Osmotic Pressure Drop Based on Solution Diffusion Model Calculator

✖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%
✖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%
✖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 [C_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%

✖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 Drop Based on Solution Diffusion Model [Δπ]

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Formula

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Osmotic Pressure Drop Based on Solution Diffusion Model

Formula

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

Example

`"39.49743at"="81.32at"-(("0.000063kg/s/m²"*"[R]"*"298K"*"0.000013m")/("0.0000000001762m²/s"*"156kg/m³"*"0.018m³/kmol"))`

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Osmotic Pressure Drop Based on Solution Diffusion Model Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

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.
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.
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).
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).
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.

STEP 1: Convert Input(s) to Base Unit

Membrane Pressure Drop: 81.32 Atmosphere Technical --> 7974767.78 Pascal (Check conversion here)
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
Membrane Water Concentration: 156 Kilogram per Cubic Meter --> 156 Kilogram per Cubic Meter No Conversion Required
Partial Molar Volume: 0.018 Cubic Meter per Kilomole --> 1.8E-05 Cubic Meter per Mole (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Δπ = ΔP_atm-((J_wm*[R]*T*l_m)/(D_w*C_w*V_l)) --> 7974767.78-((6.3E-05*[R]*298*1.3E-05)/(1.762E-10*156*1.8E-05))

Evaluating ... ...

Δπ = 3873375.18127988

STEP 3: Convert Result to Output's Unit

3873375.18127988 Pascal -->39.4974347129741 Atmosphere Technical (Check conversion here)

FINAL ANSWER

39.4974347129741 ≈ 39.49743 Atmosphere Technical <-- Osmotic Pressure

(Calculation completed in 00.004 seconds)

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Shri Guru Gobind Singhji Institute of Engineering and Technology (SGGS), Nanded

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< 13 Membrane Characteristics Calculators

Bulk Concentration of Membrane

Go Bulk Concentration = (Solute Concentration at Membrane Surface)/((exp(Water Flux/Mass Transfer Coefficient at Membrane Surface))/(Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)))

Solute Concentration at Membrane Surface

Go Solute Concentration at Membrane Surface = (Bulk Concentration*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface))/(Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface))

Initial Flux of Membrane

Go Volumetric Water Flux Through Membrane = (Water Permeability Through Membrane*Applied Pressure Driving Force)*(1-((Universal Gas Constant)*Temperature*Molecular Weight/Initial Volume*(1/Applied Pressure Driving Force)))

Osmotic Pressure Drop Based on Solution Diffusion Model

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

Membrane Thickness Based on Solution Diffusion Model

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

Membrane Pressure Drop Based On Solution Diffusion Model

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

Membrane Temperature

Go Temperature = Initial Volume*((Applied Pressure Driving Force*Water Permeability Through Membrane)-Volumetric Water Flux Through Membrane)/([R]*Water Permeability Through Membrane*Molecular Weight)

Initial Membrane Volume

Go Initial Volume = ([R]*Temperature*Molecular Weight)/(Applied Pressure Driving Force-(Volumetric Water Flux Through Membrane/Water Permeability Through Membrane))

Membrane Pore Diameter

Go Pore Diameter = ((32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Membrane Porosity*Applied Pressure Driving Force))^0.5

Membrane Pressure Drop

Go Applied Pressure Driving Force = (Tortuosity*32*Liquid Viscosity*Flux through Membrane*Membrane Thickness)/(Membrane Porosity*(Pore Diameter^2))

Membrane Thickness

Go Membrane Thickness = (Pore Diameter^2*Membrane Porosity*Applied Pressure Driving Force)/(32*Liquid Viscosity*Flux through Membrane*Tortuosity)

Membrane Porosity

Go Membrane Porosity = (32*Liquid Viscosity*Flux through Membrane*Tortuosity*Membrane Thickness)/(Pore Diameter^2*Applied Pressure Driving Force)

Pressure Driving Force in Membrane

Go Applied Pressure Driving Force = Membrane Flow Resistance of Unit Area*Liquid Viscosity*Flux through Membrane

Osmotic Pressure Drop Based on Solution Diffusion Model Formula

What is Osmotic Pressure?

Osmotic pressure is the pressure that must be applied to a semipermeable membrane to prevent the inward flow of its pure solvent across the membrane. It is a colligative property, meaning that it depends on the concentration of the solute in the solution, but not on its identity. Osmotic pressure is a result of the difference in chemical potential of the solvent between the two sides of the membrane. The chemical potential of a solvent is a measure of its tendency to move from one region to another. In a solution, the chemical potential of the solvent is lower than in pure solvent, due to the presence of the solute. The greater the concentration of the solute, the lower the chemical potential of the solvent.

How to Calculate Osmotic Pressure Drop Based on Solution Diffusion Model?

Osmotic Pressure Drop Based on Solution Diffusion Model calculator uses Osmotic Pressure = Membrane Pressure Drop-((Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*Partial Molar Volume)) to calculate the Osmotic Pressure, Osmotic Pressure Drop Based on Solution Diffusion Model is defined as the difference in pressure between the feed and permeate sides of a semi-permeable membrane due to the osmotic pressure of the feed solution. Osmotic Pressure is denoted by Δπ symbol.

How to calculate Osmotic Pressure Drop Based on Solution Diffusion Model using this online calculator? To use this online calculator for Osmotic Pressure Drop Based on Solution Diffusion Model, enter Membrane Pressure Drop (ΔP_atm), Mass Water Flux (J_wm), Temperature (T), Membrane Layer Thickness (l_m), Membrane Water Diffusivity (D_w), Membrane Water Concentration (C_w) & Partial Molar Volume (V_l) and hit the calculate button. Here is how the Osmotic Pressure Drop Based on Solution Diffusion Model calculation can be explained with given input values -> 0.000389 = 7974767.78-((6.3E-05*[R]*298*1.3E-05)/(1.762E-10*156*1.8E-05)).

FAQ

What is Osmotic Pressure Drop Based on Solution Diffusion Model?

Osmotic Pressure Drop Based on Solution Diffusion Model is defined as the difference in pressure between the feed and permeate sides of a semi-permeable membrane due to the osmotic pressure of the feed solution and is represented as Δπ = ΔP_atm-((J_wm*[R]*T*l_m)/(D_w*C_w*V_l)) or Osmotic Pressure = Membrane Pressure Drop-((Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*Partial Molar Volume)). Membrane pressure drop is the difference in pressure between the inlet and outlet of a membrane system, housing (pressure vessel), or element, 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), Membrane water concentration (MWC) is the concentration of water in a membrane. It is typically measured in moles per cubic meter (kg/m^3) & 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.

How to calculate Osmotic Pressure Drop Based on Solution Diffusion Model?

Osmotic Pressure Drop Based on Solution Diffusion Model is defined as the difference in pressure between the feed and permeate sides of a semi-permeable membrane due to the osmotic pressure of the feed solution is calculated using Osmotic Pressure = Membrane Pressure Drop-((Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*Partial Molar Volume)). To calculate Osmotic Pressure Drop Based on Solution Diffusion Model, you need Membrane Pressure Drop (ΔP_atm), Mass Water Flux (J_wm), Temperature (T), Membrane Layer Thickness (l_m), Membrane Water Diffusivity (D_w), Membrane Water Concentration (C_w) & Partial Molar Volume (V_l). With our tool, you need to enter the respective value for Membrane Pressure Drop, Mass Water Flux, Temperature, Membrane Layer Thickness, Membrane Water Diffusivity, Membrane Water Concentration & Partial Molar Volume 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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