Initial Membrane Volume Calculator

✖Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.ⓘ Temperature [T]			+10% -10%
✖Molecular weight is the mass of a molecule, relative to the mass of a carbon-12 atom. It is also known as molecular mass.ⓘ Molecular Weight [n₀]			+10% -10%
✖Applied Pressure Driving Force is defined as the force or pressure that is intentionally exerted or applied to induce or facilitate process.ⓘ Applied Pressure Driving Force [ΔP_m]			+10% -10%
✖Volumetric Water flux through membrane is the rate at which water flows through a given area of a material per unit of time.ⓘ Volumetric Water Flux Through Membrane [J_wv]			+10% -10%
✖Water permeability through membrane is the ability of a material to allow water to pass through it. It is a measure of how easily water can flow through a material's pores.ⓘ Water Permeability Through Membrane [L_p]			+10% -10%

✖Initial volume is the volume of a substance at a specific time or point in time. It is often used in fluid mechanics to describe the volume of a fluid at the beginning of a process or experiment.ⓘ Initial Membrane Volume [V₀]

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Formula

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Initial Membrane Volume

Formula

`"V"_{"0"} = ("[R]"*"T"*"n"_{"0"})/("ΔP"_{"m"}-("J"_{"wv"}/"L"_{"p"}))`

Example

`"0.000149m³"=("[R]"*"298K"*"0.01802kg/mol")/("300000Pa"-("0.00000057m³/(m²*s)"/"0.00000002337m³/(m²*s*Pa)"))`

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Initial Membrane Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Volume = ([R]*Temperature*Molecular Weight)/(Applied Pressure Driving Force-(Volumetric Water Flux Through Membrane/Water Permeability Through Membrane))
V₀ = ([R]*T*n₀)/(ΔP_m-(J_wv/L_p))
This formula uses 1 Constants, 6 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Initial Volume - (Measured in Cubic Meter) - Initial volume is the volume of a substance at a specific time or point in time. It is often used in fluid mechanics to describe the volume of a fluid at the beginning of a process or experiment.
Temperature - (Measured in Kelvin) - Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness.
Molecular Weight - (Measured in Kilogram Per Mole) - Molecular weight is the mass of a molecule, relative to the mass of a carbon-12 atom. It is also known as molecular mass.
Applied Pressure Driving Force - (Measured in Pascal) - Applied Pressure Driving Force is defined as the force or pressure that is intentionally exerted or applied to induce or facilitate process.
Volumetric Water Flux Through Membrane - (Measured in Cubic Meter per Square Meter per Second) - Volumetric Water flux through membrane is the rate at which water flows through a given area of a material per unit of time.
Water Permeability Through Membrane - (Measured in Cubic Meter per Square Meter per Second per Pascal) - Water permeability through membrane is the ability of a material to allow water to pass through it. It is a measure of how easily water can flow through a material's pores.

STEP 1: Convert Input(s) to Base Unit

Temperature: 298 Kelvin --> 298 Kelvin No Conversion Required
Molecular Weight: 0.01802 Kilogram Per Mole --> 0.01802 Kilogram Per Mole No Conversion Required
Applied Pressure Driving Force: 300000 Pascal --> 300000 Pascal No Conversion Required
Volumetric Water Flux Through Membrane: 5.7E-07 Cubic Meter per Square Meter per Second --> 5.7E-07 Cubic Meter per Square Meter per Second No Conversion Required
Water Permeability Through Membrane: 2.337E-08 Cubic Meter per Square Meter per Second per Pascal --> 2.337E-08 Cubic Meter per Square Meter per Second per Pascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V₀ = ([R]*T*n₀)/(ΔP_m-(J_wv/L_p)) --> ([R]*298*0.01802)/(300000-(5.7E-07/2.337E-08))

Evaluating ... ...

V₀ = 0.000148839873072616

STEP 3: Convert Result to Output's Unit

0.000148839873072616 Cubic Meter --> No Conversion Required

FINAL ANSWER

0.000148839873072616 ≈ 0.000149 Cubic Meter <-- Initial Volume

(Calculation completed in 00.004 seconds)

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Created by Harsh Kadam

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

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Verified by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

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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

Initial Membrane Volume Formula

What is Water Permeability?

Water permeability, also known as hydraulic conductivity or hydraulic permeability, is a measure of a porous material's ability to allow water to flow through it. It is typically expressed in units of meters per second (m/s) or centimeters per second (cm/s).

How to Calculate Initial Membrane Volume?

Initial Membrane Volume calculator uses Initial Volume = ([R]*Temperature*Molecular Weight)/(Applied Pressure Driving Force-(Volumetric Water Flux Through Membrane/Water Permeability Through Membrane)) to calculate the Initial Volume, Initial membrane volume is the volume of fluid that is present in a membrane before filtration or purification begins. Initial Volume is denoted by V₀ symbol.

How to calculate Initial Membrane Volume using this online calculator? To use this online calculator for Initial Membrane Volume, enter Temperature (T), Molecular Weight (n₀), Applied Pressure Driving Force (ΔP_m), Volumetric Water Flux Through Membrane (J_wv) & Water Permeability Through Membrane (L_p) and hit the calculate button. Here is how the Initial Membrane Volume calculation can be explained with given input values -> 0.000149 = ([R]*298*0.01802)/(300000-(5.7E-07/2.337E-08)).

FAQ

What is Initial Membrane Volume?

Initial membrane volume is the volume of fluid that is present in a membrane before filtration or purification begins and is represented as V₀ = ([R]*T*n₀)/(ΔP_m-(J_wv/L_p)) or Initial Volume = ([R]*Temperature*Molecular Weight)/(Applied Pressure Driving Force-(Volumetric Water Flux Through Membrane/Water Permeability Through Membrane)). Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness, Molecular weight is the mass of a molecule, relative to the mass of a carbon-12 atom. It is also known as molecular mass, Applied Pressure Driving Force is defined as the force or pressure that is intentionally exerted or applied to induce or facilitate process, Volumetric Water flux through membrane is the rate at which water flows through a given area of a material per unit of time & Water permeability through membrane is the ability of a material to allow water to pass through it. It is a measure of how easily water can flow through a material's pores.

How to calculate Initial Membrane Volume?

Initial membrane volume is the volume of fluid that is present in a membrane before filtration or purification begins is calculated using Initial Volume = ([R]*Temperature*Molecular Weight)/(Applied Pressure Driving Force-(Volumetric Water Flux Through Membrane/Water Permeability Through Membrane)). To calculate Initial Membrane Volume, you need Temperature (T), Molecular Weight (n₀), Applied Pressure Driving Force (ΔP_m), Volumetric Water Flux Through Membrane (J_wv) & Water Permeability Through Membrane (L_p). With our tool, you need to enter the respective value for Temperature, Molecular Weight, Applied Pressure Driving Force, Volumetric Water Flux Through Membrane & Water Permeability Through Membrane 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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