KEVOS® MAKEOS · Hydraulics
Reverse Osmosis Pressure Check (Osmotic Pressure, Net Driving Pressure, Permeate Flow)
For a reverse osmosis unit on this feed water, how much osmotic pressure must the pump overcome, what net driving pressure is left, will the concentrate end still produce water, and does it make the permeate flow I need?
Pressure check of a reverse osmosis system: the feed osmotic pressure of a dilute solution from van ’t Hoff’s law with the dissolved solids, molar mass and dissociation factor you enter, the feed-side mean osmotic pressure from the log-mean concentration factor at the recovery, the net driving pressure, the osmotic and net driving pressure at the concentrate end, the permeate flow from the membrane water permeability and area, and the feed pressure needed for the permeate flow you want.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Feed water | ||
| Dissolved solids in the feed | mg/L | Total dissolved solids of the feed water, from a water analysis. |
| Molar mass of the dissolved salt | g/mol | Molar mass of the dominant salt (sodium chloride 58.44 g/mol). |
| Dissociation (van ’t Hoff) factor | Effective number of dissolved particles per formula unit; about 2 for fully dissociated sodium chloride, less in practice because of ion interactions. Take it from data or fit it to a measured osmotic pressure. | |
| Water temperature | °C | Feed water temperature. |
| System | ||
| Recovery (permeate ÷ feed) | % | Share of the feed that leaves as permeate. |
| Feed pressure | bar gauge | Feed pressure at the membrane inlet. |
| Pressure drop, feed to concentrate | bar | Pressure lost along the membranes from feed to concentrate (from the unit’s gauges). |
| Permeate pressure | bar gauge | Back pressure on the permeate side. |
| Membrane water permeability | L/(m²·h·bar) | Water permeability of the membrane at this temperature, from the membrane maker’s data or a performance test. |
| Total membrane area | m² | Active membrane area of all elements in service. |
| Permeate flow needed | m³/h | Permeate flow the plant needs. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
Feed water
What this means: Dissolved solids in the feed
- What it is
- The concentration of dissolved salts in the feed water, which sets how much osmotic pressure the membrane must work against.
- Units and format
- Enter a number in mg/L: mg/L. The form accepts 0 mg/L to 100000 mg/L. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 mg/L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Osmotic pressure rises in proportion, lowering the net driving pressure and the permeate flow.
- Get it right
- Use total dissolved solids from a laboratory analysis; a conductivity meter reading must be converted first.
What this means: Molar mass of the dissolved salt
- What it is
- The mass of one mole of the dominant dissolved salt, used to turn milligrams per litre into moles per cubic metre.
- Units and format
- Enter a number in g/mol: g/mol. The form accepts 1 g/mol to 1000 g/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 58.44 g/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A heavier salt gives fewer moles for the same mass, lowering the osmotic pressure.
- Get it right
- Sodium chloride is 58.44 g/mol; for mixed waters use the salt that dominates the analysis.
What this means: Dissociation (van ’t Hoff) factor
- What it is
- The effective number of dissolved particles each formula unit of salt produces, which multiplies the osmotic pressure in van ’t Hoff’s law.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.8 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Osmotic pressure rises in proportion to it.
- Get it right
- Full dissociation of sodium chloride gives 2, but real solutions behave as if it were less; fit it to a measured osmotic pressure if you can.
What this means: Water temperature
- What it is
- The temperature of the feed water, which enters van ’t Hoff’s law as absolute temperature.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0 °C to 100 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Osmotic pressure rises in proportion to the absolute temperature.
- Get it right
- Membrane permeability also changes strongly with temperature; enter the permeability for this temperature.
System
What this means: Recovery (permeate ÷ feed)
- What it is
- The share of the feed water that leaves as permeate, which concentrates the salts left in the concentrate stream.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 99%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher recovery raises the mean and concentrate osmotic pressures steeply, lowering the driving pressure.
- Get it right
- Recovery is permeate flow divided by feed flow, not by concentrate flow.
What this means: Feed pressure
- What it is
- The water pressure at the inlet of the membrane elements, supplied by the high-pressure pump.
- Units and format
- Enter a number in bar gauge: bar gauge. The form accepts 0 bar gauge to 200 bar gauge. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 bar gauge as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each bar added raises the net driving pressure by one bar and the permeate flow in proportion.
- Get it right
- Read it at the membrane inlet, after the pump discharge valve and cartridge filters.
What this means: Pressure drop, feed to concentrate
- What it is
- The pressure lost as the feed flows along the membranes from the inlet to the concentrate outlet.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0 bar to 50 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Half of it comes off the average driving pressure and all of it off the concentrate-end pressure.
- Get it right
- Take it as inlet minus concentrate gauge pressure; a rising value is a sign of fouling.
What this means: Permeate pressure
- What it is
- The pressure on the permeate side of the membrane, which opposes the flow of water through it.
- Units and format
- Enter a number in bar gauge: bar gauge. The form accepts 0 bar gauge to 50 bar gauge. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 bar gauge as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each bar of permeate pressure removes a bar of net driving pressure.
- Get it right
- Include the back pressure from permeate pipework or a raised storage tank.
What this means: Membrane water permeability
- What it is
- The volume of water the membrane passes per square metre per hour for each bar of net driving pressure, its water permeability.
- Units and format
- Enter a number in L/(m²·h·bar): L/(m²·h·bar). The form accepts 0.000001 L/(m²·h·bar) to 100 L/(m²·h·bar). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 L/(m²·h·bar) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Permeate flow rises in proportion; the pressures do not change.
- Get it right
- Work it out from the membrane maker’s test flow and pressure, or from your own unit’s normalised data when new.
What this means: Total membrane area
- What it is
- The total active membrane area of all the elements in service, through which the permeate flows.
- Units and format
- Enter a number in m²: square metres. The form accepts 0.000001 m² to 1000000 m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 222 m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Permeate flow rises in proportion.
- Get it right
- Multiply the area per element from the data sheet by the number of elements.
What this means: Permeate flow needed
- What it is
- The permeate flow the plant needs from this unit, against which the calculated flow is compared.
- Units and format
- Enter a number in m³/h: cubic metres per hour. The form accepts 0 m³/h to 100000 m³/h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 m³/h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the flow check and the feed pressure needed; the driving pressure does not change.
- Get it right
- Use the flow needed at the coldest feed temperature, when the membranes pass least water.
Method and formulas
- Feed osmotic pressure π_f = i (C ÷ M) R T, the van ’t Hoff law for dilute solutions (Fermi eq 166), with C in g/m³ giving mol/m³.
- Log-mean concentration factor CF = ln [1 ÷ (1 − r)] ÷ r; mean osmotic pressure = CF π_f; net driving pressure NDP = P_f − ½ ΔP − CF π_f − P_p (Hydranautics normalization).
- Concentrate osmotic pressure ≈ π_f ÷ (1 − r) (full rejection); concentrate-end NDP = P_f − ΔP − P_p − π_c; permeate flow = A × NDP × area; feed pressure needed = Q ÷ (A × area) + ½ ΔP + CF π_f + P_p.
- Example: feed osmotic pressure 1.5271 bar, NDP 10.927 bar and 7.2776 m³/h of permeate.
Limitations
- Van ’t Hoff’s law is for dilute ideal solutions; it overstates the osmotic pressure of real salt solutions unless the factor i is reduced to suit, and it is unreliable for brackish-to-seawater concentrations without measured data.
- Single-stage average model: membrane fouling, concentration polarisation and permeate salt passage are not modelled; use the membrane maker’s design software for a full design.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a feed pump can drive an RO unit at a higher recovery
- Estimate the effect of more saline feed water on output
- Sanity-check an RO supplier’s pressure and flow figures
Who it is for
- Plant and utilities engineers
- Water treatment technicians
- Maintenance engineers
What you get
- Feed and mean osmotic pressure
- Net driving pressure and permeate flow
- Concentrate-end osmotic and net driving pressure
- Feed pressure needed for the flow wanted
Interpreting the result
- Raising recovery concentrates the brine, so the osmotic pressure at the concentrate end climbs steeply: at 90 % recovery it is ten times the feed value.
References
- Fermi E., Thermodynamics (Dover Publications, 1956; first published by Prentice-Hall, 1937), pp. 118–122. Method reference; no text, examples or tables are reproduced.
- Hydranautics, What Is Membrane Performance Normalization? (2001), net driving pressure and log-mean concentration factor — https://www.lenntech.com/data-sheets/Hydranautics-normaliz-L.pdf
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Flux, permeability and the net driving pressure
In Reverse Osmosis by the Numbers
What it covers: The solution-diffusion equations for water and salt, membrane permeability from an element data sheet, element count from a design flux, permeate flow and the feed pressure needed.
Useful alongside · Library collection
Clean water as an engineered system: barriers, gravity and supply security, and lessons for operations
In How Engineering Shaped Industry: From Aqueducts to the Grid
What it covers: Urban water supply saved more lives than almost any other engineering. How treatment, sewerage, storage and desalination developed, and what they teach about barriers and monitoring.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.