Concept

Flow metering — where it appears

Inferring a flow rate from something easier to measure — a pressure difference, a depth, a frequency. Every meter costs something for its reading, and the cheapest is one that measures a feature the flow was going to produce anyway.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The same reading, and only one of them gives it back. A Venturi and an orifice plate at the same diameter ratio, with the pressure along the axis drawn beneath each. Both narrow the flow by the same amount, both read the same difference between the pipe and the narrowest section, and both infer the same flow rate from it. Downstream they part company: the Venturi's diffuser turns the throat's speed back into pressure, and the orifice's jet expands into the pipe and destroys 73% of the reading. The picture is a section rather than a solved field: nothing here computes the jet, and the recirculating corner is not drawn.

The price of knowing the flow rate

Two flowmeters can narrow a pipe by the same amount, read the same pressure difference and infer the same flow rate, and cost pressures that differ by an order of magnitude. What separates them is not viscosity, and not workmanship — it is whether the flow is decelerated or abandoned.

applied · Metering $The depth at the edge, against how much pressure is left there. The brink depth as a fraction of the critical depth, against the share of the hydrostatic pressure the brink is taken to retain. A free jet — no pressure at all — gives exactly two thirds, to 1e-16. The measured ratio of 0.715 is met at 40 per cent of hydrostatic, which is more residual pressure than a falling nappe looks as though it should have.$

The depth at the edge is not the critical one

Every open-channel calculation assumes the pressure is hydrostatic, and usually says so nowhere. At a free overfall it is not, the assumption's failure can be measured, and the measurement is one number — a brink depth that is 0.715 of the critical depth where a hydrostatic reading would make it one.

applied · Open-channel

Named alongside it

The objects these essays reach for when they reach for this one.

Measurement Bernoulli's equation The Borda–Carnot loss Conservation Contraction coefficient Control volume Critical depth Discharge coefficient Froude number Hydrostatic Model limit Momentum theorem

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