Governing Formula
Osmotic pressure is the hydraulic pressure required to oppose the natural tendency of water to diffuse across a semipermeable membrane toward the more concentrated solution. In reverse osmosis, feed salinity and temperature strongly influence the pressure demand on the high-pressure pump.
π = i × C × R × T Where:
-
π= Osmotic pressure exerted by dissolved solutes across the membrane [bar] -
i= Van’t Hoff factor reflecting effective particle count [dimensionless] -
C= Solute molar concentration in the feed stream [mol/L] -
R= Universal gas constant for pressure-volume work [L·bar/(mol·K)] -
T= Absolute temperature of the feed solution [K]
Derived Equations:
C = TDS (mg/L) / 1000 / MW π = i × C × R × T π (psi) = π (bar) × 14.5038 How the Estimation Works
- Convert the feed TDS value into a molar concentration using the solute molar mass: TDS (mg/L) / 1000 / MW.
- Apply the van’t Hoff relationship with the selected van’t Hoff factor and absolute temperature in kelvin.
- Report osmotic pressure in both bar and psi for a quick design check.
This is a simplified TDS-based estimate using a NaCl-equivalent assumption for engineering screening. It is not detailed membrane-element projection software. Real RO systems are affected by ion-specific activity, temperature, concentration polarization, and membrane-specific transport behavior.
Worked Engineering Example
Seawater RO Feed Screening
A seawater RO feed has 35,000 mg/L TDS, a temperature of 25°C, and can be approximated as NaCl-equivalent solute with MW = 58.44 g/mol and i = 2.0.
C = 35,000 / 1000 / 58.44 = 0.599 mol/LT = 25 + 273.15 = 298.15 Kπ = 2.0 × 0.599 × 0.08314 × 298.15 = 29.6 barπ (psi) = 29.6 × 14.5038 ≈ 429 psi
Assumptions & Limitations
- Assumes the feed behaves as a dilute, largely monovalent-equivalent solution for screening purposes.
- Uses a simplified TDS-based, NaCl-equivalent single-solute approximation rather than full ion-by-ion osmotic modeling.
- Does not replace detailed membrane-element projection software or project-specific thermodynamic modeling.
- Temperature changes significantly affect osmotic pressure and membrane performance, so process validation remains essential.
Continue in the RO Engineering Workbench
Carry your feed TDS and temperature into the RO Engineering Workbench, where osmotic pressure joins feed flow, recovery, and rejection to resolve the complete train balance — concentrate salinity, permeate quality, and scaling-risk screening in one saved project.
Frequently Asked Questions
Why does osmotic pressure limit RO recovery?
As recovery increases, feed salinity concentrates downstream in the pressure vessel and the brine osmotic pressure rises. When brine osmotic pressure approaches the applied feed pressure, net driving pressure drops toward zero and no further permeate is produced — setting the practical recovery ceiling for a given pump and membrane.
Does temperature raise or lower osmotic pressure?
Osmotic pressure rises slightly with absolute temperature (π = iCRT is linear in Kelvin), so a cold feed has marginally lower osmotic pressure. In practice the far larger temperature effect is on membrane water permeability, which increases roughly 3% per °C.
Why is NaCl-equivalent TDS a simplification?
Real feed waters are mixtures of ions with different charge, molar mass, and activity coefficients. Approximating them as NaCl with a van't Hoff factor of 2.0 is a screening estimate; rigorous RO design uses ion-by-ion speciation to compute osmotic pressure of the actual stream.
Engineering Disclaimer
Preliminary Estimate Only. This calculator provides a simplified TDS-based, NaCl-equivalent screening value for osmotic pressure based on TDS and temperature. It is not detailed membrane-element projection software. Final RO design should be checked against membrane manufacturer data, the actual ionic composition of the water, pretreatment conditions, and detailed process design tools.
Technical References
- DuPont FilmTec™ Reverse Osmosis and Nanofiltration Technical Manual.
- AWWA Manual M46: Reverse Osmosis and Nanofiltration, American Water Works Association.