Liquid Valve Cv: Worked Example

1. Calculator Inputs

Select the units below before entering the numbers. These are fixed benchmark inputs for checking the calculator.

2. Step-by-step Math

Start with the US Cv equation

Q = Cv × √(ΔP / SG)
Cv = Q × √(SG / ΔP)

Use US gpm and psi in this form. The pressure input is inlet pressure minus outlet pressure across the valve, not inlet pressure alone.

Calculate the required Cv

Cv = 100 × √(1 / 16)
Cv = 100 × 0.25 = 25
Kv = Cv / 1.156099 ≈ 21.6

The Kv conversion uses the same factor as the calculator. Required Cv must be compared with the manufacturer’s capacity at the intended opening.

Check the reverse calculation: flow

Q = 25 × √(16 / 1) = 100 gpm
100 gpm = 22.712470704 m³/h

Select Flow rate under Solve for. Enter Cv = 25, specific gravity = 1, and pressure drop = 16 psi.

Check the reverse calculation: pressure

ΔP = SG × (Q / Cv)²
ΔP = 1 × (100 / 25)² = 16 psi
ΔP = 16 × 6.894757293168 ≈ 110 kPa

Select Pressure drop under Solve for. Enter Cv = 25, specific gravity = 1, and flow = 100 gpm.

3. Compare Your Answers

Keep full precision during the calculation. The calculator may display fewer digits; compare answers rounded to three significant figures; retain unrounded intermediate values.

Second check

At unchanged Cv and pressure drop, raising specific gravity from 1 to 1.44 lowers flow to 25 × √(16 / 1.44) = 83.3 gpm. Denser liquid needs more pressure drop for the same flow.

4. Assumptions and Method

This is the basic single-phase incompressible liquid equation. It omits viscosity corrections, reducers, pressure-recovery factors, cavitation, flashing, and choked flow. It does not size gas or steam valves.

Equation definitions and implementation: Liquid Valve Cv Calculator. See also calculation methodology and other worked examples.