Venturi Meter Calculator Formula

Understand the math behind the venturi meter calculator. Each variable explained with a worked example.

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Formulas Used

Velocity at Wide Section

v1 = sqrt(2 * pressure_diff / (density * (pow(area_wide / area_narrow, 2) - 1)))

Volume Flow Rate

flow_rate = area_wide * sqrt(2 * pressure_diff / (density * (pow(area_wide / area_narrow, 2) - 1)))

Variables

VariableDescriptionDefault
pressure_diffPressure Difference(Pa)5000
densityFluid Density(kg/m3)1000
area_wideWide Section Area (A1)(m2)0.01
area_narrowNarrow Section Area (A2)(m2)0.005

How It Works

Venturi Meter

A Venturi meter measures flow rate by measuring the pressure drop in a constriction.

Formula

From Bernoulli + continuity (A1 v1 = A2 v2):

v1 = sqrt(2 dP / (rho ((A1/A2)^2 - 1)))

The flow rate is Q = A1 * v1.

Worked Example

Water, A1 = 0.01 m2, A2 = 0.005 m2, dP = 5000 Pa.

pressure_diff = 5000density = 1000area_wide = 0.01area_narrow = 0.005
  1. 01(A1/A2)^2 = (0.01/0.005)^2 = 4
  2. 02v1 = sqrt(2 * 5000 / (1000 * 3))
  3. 03v1 = sqrt(10000 / 3000)
  4. 04v1 = sqrt(3.333) = 1.826 m/s
  5. 05Q = 0.01 * 1.826 = 0.01826 m3/s

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