Steam

Steam line sizing and verification with IAPWS-IF97

Q: Why are pressure drop and heat loss calculated together?

Because each changes the other. Heat loss changes the enthalpy and, with it, the steam quality and density; density changes velocity, friction and the acceleration term; pressure changes the saturation temperature and, with it, the heat loss. The calculator marches the line in segments (100 by default), updates the state with IAPWS-IF97 in each one and uses the Heun predictor-corrector scheme (second order), with acceleration and kinetic energy iterated to consistency with the end-of-segment state.

Q: What maximum velocity does the calculator use for steam?

The LOGOS default is 40 m/s for saturated or wet steam and 70 m/s for superheated steam (D124), and you can enter another limit. Velocity is checked independently of pressure: a line can meet the pressure and be too fast, or the other way round, and both checks must pass. At start-up, velocity above the steady-operation criterion is flagged as attention, because it is a transient.

Q: How is start-up calculated if I do not enter its flow?

At start-up the valve is 100% open (rated Cv) and the consumer is cold at the start-up pressure — 0 bar(g) by default, an explicit and adjustable assumption. The flow comes from the pressure balance between the header and the consumer, adding the line, fittings and valve losses, including choked flow. It is usually larger than maximum operation. Without a valve, it is the flow the line passes down to the start-up pressure. Without the valve rated Cv, start-up is not evaluated.

Q: Why does the calculator assume a separator ahead of the valve?

It is LOGOS assumption D169, stated in the result and in the calculation report: the moisture reaching the valve (from the inlet or formed along the line) is separated and drained by a separator with a steam trap right ahead of it, and the valve receives dry saturated steam — pressure-reducing station practice. The line therefore carries the consumption plus that condensate. If the valve received wet steam, IEC 60534-2-1 would not apply and the Cv would only be an estimate, which the calculator flags.

Q: Is the Mach number a pipe design limit?

No. It states the validity of the marching model: up to 0.3 the model is comfortably within its domain, between 0.3 and 0.5 there is a compressibility warning and above 0.5 a refined calculation is required; at start-up, above 0.5 is a critical alert with no favourable verdict. These are applicability limits of this model version, not normative limits. At wet-steam points Mach uses the homogeneous equilibrium (HEM) speed of sound, a² = (∂p/∂ρ)_s, because IAPWS-IF97 does not define the speed of sound in the two-phase region.

Q: Does the calculator classify the line under NR-13?

No. NR-13 (Brazil) appears as a documentation reference and interface with the legally qualified professional. LOGOS does not perform legal classification nor replace the applicable construction code; water steam piping is treated by NR-13 in a differentiated manner, and the applicable maintenance provisions and construction codes must be observed.

The calculator marches the steam line from the header to the consumer in segments, with IAPWS-IF97 properties, coupling the pressure drop (friction, fittings, elevation and acceleration) with the heat loss through the insulation (ISO 12241:1998), and checks consumer pressure, velocity, Mach and condensate formed at maximum operation, minimum operation and start-up.

When to use

Use it to size or check a saturated or superheated steam distribution line between the header and a consumer — with or without a pressure-reducing or control valve next to it. The line is handled as a single section (internal diameter, length, elevation change and fittings by count), insulated or not. The calculator always solves three scenarios: maximum and minimum operation (the flow is the equipment consumption and the valve throttles to hold the set point at the consumer) and start-up (valve 100% open and cold consumer, with the flow coming from the pressure balance). It returns the consumer pressure, the valve required Cv and opening, the maximum velocity, Mach, the heat lost, the condensate formed along the line and the pipe steel warm-up load at start-up — the numbers you need to choose the diameter, check the valve and plan drainage and steam traps. The product limit is 100 bar(a) of pressure.

What the calculator solves

A steam line loses pressure by friction and heat through the insulation at the same time, and each affects the other. The LOGOS Steam Steam line calculator treats the section from the header to the consumer as a one-dimensional march: in each segment it computes the heat loss per ISO 12241:1998, updates the enthalpy by the energy balance, subtracts friction (Darcy-Weisbach with Colebrook), fittings and elevation, obtains the new state from IAPWS-IF97 (phase, quality, density) and adds the acceleration term and kinetic energy. Pressures are handled internally as absolute; input and output are in bar(g).

When there is a pressure-reducing or control valve, it is always next to the consumer and the set point is the pressure at its outlet. The valve physics is that of IEC 60534-2-1 (Eq. N6, Kv form), the same as the LOGOS steam control valve calculator, with ρ₁ and κ from the actual state reaching the valve.

Three scenarios, always

Maximum operation — the flow is the equipment consumption. It is the top of the result: consumer pressure and temperature, loss breakdown, velocity, Mach, heat lost and condensate.
Minimum operation — same line at minimum flow; shows the required Cv and whether the valve falls below its controllable range (rated Cv ÷ R).
Start-up — valve 100% open and cold consumer (0 bar(g) by default). The flow is not typed in: it comes from the pressure balance, including choked flow. If you enter warm-up time, initial temperature and steel cp, the calculator adds the pipe steel warm-up load in kg/h.

How to read the verdicts

Pressure — without a valve: meets with margin, meets without design margin or does not meet, against the required pressure and margin entered. With a valve: set point reached or not; the design margin does not apply. If pressure is exhausted before the end of the line, the result is “not met — pressure exhausted” and shows how far the march reached.
Velocity — independent of pressure, against 40 m/s (saturated/wet) or 70 m/s (superheated) by default, adjustable.
Mach — model validity, not a design limit; at two-phase points it uses the homogeneous equilibrium (HEM) speed of sound.
Quality domain — minimum quality ≥ 0.95 is the declared domain; between 0.80 and 0.95 the verdicts are indicative; below 0.80 there is no verdict.
Scenario — each scenario is summarised as meets, attention, does not meet or not evaluated; at start-up, Mach above 0.5 is a critical alert.

Condensate and drainage

Heat loss forms condensate along the line, which must be drained at low points and regular intervals. With a valve, assumption D169 places a separator with a steam trap right ahead of it: the valve receives dry saturated steam and the line carries the consumption plus that condensate. At start-up, the pipe steel warm-up load is added to the steam trap load and can be much larger than the steady-state condensate — in the worked example, 72.7 kg/h against 4.6 kg/h.

Declared limits

The homogeneous two-phase model is valid for quality from about 0.95. The heat loss neglects the internal surface resistance and the steel wall. The warm-up load excludes flanges, valves, fittings, the insulation heat capacity and the loss during warm-up. If the whole flow condenses, the consumer pressure is not evaluated. The product limit is 100 bar(a). NR-13 (Brazil) enters as a documentation reference: LOGOS does not perform legal classification nor replace the construction code.

Formulas and fundamentals

Friction loss — Darcy-Weisbach with Colebrook Δp_friction = f·(Δx/D)·ρv²/2; 1/√f = −2·log₁₀[(ε/D)/3.7 + 2.51/(Re·√f)]

Applied to each segment Δx of the line, with ρ, v and Re from the local state. f = Darcy friction factor [-]; D = internal diameter [m]; ρ = density (homogeneous when two-phase) [kg/m³]; v = velocity [m/s]; ε = absolute roughness [m], default 0.045 mm (commercial steel); Re = Reynolds number with the IAPWS R12-08 viscosity (in two-phase, that of saturated vapour). Fittings enter as Δp = (ΣK/n)·ρv²/2, with the same list and the same K as the hydraulics calculators.

Energy balance and acceleration term h₂ = h₁ − q_l·Δx/ṁ − g·Δz/n − (v₂² − v₁²)/2; Δp_acceleration = G²·(1/ρ₂ − 1/ρ₁)

In each segment the enthalpy h [kJ/kg] drops with the heat loss q_l [W/m], elevation and kinetic energy; the new state (phase, quality, density) comes from IAPWS-IF97 at (p, h). G = ṁ/A is the mass flux [kg/(m²·s)]. Source terms are averaged between the start and a provisional end of the segment (Heun predictor-corrector, second order), and acceleration and kinetic energy are iterated to consistency with the end state: pressure drop and heat loss are coupled.

Linear heat loss — ISO 12241:1998 q_l = (T_fluid − T_amb) / [ Σ ln(D_e,j/D_i,j)/(2π·λ_j) + 1/(h_se·π·D_e) ]

Multilayer cylinder (Eqs. 7, 8 and 22). λ_j = insulation conductivity at the layer mean temperature [W/(m·K)], catalogue data; D_e = final outside diameter [m]; h_se = h_r + h_cv = external surface coefficient [W/(m²·K)], with radiation from the Table 2 emissivity (Eqs. 15–17) and natural convection of a horizontal pipe (18c/18d) or, outdoors, the larger of natural and wind-forced convection (18g/18h). The outer surface temperature is iterated.

Valve at the consumer — IEC 60534-2-1, Eq. N6 (Kv form)

W = 31.6·F_P·Kv·Y·√(x·P₁·ρ₁);   x = (P₁ − P₂)/P₁ ≤ Fγ·xT;   Y = 1 − x/(3·Fγ·xT) ≥ 0.667;   Fγ = κ/1.4

W in kg/h; P₁ = pressure at the end of the line, ahead of the valve [bar abs]; P₂ = set point at the consumer; ρ₁ and κ from the actual valve inlet state (IAPWS-IF97). With x ≥ Fγ·xT the flow is choked. Cv = 1.1561·Kv. Opening from the inherent characteristic: equal percentage = 1 + log(Kv/Kv_rated)/log(R); linear = Kv/Kv_rated.

Mach number (model validity) Ma = v/a; two-phase: a² = (∂p/∂ρ)_s (homogeneous equilibrium, HEM)

At single-phase points a is the IAPWS-IF97 speed of sound w; at two-phase points, the homogeneous equilibrium speed of sound, from the mixture ρ(p, s) via the IF97 backward equations. Mach states the validity of the marching model; it is not a pipe design limit.

Pipe steel warm-up load at start-up m_cond = M_steel·c_p·(T_steam − T_initial)/h_fg(p); load = m_cond/t; W_pipe = 0.0246615·(D − t)·t

M_steel = pipe mass [kg], from the ASME B36.10M linear mass (D and t in mm, W in kg/m); c_p = mean specific heat of steel [kJ/(kg·K)], user data (reference ASME II-D, Table TCD); h_fg = latent heat at the section pressure; t = warm-up time entered. Flanges, valves, fittings, the insulation heat capacity and the heat loss during warm-up are not included.

Standards & methods

IAPWS R7-97(2012) — IAPWS-IF97, thermodynamic properties of water and steam (with the supplementary backward equations SR2-01, SR3-03, SR4-04 and SR5-05)
IAPWS R12-08 — viscosity (industrial form)
IAPWS R15-11 — thermal conductivity (industrial form)
ISO 12241:1998 — thermal insulation for building equipment and industrial installations, calculation rules (LOGOS implements the 1998 edition)
IEC 60534-2-1:2011 — control valve sizing (Eq. N6), the same physics as the LOGOS steam control valve calculator
ASME B36.10M — steel pipe (linear mass for the warm-up load)
NR-13 (Brazil) — documentation reference and interface with the legally qualified professional; LOGOS does not perform legal classification nor replace the applicable construction code

Typical reference values

Quantity	Typical range	Note
Velocity limit — saturated or wet steam	40 m/s	LOGOS default (D124), adjustable. Checked independently of pressure.
Velocity limit — superheated steam	70 m/s	LOGOS default (D124), adjustable.
Default roughness	0.045 mm	Commercial steel (D123). For an existing line, enter the effective roughness or calibrate it with field data.
Mach number (model domain)	≤ 0.3 domain; 0.3–0.5 warning; > 0.5 refined calculation	LOGOS applicability criterion, not a normative limit. At start-up, above 0.5 is a critical alert with no favourable verdict; from 0.95 the model is not supported.
Minimum quality along the line	≥ 0.95 declared; 0.80–0.95 indicative; < 0.80 not evaluated	Domain of the homogeneous two-phase model — a LOGOS criterion, not a normative limit.
Line rising in the flow direction	up to 15 m/s; slope ≥ 1:40; drains every ≤ 15 m	Recommendation shown by the calculator when the line rises and velocity exceeds 15 m/s, so condensate is not carried against the steam.
Outer jacket emissivity (ISO 12241, Table 2)	0.05 (bright aluminium) to 0.94 (non-metallic)	Oxidized aluminium 0.13; stainless steel 0.15; aluminium-zinc 0.18; clean galvanized 0.26; dusty galvanized 0.44.

Worked example

40 m line with a pressure-reducing valve at the consumer (dry saturated steam at 10 bar(g))

Inputs

Header pressure (saturated steam, quality 1): 10 bar(g)
Maximum / minimum operating flow: 2,000 / 400 kg/h
Pipe internal / outside diameter: 77.92 / 88.9 mm
Length / elevation change: 40 / 0 m
Fittings: 3 × 90° elbow + 1 open gate valve -
Pressure-reducing valve — set point at the consumer: 4 bar(g)
Valve — rated Cv / xT / characteristic / R: 25 / 0.7 / equal percentage / 50 -
Insulation (1 layer, oxidized aluminium, indoors, 20 °C): 50 mm · λ 0.061 W/(m·K)
Start-up — cold consumer / time / initial steel T / steel cp: 0 bar(g) / 15 min / 20 °C / 0.49 kJ/(kg·K)

Results

Header temperature (saturation): 184.1 °C
Line loss: friction / fittings / acceleration: 0.112 / 0.035 / 0.0003 bar
Pressure ahead of the valve (P₁) / valve ΔP: 9.85 / 5.85 bar(g) / bar
Consumer pressure / temperature: 4.00 / 165.6 bar(g) / °C
Maximum velocity / maximum Mach: 20.9 / 0.044 m/s / -
Heat lost / condensate formed (drained at the separator): 2.85 / 4.6 kW / kg/h
Maximum operation: required Cv / opening: 17.76 / 91% -
Minimum operation: required Cv / opening: 3.50 / 50% -
Start-up: flow (choked) / velocity / Mach: 2,811 / 29.7 / 0.063 kg/h / m/s / -
Pipe steel warm-up load (451.7 kg of pipe): 18.2 kg → 72.7 kg/h in 15 min
Capacity at the set point (valve 100% open): 2,777 kg/h

At maximum operation the 40 m line costs little: 0.112 bar of friction, 0.035 bar of fittings and a negligible acceleration term, so 9.85 bar(g) reaches the valve, which throttles 5.85 bar to hold 4 bar(g) at the consumer — pressure verdict: set point reached. The maximum velocity (20.9 m/s) is well below the 40 m/s default limit and Mach (0.044) is within the model domain. The 50 mm insulation lets 2.85 kW through, forming 4.6 kg/h of condensate; the minimum quality along the line is 0.9977 (declared domain), and under assumption D169 this condensate leaves through a separator with a steam trap ahead of the valve, which receives dry saturated steam. Since the expansion in the valve is isenthalpic, the steam reaches the consumer slightly superheated (165.6 °C, IF97 region 2). The point to watch is the valve: with a required Cv of 17.76 against 25 rated it runs 91% open at maximum flow, with little headroom — the capacity at the set point with the valve fully open is 2,777 kg/h. At minimum operation (400 kg/h) it opens 50%, within the controllable range, and the condensate formed is 5.1 kg/h: the heat loss hardly changes with flow, so neither does the trap load. At start-up, with the valve 100% open and the consumer cold at 0 bar(g), the flow rises to 2,811 kg/h in choked flow, at 29.7 m/s and Mach 0.063 — it meets. Heating the 451.7 kg of steel from 20 °C to 184.1 °C condenses 18.2 kg of steam, or 72.7 kg/h over 15 min, a load to be added to the steam traps at start-up and far larger than the 4.6 kg/h in steady operation.

Run your own calculation Create a free account and get this for your own inputs in seconds.

Common mistakes

Entering absolute pressure where gauge is asked. The input is in bar(g), as read on the gauge; the local atmospheric pressure only changes at altitude.
Using the nominal diameter instead of the internal one. A DN 100 Sch 40 is 102.26 mm inside and Sch 80 is 97.18 mm — the pressure drop changes by about 25%.
Converting fittings into equivalent length and adding them again. Use the real routing length and count bends, valves and tees under Fittings (same list and same K as hydraulics).
Taking the insulation λ at the wrong temperature. Catalogue λ changes with temperature: use the value at the mean between steam and surface temperature.
Entering the insulation outside diameter as the pipe outside diameter. The field is the steel OD (114.3 mm for DN 100); insulation layers are added outside it.
Treating the set point as the pressure right after the valve, or making up the valve data. The set point is the pressure held at the consumer inlet; rated Cv, xT, characteristic and rangeability come from the catalogue — there are no defaults, and without the rated Cv start-up is not evaluated.
Checking maximum operation only. At start-up the valve is fully open and the consumer is cold: the flow is usually larger than maximum operation, and velocity and Mach must be checked in that scenario.

Frequently asked questions

Why are pressure drop and heat loss calculated together?

Because each changes the other. Heat loss changes the enthalpy and, with it, the steam quality and density; density changes velocity, friction and the acceleration term; pressure changes the saturation temperature and, with it, the heat loss. The calculator marches the line in segments (100 by default), updates the state with IAPWS-IF97 in each one and uses the Heun predictor-corrector scheme (second order), with acceleration and kinetic energy iterated to consistency with the end-of-segment state.

What maximum velocity does the calculator use for steam?

The LOGOS default is 40 m/s for saturated or wet steam and 70 m/s for superheated steam (D124), and you can enter another limit. Velocity is checked independently of pressure: a line can meet the pressure and be too fast, or the other way round, and both checks must pass. At start-up, velocity above the steady-operation criterion is flagged as attention, because it is a transient.

How is start-up calculated if I do not enter its flow?

At start-up the valve is 100% open (rated Cv) and the consumer is cold at the start-up pressure — 0 bar(g) by default, an explicit and adjustable assumption. The flow comes from the pressure balance between the header and the consumer, adding the line, fittings and valve losses, including choked flow. It is usually larger than maximum operation. Without a valve, it is the flow the line passes down to the start-up pressure. Without the valve rated Cv, start-up is not evaluated.

Why does the calculator assume a separator ahead of the valve?

It is LOGOS assumption D169, stated in the result and in the calculation report: the moisture reaching the valve (from the inlet or formed along the line) is separated and drained by a separator with a steam trap right ahead of it, and the valve receives dry saturated steam — pressure-reducing station practice. The line therefore carries the consumption plus that condensate. If the valve received wet steam, IEC 60534-2-1 would not apply and the Cv would only be an estimate, which the calculator flags.

Is the Mach number a pipe design limit?

No. It states the validity of the marching model: up to 0.3 the model is comfortably within its domain, between 0.3 and 0.5 there is a compressibility warning and above 0.5 a refined calculation is required; at start-up, above 0.5 is a critical alert with no favourable verdict. These are applicability limits of this model version, not normative limits. At wet-steam points Mach uses the homogeneous equilibrium (HEM) speed of sound, a² = (∂p/∂ρ)_s, because IAPWS-IF97 does not define the speed of sound in the two-phase region.

What does the calculator not cover?

The homogeneous two-phase model is valid for quality from about 0.95; between 0.80 and 0.95 the result is indicative and below 0.80 there is no verdict. If heat loss condenses the whole flow, the consumer pressure is not evaluated (there is no validated liquid model in this calculator). The heat loss neglects the internal surface resistance and the steel wall; the warm-up load excludes flanges, valves, fittings, the insulation and the heat loss during warm-up. The product limit is 100 bar(a).

Does the calculator classify the line under NR-13?