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We asked the question at the start of this journey, how can you measure flow in a large bore pipe, that's underground. The obvious requirement is simple, requiring little to no maintenance.
Without this requirement the obvious thing to do is to use a pump action in reverse. In that the water flow presses against the pump blade and turns the shaft. The mechanical power (and slight drop in pressure because of it) taken from the water flow can then drive the meter. Moving parts, in large pipes underground, is not the solution. So how?
We know is we restrict flow
Pressure Difference (P2-P1) = Flow x Resistance
If R = constant (related to the parameters , throttle of pipe)
Then Pdiff is proportional to Flow, Eureka, the venturi effect.
Flow of water is extremely similar to the problem in high voltage /current electric circuits, and where to measure current (equivalent to flow) you have to break the circuit, unless you find an indirect method of measurement. The venturi effect is such and indirect method of measuring medium pressure high flow.
If you imagine a pipe, if you put in a section which has a throttle, then the differential pressure across the 'venturi pipe' is proportional to the flow. This is a bit like the electrical equivalent; if you put a series resistor in a circuit and measure the resistance, using ohms law (V=I*R) I = V/R and by measuring V (voltage, relatively simple) and knowing R (series resistance) you can calculate I the current. In terms of water flow, then F = Pd /Tr (F = Flow, Pd = Pressure differential & Tr is the venturi pipe constant).
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