1. Principle of differential pressure flow measurement

The principle of flowing a fluid through a constriction has been exploited since ancient times: time measurement using hourglasses and clepsydras, "billing" of water distributed by Roman aqueducts. However, the first scientific analysis of the differential pressure flowmeter dates back only to the early 17th century, when Castelli and Toricelli established that the flow in an orifice is the product of its cross-sectional area and the fluid's flow velocity, and that it varies as the square root of the pressure drop between upstream and downstream. A century later, Bernouilli formulated the theorem that rigorously described this phenomenon, while a few years earlier, Henri Pitot had invented a probe for measuring the flow velocity of a fluid. A little later, Venturi described the first instrument for measuring flow in a pipe. Finally, the...