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

✖The Initial Moisture Content for Constant 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 Constant Rate Period [X_i(Constant)]			+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 Constant Rate Drying Time is the time taken for drying operation in the constant rate period.ⓘ Constant Rate Drying Time [t_c]			+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 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 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.ⓘ Critical Moisture Content based on Initial Moisture Content for Constant Rate Period [X_c]

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Formula

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

Formula

`"X"_{"c"} = "X"_{"i(Constant)"}-(("A"*"t"_{"c"}*"N"_{"c"})/"W"_{"S"})`

Example

`"0.11"="0.49"-(("0.1m²"*"190s"*"2kg/s/m²")/"100kg")`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
X_c = X_i(Constant)-((A*t_c*N_c)/W_S)
This formula uses 6 Variables

Variables Used

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.
Initial Moisture Content for Constant Rate Period - The Initial Moisture Content for Constant 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.
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.
Constant Rate Drying Time - (Measured in Second) - The Constant Rate Drying Time is the time taken for drying operation in the constant rate period.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Initial Moisture Content for Constant Rate Period: 0.49 --> No Conversion Required
Drying Surface Area: 0.1 Square Meter --> 0.1 Square Meter No Conversion Required
Constant Rate Drying Time: 190 Second --> 190 Second 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
Dry Weight of Solid: 100 Kilogram --> 100 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

X_c = X_i(Constant)-((A*t_c*N_c)/W_S) --> 0.49-((0.1*190*2)/100)

Evaluating ... ...

X_c = 0.11

STEP 3: Convert Result to Output's Unit

0.11 --> No Conversion Required

FINAL ANSWER

0.11 <-- Critical Moisture Content

(Calculation completed in 00.004 seconds)

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< 11 Drying from Initial to Critical Moisture Calculators

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)

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

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)

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 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)

Rate of Constant Drying Period based on Critical Weight of Moisture

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

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)

Initial Weight of Moisture based on Critical Weight of Moisture for Constant Rate Period

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

Critical Weight of Moisture based on Initial Weight of Moisture for Constant Rate Period

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

< 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)