Worked problem

Control Valve Sizing: Calculate Cv for a Water Line

Calculate the flow coefficient Cv for 100 GPM of water across a 25 psi pressure drop, and see how Cv changes with flow and pressure drop.

Controls & Instrumentation · Last reviewed

Given

Water (specific gravity 1.0) at 100 GPM must flow through a control valve with a pressure drop of 25 psi at that flow. Liquid service, no flashing or cavitation.

Find

The required Cv.

Solution

Cv = Q × √(SG ÷ ΔP) (Q in GPM, ΔP in psi)
  1. Cv = 100 × √(1.0 ÷ 25) = 100 × 0.2 = 20.
  2. By definition, Cv is the flow in GPM of 60 °F water that gives a 1 psi drop. A valve with Cv = 20 passes 20 GPM at 1 psi.
  3. Sensitivity: double the flow at the same ΔP and Cv doubles (40). Double the ΔP at the same flow and Cv falls to 14.1.

Answer

Cv = 20 at 100 GPM and 25 psi

Choosing the valve

Pick a valve whose rated Cv, at the planned operating opening, is above the required value, so the valve works at a mid-range opening and has room for higher flow. Valves are usually sized so the normal flow sits between about 20% and 80% open. Oversized valves control poorly near closed.

Common mistakes

  • Using the total system pressure drop instead of the pressure drop across the valve.
  • Mixing units. Metric Kv uses m³/h and bar and is about 0.865 × Cv.
  • Ignoring cavitation and flashing at high pressure drop, which need a different calculation and often a different valve.
  • Skipping the valve authority check. If the valve takes only a small share of the system pressure drop, its flow characteristic becomes distorted.

Try two variations

  1. Water, 250 GPM at a 10 psi drop: Cv = 250 × √(1.0 ÷ 10) = 79.1.
  2. Light oil with a specific gravity of 0.8, 100 GPM at a 25 psi drop: Cv = 100 × √(0.8 ÷ 25) = 17.9.

Because the specific gravity is under the square root, a lighter liquid needs a smaller Cv for the same flow and pressure drop.

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

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Questions

What about gas or steam?

Compressible fluids use different equations with expansion factors, and the flow can choke at high pressure drop. Use the standard (such as ISA/IEC 60534) or the manufacturer method.

What is valve authority?

The ratio of the valve pressure drop to the total circuit drop with the valve fully open. A low value gives a flatter response and poor control.

What is the difference between Cv and Kv?

Cv uses US gallons per minute and psi. Kv uses cubic metres per hour and bar. Kv is about 0.865 times Cv.

How do I choose between an equal-percentage and a linear characteristic?

Equal-percentage valves suit systems where the pressure drop across the valve changes a lot with flow. Linear valves suit systems where the drop stays nearly constant. The valve authority helps decide.

What is rangeability?

The ratio of the largest to the smallest flow over which the valve still controls well. A high rangeability valve works across a wider range of loads.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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