Control Valve Flow (Cv)
Q = Cv × √(ΔP / SG)
Quick answer
This calculator solves Q = Cv × √(ΔP / SG) for Flow Rate. With Valve Cv 0.5, Pressure Drop 15 PSI, Specific Gravity 1.1, the result is 1.846 GPM.
Calculator
Formula
Description
The valve flow coefficient Cv quantifies the flow capacity of a control valve: it is the number of US gallons per minute of water at 60°F that will flow through the valve with a pressure drop of 1 PSI. For fluids other than water, the specific gravity correction adjusts for the difference in density. This sizing equation is fundamental to process control engineering and is used to select valves that can deliver the required flow rate at the available pressure drop. Oversized valves give poor control resolution, while undersized valves limit throughput.
Variables
- Q — Volumetric flow rate (US GPM)
- Cv — Valve flow coefficient (dimensionless)
- ΔP — Pressure drop across the valve (PSI)
- SG — Specific gravity of the fluid relative to water (dimensionless)
Practical Notes
Water at 60°F has SG = 1.0. For gases, a different Cv equation is used that accounts for compressibility. The Kv coefficient used in metric countries relates to Cv by Kv = 0.865 × Cv. Valve sizing should target 60-80% open at normal flow to allow room for control. ISA-75.01 provides the full valve sizing equations including choked flow, two-phase flow, and Reynolds number corrections.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Q | Flow Rate | GPM | GPM |
| Cv | Valve Cv | — | — |
| dP | Pressure Drop | PSI | PSI |
| SG | Specific Gravity | — | — |
Step by step
- 1. What you know: Valve Cv 0.5, Pressure Drop 15 PSI, Specific Gravity 1.1
- 2. The relation: Q = Cv × √(ΔP / SG)
- 3. Substitute: Cv = 0.5, dP = 15 PSI, SG = 1.1
- 4. Result: Flow Rate = 1.846 GPM
Worked examples
Minimum range
Given: Valve Cv 0.025, Pressure Drop 0.1 PSI, Specific Gravity 0.055
Result: Flow Rate = 0.03371 GPM
Low range
Given: Valve Cv 0.25, Pressure Drop 1 PSI, Specific Gravity 0.55
Result: Flow Rate = 0.3371 GPM
Typical
Given: Valve Cv 0.5, Pressure Drop 15 PSI, Specific Gravity 1.1
Result: Flow Rate = 1.846 GPM
High range
Given: Valve Cv 0.8, Pressure Drop 100 PSI, Specific Gravity 1.76
Result: Flow Rate = 6.03 GPM
Maximum range
Given: Valve Cv 8, Pressure Drop 1000 PSI, Specific Gravity 17.6
Result: Flow Rate = 60.3 GPM
How Flow Rate changes with Valve Cv
| Valve Cv (input) | Flow Rate (result) |
|---|---|
| 0.05 | 0.1846 GPM |
| 0.125 | 0.4616 GPM |
| 0.25 | 0.9232 GPM |
| 0.375 | 1.385 GPM |
| 0.5 | 1.846 GPM |
| 0.75 | 2.77 GPM |
| 1 | 3.693 GPM |
| 2 | 7.385 GPM |
| 3.5 | 12.92 GPM |
| 5 | 18.46 GPM |
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<p><a href="https://vbatpower.com/formulas/valve-cv/">Control Valve Flow (Cv)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Control Valve Flow (Cv)?
Use Q = Cv × √(ΔP / SG). With Valve Cv 0.5, Pressure Drop 15 PSI, Specific Gravity 1.1, Flow Rate works out to 1.846 GPM.
What is the formula for Control Valve Flow (Cv)?
The formula is Q = Cv × √(ΔP / SG). The valve flow coefficient Cv quantifies the flow capacity of a control valve: it is the number of US gallons per minute of water at 60°F that will flow through the valve with a pressure drop of 1 PSI.
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