OpenSpecEngineering

Finds the flow coefficient a control valve needs to pass a liquid flow at a given pressure drop, as Cv (US units) and Kv (metric), using the IEC 60534-2-1 / ISA-75.01.01 sizing equations for turbulent, non-viscous liquids [1]. It also checks for choked flow, where cavitation or flashing caps the flow. Instrument engineers use it to pick a valve from a maker’s Cv tables.

Equations

F_F = 0.96 − 0.28·√(P_v/P_c)

ΔP_choked = F_L²·(P₁ − F_F·P_v)

C_v = Q·√(SG/ΔP_s)     K_v = 0.865·C_v

Q is the flow, P₁ the absolute upstream pressure and ΔP the drop across the valve. SG is the liquid’s density at flowing temperature divided by that of water at 15 °C. P_v is its vapor pressure and P_c its critical pressure, both absolute. F_F is the liquid critical pressure ratio factor. F_L is the liquid pressure recovery factor of the valve. ΔP_s is the sizing drop: ΔP, or ΔP_choked if that is smaller. In the C_v equation Q is in US gpm and ΔP_s in psi. K_v is in m³/h at a drop of 1 bar.

Inputs

• Choosing a Liquid fills in SG, P_v and P_c for water from 5 to 100 °C [3], [4], or for ethanol or methanol at 25 °C [5], [6].
• Choosing a Valve Style fills in the typical F_L at full travel from IEC 60534-2-1 Table 2 [1]. Use the maker’s F_L when you know it [2]. A rotary valve’s F_L falls as it opens.

Limits and common mistakes

• The valve is taken as line-size, with no reducers (F_P = 1). Reducers lower the effective capacity.
• Viscous liquids need the correction F_R, which is not applied.
• Use absolute pressures for P₁ and P_v. A gauge P₁ understates ΔP_choked.
• “Choked” means more drop gives no more flow, and the valve will cavitate or flash. Cavitation damage can start below ΔP_choked.
• Pick a valve that passes the design flow at about 60 to 80 % of travel.

Worked example

A valve must pass 60 m³/h of water at 90 °C, with 400 kPa absolute upstream and 250 kPa available for the drop. Will a 70°-open butterfly valve work, or is a globe valve needed?

1. Enter Flow Rate 60 m³/h, Upstream Pressure 400 kPa and Pressure Drop Across Valve 250 kPa.
2. Choose Liquid Water, 90°C. It fills in SG = 0.966, P_v = 70.182 kPa and P_c = 22,064 kPa.
3. Choose Valve Style Butterfly, swing-through disc, 70° open (F_L 0.62) and press Solve: Liquid critical pressure ratio factor FF: 0.944208
   Choked pressure drop ΔP_choked: 128.287 kPa
   Flow condition: Choked (flashing/cavitating) — sized at ΔP_choked
   Required Cv (US units): 60.1979
   Required Kv (metric): 52.0712
4. The butterfly valve would cavitate. Choose Valve Style Globe, single port, contoured plug, flow tends to open (F_L 0.90) and press Solve: Liquid critical pressure ratio factor FF: 0.944208
   Choked pressure drop ΔP_choked: 270.324 kPa
   Flow condition: Non-choked
   Required Cv (US units): 43.1224
   Required Kv (metric): 37.3009

Check by hand with the SI form of the equation, K_v = 10Q·√(SG/ΔP) with ΔP in kPa: F_F = 0.96 − 0.28 × √(70.18/22,064) = 0.9442, and ΔP_choked = 0.81 × (400 − 66.27) = 270.3 kPa, more than 250 kPa. Then K_v = 600 × √(0.9662/250) = 37.30, and C_v = 37.30/0.865 = 43.1.