Venturi Meter Flow

Clemens Herschel patented the Venturi tube in 1887, naming it after Giovanni Venturi, and the arithmetic is identical to the orifice plate's. Only the coefficient changes. Because the convergent cone guides the flow instead of shearing it, there is no vena contracta and $C$ sits near 0.98 rather than 0.61. A 200/100 mm Venturi on 30 kPa passes about 3695 L/min of water.

The real argument for a Venturi is not accuracy but permanent pressure loss. An orifice plate throws away most of the differential it creates, typically 60 to 80% of it, forever, as heat and turbulence. A classical Venturi with its long 7 to 8 degree divergent recovery cone gives back most of what it borrowed and loses perhaps 10 to 15%. On a large pumped main running continuously, that difference is a genuine and permanent pump-energy line item, and it is what justifies the Venturi's much higher purchase price and its much greater length.

Two things worth knowing. The Venturi tolerates dirty and slurry service that would erode an orifice edge into uselessness, which is why they are standard on raw water, sewage and mineral slurries. And because the coefficient is so close to 1 and so flat with Reynolds number, a Venturi can often be used uncalibrated to within a percent, whereas an orifice plate near the low end of its range genuinely needs its $C_d$ computed rather than assumed.