Type a line (dew point air 22 °C RH 75 % steel 18 °C, or pressure dew point 3 °C at 7 bar) or fill in the fields: the line and the fields stay in step.
Enter the air temperature with the relative humidity, and the calculator gives the dew point: the temperature at which the air is saturated and water condenses on a colder surface. Add the steel surface temperature for the margin over the dew point and a pass or below check against the usual 3 °C rule for coating work. It also gives the relative humidity back from a dew point, and converts the pressure dew point of compressed air after a dryer to the atmospheric dew point, or back. It shows the working with your numbers, draws the temperatures on one scale, and gives a line you can copy or add to a request.
The dew point comes from the Magnus formula with the coefficients 17.625 and 243.04 °C, fitted to the saturation vapour pressure over water from -40 to 50 °C. The only check is against the usual 3 °C rule of coating practice; the calculator gives no humidity limits, no drying times and no dryer classes. A pressure without a mark is read as gauge, and the atmospheric pressure is 1.013 bar, assumed.
With g = ln(RH / 100) + 17.625 t / (243.04 + t), the dew point is td = 243.04 g / (17.625 - g). Air at 22 °C and 75 % RH: g = -0.28768 + 1.46299 = 1.1753, td = 243.04 x 1.1753 / (17.625 - 1.1753) = 17.4 °C. Back from a dew point, the relative humidity is RH = 100 es(td) / es(t): air at 10 °C with a dew point of 7 °C is at 81.6 % RH.
The margin is the steel surface temperature less the dew point. With the air at 22 °C and 75 % RH and the steel at 18 °C it is 18 - 17.4 = 0.6 °C: under the 3 °C that the usual rule of coating practice checks the margin against. When the surface is not warmer than the dew point, water condenses on the steel.
Compressing the air raises the water vapour pressure with the absolute pressure, so a pressure dew point is higher than the dew point of the same air at atmospheric pressure. es(3 °C) = 7.574 hPa; at 7 bar(g), 8.013 bar(a), the vapour pressure after expansion to 1.013 bar(a) is 7.574 x 1.013 / 8.013 = 0.9575 hPa, and the atmospheric dew point is -23.1 °C.
| Quantity | Relation | Note |
|---|---|---|
| Saturation vapour pressure | es(t) = 6.1094 exp(17.625 t / (t + 243.04)) | hPa, t in °C, over water, -40 to 50 °C |
| Dew point | td = 243.04 g / (17.625 - g) | g = ln(RH / 100) + 17.625 t / (243.04 + t) |
| Relative humidity | RH = 100 es(td) / es(t) | from the air temperature and the dew point |
| Surface margin | ts - td | the usual rule: 3 °C or more |
| Atmospheric dew point | es(td atm) = es(PDP) x p(atm) / p(a) | absolute pressures; p(atm) = 1.013 bar(a), assumed |
| Absolute pressure | p(a) = p(g) + 1.013 | bar; a pressure with no mark is gauge |
| Units | t in °C = (t in °F - 32) / 1.8 | 1 psi = 0.06894757293168 bar; 1 MPa = 10 bar |
The formula is for saturation over water. The atmospheric pressure of 1.013 bar(a) is the standard atmosphere, rounded; in the conversion of a pressure dew point the share of water vapour in the air does not change when the air is compressed or expanded.
The Magnus formula with the coefficients 17.625 and 243.04 °C, and the range of -40 to 50 °C they are fitted to, are given in independent meteorological and engineering references and humidity calculators; its inverse gives the relative humidity from the dew point. The rule that the steel surface should be at least 3 °C above the dew point is stated in the international performance standard for protective coatings of ships and in coating inspection guidance. The conversion of a pressure dew point, the vapour partial pressure scaled by the ratio of the absolute pressures (Dalton’s law), is given in a compressed air knowledge base and in a humidity instrument maker’s application note on Dalton’s law.
With the Magnus formula. First g = ln(RH / 100) + 17.625 t / (243.04 + t), with t the air temperature in °C; then the dew point is td = 243.04 g / (17.625 - g). Air at 22 °C and 75 % RH: g = -0.28768 + 1.46299 = 1.1753, and td = 243.04 x 1.1753 / (17.625 - 1.1753) = 17.4 °C. Air at 30 °C and 85 % RH has its dew point at 27.2 °C. The coefficients 17.625 and 243.04 °C are fitted to the saturation vapour pressure over water from -40 to 50 °C, and the calculator takes air temperatures and dew points in that range.
From the saturation vapour pressure, es(t) = 6.1094 exp(17.625 t / (t + 243.04)) hPa: the vapour in the air is at the saturation pressure of its dew point, so RH = 100 es(td) / es(t). Air at 10 °C with a dew point of 7 °C: es(7 °C) = 10.007 hPa, es(10 °C) = 12.260 hPa, and RH = 100 x 10.007 / 12.260 = 81.6 %. A dew point above the air temperature would mean a relative humidity over 100 %, and the calculator says so instead of giving a figure.
It is common coating practice: blast cleaning and coating are not done while the steel surface is less than 3 °C above the dew point of the air, so that no moisture condenses on it. The calculator gives the margin, the surface temperature less the dew point, and checks it against that figure: pass at 3 °C or more, below under 3 °C. Air at 22 °C and 75 % RH with the steel at 18 °C: the dew point is 17.4 °C, the margin 0.6 °C, below the rule. The calculator only checks the figure: the coating specification for the job sets the conditions, and the calculator gives no others.
The pressure dew point is the dew point of compressed air at its own pressure, as read after a dryer. When the air is expanded, the share of water vapour stays the same, so the vapour partial pressure falls with the absolute pressure: es(td atm) = es(PDP) x p(atm) / p(a). A pressure dew point of 3 °C at 7 bar(g), 8.013 bar(a): es(3 °C) = 7.574 hPa, 7.574 x 1.013 / 8.013 = 0.9575 hPa, and the atmospheric dew point is -23.1 °C. The reverse multiplies by p(a) / p(atm) instead.
The air temperature with the relative humidity in %, or with the dew point; the steel surface temperature if wanted; or a pressure dew point (or an atmospheric dew point) with the pressure. Temperatures in °C or °F, from -40 to 50 °C for the air and the dew points; pressures in bar, psi, MPa or kPa, gauge or absolute, read as gauge when they have no mark and made absolute with an atmospheric pressure of 1.013 bar, assumed. A result outside -40 to 50 °C is shown as an estimate.
It gives the dew point, the relative humidity, the margin of the surface over the dew point with the check against the usual 3 °C rule, and the conversion between a pressure dew point and the atmospheric dew point. It gives no humidity limits for coating work, no drying or overcoating times and no dryer class tables.
The calculator gives the dew point and the margin over it. When parts for a compressed air dryer, a dehumidifier or the coating equipment are needed, send the line from the calculator with the equipment details and a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
