A Venturi meter is a horizontal constricted tube that is used to measure the flow speed through a pipeline. The constricted part of the tube is called the throat. Although a Venturi meter can be used for a gas, they are most commonly used for liquids. As the fluid passes through the throat, the higher speed results in lower pressure at point 2 than at point 1. This pressure difference is measured from the difference in height h of the liquid levels in the U-tube manometer containing a liquid of density ρm (from below figure). The following treatment is limited to an incompressible fluid.
Venturi tube (Venturi meter)
Let A1 and A2 be the cross-sectional areas at points 1 and 2, respectively. Let v1 and v2 be the corresponding flow speeds, p is the density of the fluid in the pipeline. By the equation of continuity,
v1A1 = v2A2 …………. (1)
Since the meter is assumed to be horizontal, from Bernoulli’s equation we get,
The pressure difference is equal to pm gh, where h is the differences in liquid levels in the manometer. Then,
Equation (3) gives the flow speed of an incompressible fluid in the pipeline. The flow rates of practical interest are the mass and volume flow ‘ rates through the meter.
Volume flow rate = A1V1
and mass flow rate = density x volume flow rate = ρA1v1
[Note ; When a Venturi meter is used in a liquid pipeline, the pressure difference is measured from the difference in height h of the levels of the same liquid in the two vertical tubes, as shown in below figure. Then, the pressure difference is equal to ρgh.
The flow meter is named after Giovanni Battista Venturi (1746-1822), Italian physicist.]
