Pipe Pressure Drop and Orifice Sizing Calculations

Pressure drop in a pipe: Darcy–Weisbach

Δp = f (L/D) (ρ v² / 2) + Σ K (ρ v² / 2) + ρ g Δz

The Darcy friction factor f comes from the Colebrook equation for turbulent flow, 1/√f = −2 log₁₀(ε/(3.7 D) + 2.51/(Re √f)), and f = 64/Re for laminar flow. Fittings and valves add K values (Crane Technical Paper 410).

Example. Water at 20 °C, 100 m³/h in 4-inch Schedule 40 steel pipe (inside diameter 102.3 mm, roughness 0.046 mm): velocity 3.38 m/s, Reynolds number 3.4 × 10⁵, f = 0.0177, so the friction loss is about 0.99 bar per 100 m. In 6-inch Schedule 40 (154.1 mm) the velocity falls to 1.49 m/s and the loss to 0.13 bar per 100 m. Line sizing is choosing the size that balances pressure drop against pipe cost — the pressure drop calculator shows every size at once.

Gas and steam lines

For gases the density changes along the line. When the drop is small an average density is enough; for long lines use isothermal flow, and for short plant lines adiabatic flow with friction. As the outlet pressure falls the velocity approaches sonic and the flow chokes — reducing the outlet pressure further does not increase the flow. The PlantCalcKit pipe tool flags choking and gives the Mach number.

Orifice plate sizing to ISO 5167-2

q_m = C / √(1 − β⁴) · ε · (π/4) d² · √(2 Δp ρ₁)

with β = d/D, the discharge coefficient C from the Reader-Harris/Gallagher equation (which depends on β, the Reynolds number and the tap arrangement — flange, corner or D and D/2), and the expansibility factor ε = 1 − (0.351 + 0.256 β⁴ + 0.93 β⁸)[1 − (p₂/p₁)^1/κ] for gases (ε = 1 for liquids). Sizing means finding the bore d that gives your full-scale differential at the maximum flow; because C depends on β, it is solved by iteration.

ISO 5167-2 applies within limits: bore d ≥ 12.5 mm, pipe 50 mm ≤ D ≤ 1000 mm, 0.1 ≤ β ≤ 0.75, and a minimum Reynolds number. The permanent pressure loss is roughly (1 − β^1.9) of the differential, and the plate needs enough straight pipe upstream and downstream (ISO 5167-2, Table 3).

Control valve Cv

C_v = Q_gpm √(SG / Δp_psi) K_v = Q_m³/h √(SG / Δp_bar) C_v = 1.156 K_v

For liquids the flow chokes when the pressure drop exceeds F_L² (p₁ − F_F p_v) (IEC 60534-2-1); beyond that the valve cavitates or flashes and more pressure drop gives no more flow.

Gas flow compensation

A gas flow meter calibrated at design conditions reads wrongly when the pressure, temperature or composition change. For a differential-pressure meter giving standard volume flow the correction is √[(p/p_d)(T_d/T)(Z_d/Z)] for a gas of unchanged molecular weight; a volumetric meter is corrected by (p/p_d)(T_d/T)(Z_d/Z) without the square root.

Calculators for this

Free calculators

Pipe pressure drop and sizing — Friction, fittings and elevation by Darcy-Weisbach, plus velocity and pressure drop for every Schedule 40 size.
Gas pipeline pressure drop — Outlet pressure and velocity of a gas line by the isothermal compressible-flow equation, for every Schedule 40 size.
Steam pipe sizing — Velocity and pressure drop of saturated or superheated steam for every Schedule 40 size (IAPWS-IF97).
Reynolds number and line velocity — Velocity, Re, flow regime and friction factor for water or any liquid in any pipe.
Orifice plate flow — Flow from differential pressure by ISO 5167-2 (Reader-Harris/Gallagher), for liquids and gases.
Restriction orifice sizing — Bore for a given pressure drop — liquids with the cavitation check and plates in series, gases with choked flow.
Control valve Cv — Required Cv and Kv for liquids, with the choked-flow and cavitation check (IEC 60534).
Control valve Cv for gas and steam — Required Cv and Kv for gas, vapour and steam by IEC 60534-2-1, with the expansion factor and choked flow.
Gas flow compensation — Correct a gas flow meter for actual pressure, temperature, molecular weight and Z — DP and volumetric meters.
Water hammer surge pressure — Joukowsky surge, wave speed for steel, iron, PVC and HDPE pipe, critical closing time and column separation.
Pipe wall thickness (ASME B31.3) — Minimum wall for internal pressure with allowances and mill tolerance, and the lightest schedule that meets it.
Relief valve (PSV) sizing — Required orifice area and API 526 letter for gas, steam and liquid — API 520 Part I equations.

Online tools and Excel tools

Pipe Sizing and Pressure Drop — Pressure drop or allowable flow for liquid, gas and steam lines, with fittings, elevation, choked-flow and flashing checks and a size table over every NPS of your schedule. Use online · Excel tool, USD 29
Orifice Plate Sizing — Orifice bore for a flow and transmitter range, the flow from a measured differential, or the differential for a flow, by ISO 5167-2 — with β, C, ε, permanent loss, limit checks and straight lengths. Use online · Excel tool, USD 29

Questions

How do I calculate pressure drop in a pipe?

Use the Darcy–Weisbach equation: Δp = f(L/D)(ρv²/2), with the friction factor from the Colebrook equation, plus K values for fittings and the elevation change.

How do I size an orifice plate?

Choose the full-scale differential and maximum flow, then solve the ISO 5167-2 flow equation for the bore d. The discharge coefficient depends on β and the Reynolds number, so the solution is iterative; check the result against the ISO 5167 limits.

What β ratio should an orifice plate have?

ISO 5167-2 allows 0.1 to 0.75. Values around 0.4 to 0.7 are common; a higher β gives less permanent pressure loss but needs longer straight lengths.

More calculation guides

These guides and calculators give engineering estimates for screening, troubleshooting and training. Check important decisions against site data, your equipment maker and your plant's approved procedures.

Pipe pressure drop and orifice sizing