Cone (V Cone) Flow Meter Calculator
Calculate flow through a cone (V cone style) differential pressure meter from its DP. The beta ratio comes from the cone and pipe diameters; use the calibrated discharge coefficient of the meter, or C = 0.80 from ISO 5167-5 for an uncalibrated standard cone.
- β = √(1 − dcone² ÷ D²) = 0.6801
- qm = C ÷ √(1 − β⁴) × ε × (π/4) D²β² × √(2ΔPρ) = 15.326 kg/s
Cone Meter Equation
qm = C ÷ √(1 − β⁴) × ε × (π/4) × D² × β² × √(2 × ΔP × ρ1)
D is the pipe inside diameter, dcone the cone diameter, β the equivalent beta ratio (the annular flow area equals that of an orifice with bore βD), C the discharge coefficient and ε the expansibility (1 for liquids). ISO 5167-5 gives C = 0.80 for uncalibrated standard cones within 0.45 ≤ β ≤ 0.75 and Re from 8 × 10⁴ to 1.2 × 10⁷, with an uncertainty of about 5 %. Commercial cone meters are flow calibrated and supplied with their own C.
Worked example
Water in a 4" Sch 40 line (102.3 mm) with a 75 mm cone (β ≈ 0.68) at 100 mbar and C = 0.80 gives about 55,200 kg/h (55.3 m³/h).
Frequently Asked Questions
How does a cone flow meter work?
A cone in the pipe centre makes the flow accelerate through the annulus around it. The DP between upstream and the cone rear is related to flow like an orifice.
What is the beta ratio of a cone meter?
β = √(1 − d²/D²), so the annular area equals the bore area of an orifice with the same beta.
Why calibrate a cone meter?
The standard coefficient has about 5 % uncertainty; flow calibration reduces it to well under 1 %.
Learn more on the blog
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