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Category Engineering Calculators

Medium Type

Flow Rate

Volumetric flow for liquids/gases

Mass Flow Rate

Upstream Pressure (P⊂1⊂)

Pressure Drop (ΔP)

psi

Specific Gravity

Relative to water (liquids) or air (gases)

Gas Temperature

Pressure Ratio Factor (x_T)

Typical: 0.70 (globe), 0.55 (butterfly)

Enter values and click Calculate

Flow Coefficient — C_v

Metric Equivalent — K_v

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About

Incorrect valve sizing causes either cavitation damage or insufficient flow capacity. Both outcomes cost thousands in downtime and replacement parts. The flow coefficient C_v quantifies how much fluid a valve passes at a pressure drop ΔP of 1 psi with water at 60 °F. This calculator implements ISA/IEC 60534 sizing equations for liquids, compressible gases, and steam. It detects choked (critical) flow conditions where increasing ΔP no longer raises flow rate. All intermediate values - including the pressure ratio factor x_T - are shown so you can cross-check against manufacturer datasheets.

Limitations apply. The equations assume turbulent, single-phase, Newtonian flow. Two-phase mixtures, slurries, and non-Newtonian fluids require correction factors not covered here. For gases, the tool assumes ideal gas behaviour; real-gas compressibility factor Z is set to 1.0. Pipe reducer corrections (F_P) are omitted. Always verify results against vendor catalogs before specifying a valve.

Formulas

The liquid sizing equation per ISA/IEC 60534:

C_v = Q × √SGΔP

where Q = volumetric flow rate in US GPM, SG = specific gravity relative to water at 60 °F, ΔP = pressure differential across the valve in psi.

For compressible gas service (sub-critical flow, x < x_T):

C_v = Q963 × N₂ × P₁ × Y × √xSG × T × Z

where x = ΔP ÷ P₁ (pressure ratio), Y = 1 − x3 × x_T (expansion factor), P₁ = upstream absolute pressure in psia, T = absolute temperature in °R, Z = compressibility factor (assumed 1.0), SG = gas specific gravity relative to air, N₂ = numerical constant per unit system.

For saturated and superheated steam:

C_v = W63.5 × √ΔP × (P₁ − 0.55 × ΔP)

where W = mass flow in lb/h, P₁ = upstream pressure in psia. This approximation holds for dry saturated steam. For superheated steam, multiply C_v by 1 + 0.00065 × ΔT_sh where ΔT_sh is degrees of superheat in °F.

To convert between the metric coefficient K_v and C_v: C_v = 1.1560 × K_v.

Reference Data

Valve Type	Typical C_v Range	x_T (Pressure Ratio Factor)	F_L (Liquid Pressure Recovery)	Typical Application
Globe, Single Seat	0.1 - 1200	0.70	0.90	General throttling service
Globe, Double Seat	5 - 2000	0.75	0.85	High-capacity process lines
Globe, Cage Trim	1 - 1500	0.70	0.90	Low-noise applications
Butterfly, 60° Open	50 - 30000	0.55	0.55	Large HVAC & water systems
Butterfly, 90° Open	100 - 50000	0.40	0.48	On/off isolation service
Ball, Full Bore	10 - 40000	0.50	0.60	Pipeline isolation
Ball, Segmented (V-port)	5 - 5000	0.60	0.70	Slurry & fibrous media
Plug Valve	20 - 12000	0.55	0.65	Chemical & refinery service
Eccentric Disc	30 - 8000	0.60	0.68	Moderate-pressure throttling
Diaphragm (Weir)	1 - 800	0.45	0.50	Corrosive & sterile fluids
Pinch Valve	5 - 2000	0.40	0.48	Abrasive slurries, mining
Gate Valve (Fully Open)	50 - 60000	0.85	0.95	On/off service only
Needle Valve	0.01 - 10	0.70	0.90	Precision metering
Angle Valve	1 - 800	0.72	0.80	High ΔP, cavitation-prone
Three-Way Globe	1 - 500	0.65	0.85	Mixing / diverting service

Frequently Asked Questions

Cv (US flow coefficient) measures flow in US GPM of water at 60 °F through a valve with a 1 psi pressure drop. Kv (European metric coefficient) measures flow in m³/h of water at 15 °C through a valve with a 1 bar pressure drop. The conversion is Cv = 1.1560 × Kv. Use Cv when working with ANSI/ISA standards common in North America. Use Kv with European DIN/IEC valve specifications. Mixing them without conversion leads to valve mis-sizing by roughly 15.6%.

When the pressure ratio x = ΔP / P1 exceeds the valve's critical pressure ratio xT, the flow velocity at the vena contracta reaches sonic speed. Beyond this point, further increasing ΔP does not increase flow. The expansion factor Y is clamped at 2/3 (0.667), and the effective ΔP used in the formula is limited to xT × P1. If this calculator detects x > xT, it switches to choked-flow equations and displays a warning. Typical xT values range from 0.40 for butterfly valves to 0.85 for gate valves.

Specific gravity (SG) accounts for fluid density relative to the reference substance (water for liquids, air for gases). A higher SG means more mass per unit volume and therefore a larger Cv required for the same volumetric flow rate. For liquids, SG = fluid density / 999.97 kg/m³. For gases, SG = molecular weight of gas / 28.966 (molecular weight of air). Common values: glycol SG ≈ 1.11, gasoline SG ≈ 0.74, natural gas SG ≈ 0.60, nitrogen SG ≈ 0.967.

Temperature indirectly affects liquid Cv through changes in viscosity and specific gravity. At temperatures above approximately 200 °F (93 °C), water's SG drops below 0.96, increasing the required Cv by 2-4%. Viscosity changes can shift the flow regime from turbulent to laminar, requiring a Reynolds number correction factor (FR) per IEC 60534-2-1. This calculator does not apply FR corrections; for viscous fluids (kinematic viscosity above 10 cSt), consult manufacturer sizing software.

Flashing occurs when downstream pressure P2 falls below the fluid's vapor pressure Pv. Cavitation occurs when pressure recovers above Pv after the vena contracta, collapsing vapor bubbles. Both conditions limit actual flow below what the basic Cv equation predicts. The liquid pressure recovery factor FL (provided in the reference table) determines the maximum usable ΔP: ΔP_max = FL² × (P1 − FF × Pv), where FF ≈ 0.96 − 0.28 × √(Pv / Pc) and Pc is the critical pressure of the fluid. This calculator flags when ΔP exceeds a conservative cavitation threshold.

No. The ISA/IEC 60534 equations implemented here assume single-phase, Newtonian, turbulent flow. Two-phase (liquid + gas) sizing requires separate Cv calculations for each phase, then combining them using methods such as the Omega parameter approach (API 520). Slurries introduce erosion and viscosity complications that demand empirical corrections from the valve manufacturer. Attempting to use single-phase equations for two-phase flow typically under-sizes the valve by 30-60%.