8.8 Venturi tube

A Venturi tube is a device used to measure the flow rate of a fluid in a pipe. The device exploits the Venturi effect4, i.e. that pressure reduces when the fluid flows through a restriction.

The volumetric flow rate eqn is calculated according to

 C q ---- Q = -p----------A 2 p; D=Dt 1 \relax \special {t4ht=
where: eqn is the decrease in kinematic pressure eqn between the Venturi inlet and throat; eqn and eqn are the inlet and throat diameter, respectively; the cross-sectional area is eqn; and, eqn is a discharge coefficient. A coefficient of eqn satisfies the Bernoulli equation, eqn , between the inlet and throat, where eqn is the fluid speed.

For eqn, eqn is calculated accurately using eqn values between 0.97 and 1,5 but, for eqn, suitable values of eqn decrease significantly below 1 in order to account for pressure losses due to viscous forces.

PICT\relax \special {t4ht=

A simulation was performed to calculate eqn for a Venturi tube, shown in the figure, with eqn and an inlet eqn. The inlet velocity was specified using the quadratic profile in Sec. 8.7 with a mean cross-sectional speed eqn, corresponding to a maximum speed eqn.

PICT\relax \special {t4ht=

The simulation used the steady-state algorithm in Sec. 5.12, with an incompressible fluid with uniform eqn . The mesh contained 57,600 cells, with a near-wall cell height of 1.5mm, which resolved the velocity profiles as shown below. The flow recirculates near the wall downstream of the Venturi throat, causing inflow at the outlet boundary. Consequently, the total pressure and inlet-outlet-velocity boundary conditions, described in Sec. 4.7 and Sec. 4.15 respectively, were applied at the outlet to maintain stability.

PICT\relax \special {t4ht=

The flow was laminar so no turbulence modelling was required. The solution converged to within an absolute tolerance eqn, see Sec. 5.4 , in 292 iterations.

The pressure drop was eqn between the centres of the inlet and throat sections, with a corresponding eqn.

4Giovanni Battista Venturi, Recherches expérimentales sur le principe de la communication latérale du mouvement dans les fluides appliqué a l’explication de différens phénomènes hydrauliques, 1797.
5ISO 5167-4, Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full – part 4: venturi tubes, 2003.

Notes on CFD: General Principles - 8.8 Venturi tube