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Venturi flow meter

Input data

Flow

Diameter 1

Diameter 2

P¹/γ

Output data

U1²/2g

U2²/2g

hf¹²

hf¹³

P²/γ

P³/γ

Description

Given the inlet flow (Q), the upstream and throat diameters (D1, D2), and the upstream piezometric head (P1/γ), this computes the velocity heads at sections 1 and 2, the piezometric heads at the throat (P2/γ) and downstream (P3/γ), and the head losses in the nozzle (hf¹²) and diffuser (hf¹³).

Assumptions: steady, incompressible flow, same elevation reference (no elevation terms), empirical correlations for nozzle and diffuser losses.

VenturiVenturi

Equations

A1=πD124,A2=πD224U1=QA1,U2=QA2hf12=0.15 U222ghf13=2.5 U222gP2γ=P1γ+U122g−U222g−hf12P3γ=P1γ−hf13\begin{aligned} A_1 &= \frac{\pi D_1^2}{4}, \quad A_2 = \frac{\pi D_2^2}{4} \\ U_1 &= \frac{Q}{A_1}, \quad U_2 = \frac{Q}{A_2} \\ h_f^{12} &= 0.15\,\frac{U_2^2}{2g} \\ h_f^{13} &= 2.5\,\frac{U_2^2}{2g} \\ \frac{P_2}{\gamma} &= \frac{P_1}{\gamma} + \frac{U_1^2}{2g} - \frac{U_2^2}{2g} - h_f^{12} \\ \frac{P_3}{\gamma} &= \frac{P_1}{\gamma} - h_f^{13} \end{aligned}

Default input units: Q in L/s, D1 and D2 in mm; heads in m.

 

Inputs

ParameterDefault unitsDescription
FlowL/sInlet flow rate (Q)
Upstream diametermmPipe inside diameter upstream (D1)
Throat diametermmVenturi throat diameter (D2)
P¹/γmUpstream piezometric head (P1/γ)

Outputs

ParameterDefault unitsDescription
U1²/2gmVelocity head at section 1 (U1²/2g)
U2²/2gmVelocity head at throat (U2²/2g)
hf¹²mNozzle head loss (1→2)
hf¹³mDiffuser head loss (1→3)
P²/γmPiezometric head at throat (P2/γ)
P³/γmPiezometric head downstream (P3/γ)
FlowL/sOutput flow (same as input), Qout = Q

References

  • AZEVEDO NETTO, J. M. de. Manual de hidráulica. 9. ed. São Paulo: Blucher, 2015.