Tools › Fluids and Heat Transfer › Pipe Flow › Control Valve Sizing › Example
Globe control valve on water: 400 gpm at 60 lb/in² through a 3 in valve in a 4 in line (C_v, choked limit, travel and installed characteristic)
| Tool | Control Valve Sizing |
| Source | Tullis, J. P. (1993). Cavitation Guide for Control Valves. NUREG/CR-6031, U.S. Nuclear Regulatory Commission, Washington, DC (flow coefficient, eqs. 3.9 to 3.11; cavitation index, eq. 2.1; pressure recovery factor, eqs. 4.8 to 4.10; Figure 6.9); U.S. Army Corps of Engineers (1998). Heating, Ventilating and Air Conditioning (HVAC) Control Systems. Technical Instructions TI 810-11, Washington, DC, Chapter 2, paragraphs 12 to 14. |
| Level | Professional |
Problem
A 3 in equal-percentage globe valve (rated C_v 120, rangeability 50, F_L 0.90, F_d 0.46) sits between reducers in a 4 in Schedule 40 line (bore 4.026 in) and throttles water at 60 °F (vapour pressure 0.2563 lb/in² absolute, 1.12 cSt) from 150 lb/in² gauge. The normal case is 400 gpm at a 60 lb/in² drop; the minimum is 150 gpm at 85.8 lb/in² and the maximum 480 gpm at 46.8 lb/in², all on a system curve that leaves the valve 90 lb/in² at no flow. Find the required C_v and K_v of each case with the piping geometry factor, the choked pressure drop and the cavitation index, the travel, the outlet velocity, and the installed characteristic and valve authority.
Inputs to Enter
- Fluid: Liquid; relative density 1.0, vapour pressure 0.2563 lb/in² abs., critical pressure 3,200.1 lb/in² abs., viscosity 1.12 cSt
- Valve: globe, contoured plug; F_L 0.90, F_d 0.46, x_Fz 0.40; rated C_v 120, equal percentage, rangeability 50; valve size 3 in, pipe bores 4.026 in
- Cases (flow, inlet gauge, drop): Minimum 150 gpm, 150, 85.8 lb/in²; Normal 400 gpm, 150, 60; Maximum 480 gpm, 150, 46.8; atmospheric 14.696 lb/in²
- Example row 2; no-flow drop 90 lb/in²; velocity limit 33 ft/s; travel limits 10 to 90 percent
Answers
- Reducers: K_1 = 0.0989, K_2 = 0.1978, ΣK = 0.2967; without them C_v = 400/√60 = 51.64; with F_P = 0.9945 the required C_v = 51.93, K_v = 44.91 (closed form C_0/√(1 − ΣK C_0²/(890 d⁴)))
- F_F = 0.96 − 0.28 √(0.2563/3,200.1) = 0.9575; choked pressure drop (F_LP/F_P)² (P_1 − F_F P_v) = 131.5 lb/in² (133.2 for the valve alone): not choked; Re_v = 416,000, turbulent
- Cavitation index σ = (164.7 − 0.2563)/60 = 2.741, x_F = 0.365, below the incipient ratio 0.40; the minimum case (σ = 1.92, x_F = 0.52) is flagged as cavitating
- Minimum / Normal / Maximum: C_v 16.20 / 51.93 / 70.89; travel 48.8 / 78.6 / 86.5 percent; outlet velocity 6.81 / 18.2 / 21.8 ft/s; every case inside the limits
- Installed: fully open 587.2 gpm at 25.36 lb/in², valve authority N = 0.282 (the valve takes 0.667 of the system drop at the normal case); installed gain 1.76 at the normal case, 0.22 to 1.76 between 10 and 90 percent travel
Notes
The tool's default inputs are this case; press Submit. The case is illustrative (stated on the page) and has no printed source. The method is checked by test_control_valve_sizing.php (835 checks): an independent scipy script on 100 seeded cases, the published N constants recomputed from the definition of C_v, NUREG/CR-6031 section 3.2 and Examples 6.1 and 6.4 (C_v 805, ΔP_ch 30.54 lb/in²; the guide's printed 145 gpm is a misprint for 805 √30.54 = 4,449 gpm), and the TI 810-11 examples (C_v 20.41 / K_v 17.64, maximum drop 10.43 lb/in², steam C_v 11.34 and K_v 77.5). The valve factors filled by the style list are typical values, to be replaced by the maker's.