram <-- Dry Weight of Solid

(Calculation completed in 00.020 seconds)

You are here -

Home » Engineering » Chemical Engineering » Mass Transfer Operations » Drying » Falling Rate Drying Period » Drying from Initial to Final Moisture » Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period

Credits

Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

Vaibhav Mishra has created this Calculator and 300+ more calculators!

Verified by Prerana Bakli

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

Prerana Bakli has verified this Calculator and 1600+ more calculators!

< 9 Drying from Initial to Final Moisture Calculators

Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period

Go Dry Weight of Solid = (Drying Surface Area*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))))

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

Go 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

Rate of Constant Drying Period based on Initial to Final Moisture Content for Falling Rate Period

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

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

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)))

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

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

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

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

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)))

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

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

< 25 Important Formulas in Drying Mass Transfer Operation Calculators

Dry Weight of Solid based on Critical to Final Moisture Content for Falling Rate Period

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

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

Go 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

Rate of Constant Drying Period based on Critical to Final Moisture Content for Falling Rate Period

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

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

Go Drying Surface Area = (Dry Weight of Solid/Falling Rate Drying Time)*((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 from Critical to Final Moisture

Go 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)))

Rate of Constant Drying Period based on Critical to Final Weight of Moisture for Falling Rate Period

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

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

Go Drying Surface Area = ((Critical Weight of Moisture-Equilibrium Weight of Moisture)/(Falling Rate Drying Time*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 from Critical to Final Weight of Moisture

Go 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)))

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

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

Dry Weight of Solid from Initial to Final Moisture Content for Constant Rate Period

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

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

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

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

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

Rate of Constant Drying Period based on Final Moisture Content

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

Constant Drying Time from Initial to Final Moisture Content

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

Constant Drying Time from Initial to Critical Moisture Content

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))

Drying Surface Area based on Initial to Critical Moisture Content for Constant Rate Period

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

Dry Weight of Solid from Initial to Critical Moisture Content for Constant Rate Period

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

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

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)

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

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

Rate of Constant Drying Period based on Critical Moisture Content

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

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

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

Constant Drying Time from Initial to Final Weight of Moisture

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

Drying Surface Area based on Initial to Critical Weight of Moisture for Constant Rate Period

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

Constant Drying Time from Initial to Critical Weight of Moisture

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

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

Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period Formula

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 Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period?

Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period calculator uses Dry Weight of Solid = (Drying Surface Area*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)))) to calculate the Dry Weight of Solid, The Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period formula is defined as the dry weight of solids present in the system based on drying from initial to final moisture content for the specified drying conditions. Dry Weight of Solid is denoted by W_S symbol.

How to calculate Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period using this online calculator? To use this online calculator for Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period, enter Drying Surface Area (A), Falling Rate Drying Time (t_f), 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 Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period calculation can be explained with given input values -> 122.9264 = (0.1*37)/(((0.1-0.05)/2)*(ln((0.1-0.05)/(0.065-0.05)))).

FAQ

What is Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period?

The Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period formula is defined as the dry weight of solids present in the system based on drying from initial to final moisture content for the specified drying conditions and is represented as W_S = (A*t_f)/(((X_i(Falling)-X_Eq)/N_c)*(ln((X_i(Falling)-X_Eq)/(X_f(Falling)-X_Eq)))) or Dry Weight of Solid = (Drying Surface Area*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)))). The Drying Surface Area is the total area in the drying mass transfer operation i.e. exposed in contact with the drying medium, The Falling rate drying time is the time taken for drying operation in the 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, 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 Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period?

The Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period formula is defined as the dry weight of solids present in the system based on drying from initial to final moisture content for the specified drying conditions is calculated using Dry Weight of Solid = (Drying Surface Area*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)))). To calculate Dry Weight of Solid based on Initial to Final Moisture Content for Falling Rate Period, you need Drying Surface Area (A), Falling Rate Drying Time (t_f), 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 Drying Surface Area, Falling Rate Drying Time, 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 Dry Weight of Solid?

In this formula, Dry Weight of Solid uses Drying Surface Area, Falling Rate Drying Time, 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 -

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

Home

FREE PDFs

🔍 Search