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

✖The Initial Weight of Moisture for Falling Rate Period is the amount of moisture in kg present in the wet solid initially for drying operation.ⓘ Initial Weight of Moisture for Falling Rate Period [M_i(Falling)]			+10% -10%
✖The Equilibrium Weight of Moisture is the amount of moisture in kg present in the solid that is in equilibrium with the solid for the given drying conditions.ⓘ Equilibrium Weight of Moisture [M_Eq]			+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 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 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 Weight of Moisture for Falling Rate Period is the amount of moisture in kg present in the solid after the completion of drying operation.ⓘ Final Weight of Moisture based on Initial to Final Weight of Moisture for Falling Rate Period [M_f(Falling)]

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Formula

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

Formula

`"M"_{"f(Falling)"} = (("M"_{"i(Falling)"}-"M"_{"Eq"})/(exp(("A"*"t"_{"f"}*"N"_{"c"})/("M"_{"i(Falling)"}-"M"_{"Eq"}))))+"M"_{"Eq"}`

Example

`"6.138188kg"=(("10kg"-"5kg")/(exp(("0.1m²"*"37s"*"2kg/s/m²")/("10kg"-"5kg"))))+"5kg"`

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

STEP 0: Pre-Calculation Summary

Formula Used

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
M_f(Falling) = ((M_i(Falling)-M_Eq)/(exp((A*t_f*N_c)/(M_i(Falling)-M_Eq))))+M_Eq
This formula uses 1 Functions, 6 Variables

Functions Used

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

Variables Used

Final Weight of Moisture for Falling Rate Period - (Measured in Kilogram) - The Final Weight of Moisture for Falling Rate Period is the amount of moisture in kg present in the solid after the completion of drying operation.
Initial Weight of Moisture for Falling Rate Period - (Measured in Kilogram) - The Initial Weight of Moisture for Falling Rate Period is the amount of moisture in kg present in the wet solid initially for drying operation.
Equilibrium Weight of Moisture - (Measured in Kilogram) - The Equilibrium Weight of Moisture is the amount of moisture in kg present in the solid that is in equilibrium with the solid for the given drying conditions.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Initial Weight of Moisture for Falling Rate Period: 10 Kilogram --> 10 Kilogram No Conversion Required
Equilibrium Weight of Moisture: 5 Kilogram --> 5 Kilogram No Conversion Required
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
Rate of Constant Drying Period: 2 Kilogram per Second per Square Meter --> 2 Kilogram per Second per Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_f(Falling) = ((M_i(Falling)-M_Eq)/(exp((A*t_f*N_c)/(M_i(Falling)-M_Eq))))+M_Eq --> ((10-5)/(exp((0.1*37*2)/(10-5))))+5

Evaluating ... ...

M_f(Falling) = 6.13818844191906

STEP 3: Convert Result to Output's Unit

6.13818844191906 Kilogram --> No Conversion Required

FINAL ANSWER

6.13818844191906 ≈ 6.138188 Kilogram <-- Final Weight of Moisture for Falling Rate Period

(Calculation completed in 00.004 seconds)

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

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< 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

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

Final Weight of Moisture based on Initial to Final Weight of Moisture for Falling Rate Period calculator uses 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 to calculate the Final Weight of Moisture for Falling Rate Period, The Final Weight of Moisture based on Initial to Final Weight of Moisture for Falling Rate Period formula is defined as the final moisture content that can be attained from the specified initial moisture content based on the drying conditions in falling rate period. Final Weight of Moisture for Falling Rate Period is denoted by M_f(Falling) symbol.

How to calculate Final Weight of Moisture based on Initial to Final Weight of Moisture for Falling Rate Period using this online calculator? To use this online calculator for Final Weight of Moisture based on Initial to Final Weight of Moisture for Falling Rate Period, enter Initial Weight of Moisture for Falling Rate Period (M_i(Falling)), Equilibrium Weight of Moisture (M_Eq), Drying Surface Area (A), Falling Rate Drying Time (t_f) & Rate of Constant Drying Period (N_c) and hit the calculate button. Here is how the Final Weight of Moisture based on Initial to Final Weight of Moisture for Falling Rate Period calculation can be explained with given input values -> 6.138188 = ((10-5)/(exp((0.1*37*2)/(10-5))))+5.

FAQ

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

The Final Weight of Moisture based on Initial to Final Weight of Moisture for Falling Rate Period formula is defined as the final moisture content that can be attained from the specified initial moisture content based on the drying conditions in falling rate period and is represented as M_f(Falling) = ((M_i(Falling)-M_Eq)/(exp((A*t_f*N_c)/(M_i(Falling)-M_Eq))))+M_Eq or 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. The Initial Weight of Moisture for Falling Rate Period is the amount of moisture in kg present in the wet solid initially for drying operation, The Equilibrium Weight of Moisture is the amount of moisture in kg present in the solid that is in equilibrium with the solid for the given drying conditions, 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 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.

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

The Final Weight of Moisture based on Initial to Final Weight of Moisture for Falling Rate Period formula is defined as the final moisture content that can be attained from the specified initial moisture content based on the drying conditions in falling rate period is calculated using 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. To calculate Final Weight of Moisture based on Initial to Final Weight of Moisture for Falling Rate Period, you need Initial Weight of Moisture for Falling Rate Period (M_i(Falling)), Equilibrium Weight of Moisture (M_Eq), Drying Surface Area (A), Falling Rate Drying Time (t_f) & Rate of Constant Drying Period (N_c). With our tool, you need to enter the respective value for Initial Weight of Moisture for Falling Rate Period, Equilibrium Weight of Moisture, Drying Surface Area, Falling Rate Drying Time & Rate of Constant Drying Period and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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