Membrane Water Concentration Based on Solution Diffusion Model Calculator

✖Mass Water flux is defined as the rate of movement of water across a surface or through a medium.ⓘ Mass Water Flux [J_wm]			+10% -10%
✖Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.ⓘ Temperature [T]			+10% -10%
✖Membrane Layer Thickness is the distance between the two outer surfaces of a membrane. It is typically measured in nanometers (nm), which are billionths of a meter.ⓘ Membrane Layer Thickness [l_m]			+10% -10%
✖Membrane water diffusivity is the rate at which water molecules diffuse across a membrane. It is typically measured in square meters per second (m^2/s).ⓘ Membrane Water Diffusivity [D_w]			+10% -10%
✖The partial molar volume of a substance in a mixture is the change in volume of the mixture per mole of that substance added, at constant temperature and pressure.ⓘ Partial Molar Volume [V_l]			+10% -10%
✖Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element.ⓘ Membrane Pressure Drop [ΔP_atm]			+10% -10%
✖Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.ⓘ Osmotic Pressure [Δπ]			+10% -10%

✖Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3).ⓘ Membrane Water Concentration Based on Solution Diffusion Model [C_w]

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Formula

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Membrane Water Concentration Based on Solution Diffusion Model

Formula

`"C"_{"w"} = ("J"_{"wm"}*"[R]"*"T"*"l"_{"m"})/("D"_{"w"}*"V"_{"l"}*("ΔP"_{"atm"}-"Δπ"))`

Example

`"156.0096kg/m³"=("0.000063kg/s/m²"*"[R]"*"298K"*"0.000013m")/("0.0000000001762m²/s"*"0.018m³/kmol"*("81.32at"-"39.5at"))`

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Membrane Water Concentration Based on Solution Diffusion Model Solution

STEP 0: Pre-Calculation Summary

Formula Used

Membrane Water Concentration = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Partial Molar Volume*(Membrane Pressure Drop-Osmotic Pressure))
C_w = (J_wm*[R]*T*l_m)/(D_w*V_l*(ΔP_atm-Δπ))
This formula uses 1 Constants, 8 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Membrane Water Concentration - (Measured in Kilogram per Cubic Meter) - Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3).
Mass Water Flux - (Measured in Kilogram per Second per Square Meter) - Mass Water flux is defined as the rate of movement of water across a surface or through a medium.
Temperature - (Measured in Kelvin) - Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.
Membrane Layer Thickness - (Measured in Meter) - Membrane Layer Thickness is the distance between the two outer surfaces of a membrane. It is typically measured in nanometers (nm), which are billionths of a meter.
Membrane Water Diffusivity - (Measured in Square Meter per Second) - Membrane water diffusivity is the rate at which water molecules diffuse across a membrane. It is typically measured in square meters per second (m^2/s).
Partial Molar Volume - (Measured in Cubic Meter per Mole) - The partial molar volume of a substance in a mixture is the change in volume of the mixture per mole of that substance added, at constant temperature and pressure.
Membrane Pressure Drop - (Measured in Pascal) - Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element.
Osmotic Pressure - (Measured in Pascal) - Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.

STEP 1: Convert Input(s) to Base Unit

Mass Water Flux: 6.3E-05 Kilogram per Second per Square Meter --> 6.3E-05 Kilogram per Second per Square Meter No Conversion Required
Temperature: 298 Kelvin --> 298 Kelvin No Conversion Required
Membrane Layer Thickness: 1.3E-05 Meter --> 1.3E-05 Meter No Conversion Required
Membrane Water Diffusivity: 1.762E-10 Square Meter per Second --> 1.762E-10 Square Meter per Second No Conversion Required
Partial Molar Volume: 0.018 Cubic Meter per Kilomole --> 1.8E-05 Cubic Meter per Mole (Check conversion here)
Membrane Pressure Drop: 81.32 Atmosphere Technical --> 7974767.78 Pascal (Check conversion here)
Osmotic Pressure: 39.5 Atmosphere Technical --> 3873626.75 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_w = (J_wm*[R]*T*l_m)/(D_w*V_l*(ΔP_atm-Δπ)) --> (6.3E-05*[R]*298*1.3E-05)/(1.762E-10*1.8E-05*(7974767.78-3873626.75))

Evaluating ... ...

C_w = 156.009569219896

STEP 3: Convert Result to Output's Unit

156.009569219896 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

156.009569219896 ≈ 156.0096 Kilogram per Cubic Meter <-- Membrane Water Concentration

(Calculation completed in 00.004 seconds)

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< 3 Manometers Calculators

Membrane Water Concentration Based on Solution Diffusion Model

Go Membrane Water Concentration = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Partial Molar Volume*(Membrane Pressure Drop-Osmotic Pressure))

Piezometric Pressure

Go Piezometric Pressure Head = Water Density*[g]*Fluid Height

Vapor Pressure of Water using Saturation Humidity

Go Vapour Pressure of Water at DBT = Saturation Humidity/(0.6207+Saturation Humidity)

Membrane Water Concentration Based on Solution Diffusion Model Formula

What is Solution Diffusion Model?

The solution-diffusion model is a model for the transport of water and solutes through a non-porous membrane. It is based on the assumption that water and solutes dissolve in the membrane material and then diffuse through the membrane down a concentration gradient.

The solution-diffusion model is one of the most widely used models for membrane transport, and it has been used to describe a wide range of membrane separation processes, including reverse osmosis, gas separation, and pervaporation.

How to Calculate Membrane Water Concentration Based on Solution Diffusion Model?

Membrane Water Concentration Based on Solution Diffusion Model calculator uses Membrane Water Concentration = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Partial Molar Volume*(Membrane Pressure Drop-Osmotic Pressure)) to calculate the Membrane Water Concentration, Membrane Water Concentration Based on Solution Diffusion Model is a model for the transport of water and solutes through a membrane. It is based on the assumption that water and solutes dissolve in the membrane material and then diffuse through the membrane down a concentration gradient. Membrane Water Concentration is denoted by C_w symbol.

How to calculate Membrane Water Concentration Based on Solution Diffusion Model using this online calculator? To use this online calculator for Membrane Water Concentration Based on Solution Diffusion Model, enter Mass Water Flux (J_wm), Temperature (T), Membrane Layer Thickness (l_m), Membrane Water Diffusivity (D_w), Partial Molar Volume (V_l), Membrane Pressure Drop (ΔP_atm) & Osmotic Pressure (Δπ) and hit the calculate button. Here is how the Membrane Water Concentration Based on Solution Diffusion Model calculation can be explained with given input values -> 161.0943 = (6.3E-05*[R]*298*1.3E-05)/(1.762E-10*1.8E-05*(7974767.78-3873626.75)).

FAQ

What is Membrane Water Concentration Based on Solution Diffusion Model?

Membrane Water Concentration Based on Solution Diffusion Model is a model for the transport of water and solutes through a membrane. It is based on the assumption that water and solutes dissolve in the membrane material and then diffuse through the membrane down a concentration gradient and is represented as C_w = (J_wm*[R]*T*l_m)/(D_w*V_l*(ΔP_atm-Δπ)) or Membrane Water Concentration = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Partial Molar Volume*(Membrane Pressure Drop-Osmotic Pressure)). Mass Water flux is defined as the rate of movement of water across a surface or through a medium, Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness, Membrane Layer Thickness is the distance between the two outer surfaces of a membrane. It is typically measured in nanometers (nm), which are billionths of a meter, Membrane water diffusivity is the rate at which water molecules diffuse across a membrane. It is typically measured in square meters per second (m^2/s), The partial molar volume of a substance in a mixture is the change in volume of the mixture per mole of that substance added, at constant temperature and pressure, Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element & Osmotic pressure is the minimum pressure that must be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.

How to calculate Membrane Water Concentration Based on Solution Diffusion Model?

Membrane Water Concentration Based on Solution Diffusion Model is a model for the transport of water and solutes through a membrane. It is based on the assumption that water and solutes dissolve in the membrane material and then diffuse through the membrane down a concentration gradient is calculated using Membrane Water Concentration = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Partial Molar Volume*(Membrane Pressure Drop-Osmotic Pressure)). To calculate Membrane Water Concentration Based on Solution Diffusion Model, you need Mass Water Flux (J_wm), Temperature (T), Membrane Layer Thickness (l_m), Membrane Water Diffusivity (D_w), Partial Molar Volume (V_l), Membrane Pressure Drop (ΔP_atm) & Osmotic Pressure (Δπ). With our tool, you need to enter the respective value for Mass Water Flux, Temperature, Membrane Layer Thickness, Membrane Water Diffusivity, Partial Molar Volume, Membrane Pressure Drop & Osmotic Pressure 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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