Type a line (7 bar(g) steam; 10 bar(a); 180 °C; 0.7 MPa; 100 psig) or fill in the fields: the line and the fields stay in step.
Enter a steam pressure, gauge or absolute, and the calculator gives the saturation temperature of water and steam at it, in °C, K and °F; enter a temperature and it gives the saturation pressure, in bar(a), bar(g), MPa and psi(a). It uses the saturation equations of IAPWS-IF97, the industrial formulation for water and steam, shows the working with your numbers and the reverse equation as a check, marks the point on the saturation curve, and gives a line you can copy or add to a request.
Saturation temperature and pressure only: no enthalpy, entropy, specific volume or other steam-table properties, no superheat, no safety valve set pressures, no boiler or class rule figures and no typical working pressures. The equations cover the saturation line from 0 °C to the critical point, 373.946 °C and 220.64 bar(a); outside it the calculator says so instead of giving a figure.
IAPWS-IF97 Eq. (30): theta = T + n9 / (T - n10), A = theta^2 + n1 theta + n2, B = n3 theta^2 + n4 theta + n5, C = n6 theta^2 + n7 theta + n8, ps = (2C / (-B + (B^2 - 4AC)^0.5))^4 in MPa with T in kelvin. At 180 °C (453.15 K): 1.002635 MPa = 10.026 bar(a), 9.013 bar(g). The release check value: 0.00353658941 MPa at 300 K.
IAPWS-IF97 Eq. (31): beta = p^0.25 with p in MPa, E = beta^2 + n3 beta + n6, F = n1 beta^2 + n4 beta + n7, G = n2 beta^2 + n5 beta + n8, D = 2G / (-F - (F^2 - 4EG)^0.5), Ts = (n10 + D - ((n10 + D)^2 - 4 (n9 + n10 D))^0.5) / 2 in kelvin. At 7 bar(g) (0.801325 MPa): 443.63 K = 170.5 °C. The release check value: 372.755919 K at 0.1 MPa.
n1 = 1167.0521452767, n2 = -724213.16703206, n3 = -17.073846940092, n4 = 12020.824702470, n5 = -3232555.0322333, n6 = 14.915108613530, n7 = -4823.2657361591, n8 = 405113.40542057, n9 = -0.23855557567849, n10 = 650.17534844798 (IAPWS-IF97 Table 34). Both equations come from one quadratic, so a pressure taken to its saturation temperature and back returns the same pressure.
| Unit | Equals | Basis |
|---|---|---|
| 1 psi | 6.894757293168 kPa = 0.06894757293168 bar | 1 pound-force on 1 square inch |
| 1 kgf/cm2 (at) | 98.0665 kPa = 0.980665 bar | standard gravity, 9.80665 m/s2 |
| 1 MPa; 1 kPa; 1 mbar | 10 bar; 0.01 bar; 0.001 bar | the bar: 1 bar = 100 kPa |
| Standard atmosphere | 1.01325 bar(a) = 101.325 kPa | the default atmospheric pressure |
| Kelvin | T in K = t in °C + 273.15 | the Celsius scale |
| Degree Fahrenheit | t in °F = 1.8 x t in °C + 32 | T in K = (t in °F + 459.67) / 1.8 |
| p* and T* of the IAPWS-IF97 equations | 1 MPa and 1 K | the reducing quantities |
Gauge and absolute pressures differ by the atmospheric pressure, which no unit factor takes care of: p(a) = p(g) + p_atm, with p_atm 1.01325 bar(a) unless another is entered.
The equations and the coefficients n1 to n10 are those of the IAPWS-IF97 saturation line, section 8 of the IAPWS release R7-97 (Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam): Eq. (30), the saturation-pressure equation, and Eq. (31), the saturation-temperature equation, both from the implicit Eq. (29). The coefficients were checked digit for digit against a second, independent published implementation of the formulation, and the calculator reproduces the computer-program verification values of the release (Tables 35 and 36) to every stated digit. The unit factors are exact by definition: 1 bar = 100 kPa, 1 kgf/cm2 = 98.0665 kPa, 1 psi = 6.894757293168 kPa, the standard atmosphere 101325 Pa (NIST SP 811 and the SI brochure); T in K = t in °C + 273.15 and t in °F = 1.8 t in °C + 32.
From the absolute pressure, with the saturation-temperature equation of IAPWS-IF97, Eq. (31) of the IAPWS release R7-97: beta = (p / 1 MPa)^0.25; three quadratics in beta, E, F and G, with the coefficients n1 to n10; D = 2G / (-F - (F^2 - 4EG)^0.5); and Ts = (n10 + D - ((n10 + D)^2 - 4 (n9 + n10 D))^0.5) / 2 in kelvin. For 7 bar(g) the absolute pressure is 7 + 1.01325 = 8.01325 bar(a), 0.801325 MPa, and the saturation temperature is 443.63 K, 170.5 °C. The release gives 372.755919 K at 0.1 MPa as a check value, and the calculator meets it to every stated digit.
With the saturation-pressure equation of IAPWS-IF97, Eq. (30): theta = T + n9 / (T - n10) with T in kelvin; A = theta^2 + n1 theta + n2, B = n3 theta^2 + n4 theta + n5, C = n6 theta^2 + n7 theta + n8; and ps = (2C / (-B + (B^2 - 4AC)^0.5))^4 in MPa. At 180 °C, 453.15 K, the saturation pressure is 1.002635 MPa: 10.026 bar(a), or 9.013 bar(g) with the standard atmosphere. The release check value is 0.00353658941 MPa at 300 K. Both equations come from one quadratic, so each is the exact reverse of the other, and the working shows the reverse as a check.
Either, marked: bar(g), barg or psig for gauge, bar(a), bara or psia for absolute. The equations need the absolute pressure, so a gauge pressure is made absolute by adding the atmospheric pressure, 1.01325 bar(a) by default; enter the barometer reading to change it (atm 0.98 bar). A pressure without a mark is read as gauge, as a gauge shows it, and the result says so. A gauge figure below zero is a vacuum. The saturation pressure from a temperature is absolute; its gauge figure is negative below about 100 °C at the standard atmosphere.
The saturation line of IAPWS-IF97: from 273.15 K (0 °C), where the saturation pressure is 611.213 Pa, 0.00611 bar(a), to the critical point, 647.096 K (373.946 °C) and 22.064 MPa (220.64 bar(a)). Above the critical point water and steam no longer separate, so there is no saturation temperature or pressure; below 0 °C the equations do not apply. Outside the range the calculator says so and gives no figure.
No. It gives the saturation temperature and the saturation pressure only: no enthalpy, entropy, specific volume, density, dryness or superheat. It also gives no safety valve set pressures, no boiler or class rule figures and no typical working pressures; those come from the maker data, the class society rules and the full property equations of IAPWS-IF97.
Pressures in bar, mbar (hPa), kPa, MPa, psi (1 psi = 6.894757293168 kPa) or kgf/cm2 (98.0665 kPa exactly), each gauge or absolute. Temperatures in °C, K (T = t + 273.15) or °F (t in °F = 1.8 t + 32). The saturation temperature comes in °C, K and °F, the saturation pressure in bar(a), bar(g), MPa and psi(a), and the atmospheric pressure is entered as an absolute figure, such as atm 0.98 bar or atm 1013 hPa.
The calculator gives the saturation temperature and pressure only. When a steam valve, a steam trap, a gauge, a thermometer or a seal rated for the temperature is needed, send the line from the calculator with a photograph of the nameplate or the part, and Vessel Core checks the details before an offer goes back.
