The Parshall Flume

A Parshall flume is not a shape someone can improvise. Its published discharge equations were obtained by calibration of specific geometries, so if you change the proportions the equations no longer apply and you have built something that needs its own calibration from scratch. Build it to the standard and the century of published rating data is yours. BUILD A 3-INCH (76 MILLIMETRE) THROAT FLUME, which is the smallest standard size and a sensible bench scale. From 5 millimetre acrylic or exterior plywood sealed with resin, make a channel with three sections in series. The CONVERGING section: walls angled inward, floor level, 466 millimetres long, narrowing from 178 millimetres wide at the entrance to the 76 millimetre throat. The THROAT: 76 millimetres wide, 152 millimetres long, and here the floor DROPS — it slopes down at 1 in 4 through the throat. That drop is Parshall's contribution and it is not optional. It is what accelerates the flow enough to keep solids moving through, and what allows the flume to keep reading under partial submergence. The DIVERGING section: 457 millimetres long, widening back out to 178 millimetres, with the floor rising again at 1 in 6. The rise recovers some energy and, more importantly, sets the tailwater condition that determines whether the flume stays in free flow. THE GAUGE POINTS matter as much as the walls. Ha, the upstream head, is measured in the converging section at two-thirds of its length back from the throat entrance — for this size, 311 millimetres upstream of the throat. Hb, the downstream head, is measured in the throat itself near its lower end. Both are measured from the FLOOR OF THE THROAT ENTRANCE as datum, not from the local floor, which is a common and expensive mistake. Fit a stilling well at each gauge point: a vertical tube of 32 millimetre pipe connected to the channel through a small hole, so the water surface inside is still even while the channel surface is disturbed. Read the level in the tube against a scale. Trying to read a moving water surface directly gives you an error larger than the measurement. SET IT LEVEL. The floor of the converging section must be horizontal in both directions to within a millimetre over its length. A flume out of level reads consistently wrong, and there is nothing in the reading to warn you. SUPPLY IT. A recirculating loop — a submersible pump in a sump, feeding a stilling basin ahead of the flume through a length of pipe, with the flume discharging back to the sump. The stilling basin matters: flow arriving at the flume must be smooth and parallel, so put a baffle or a coarse mesh across the approach and give it at least ten channel widths of straight run.

Every flow meter is a claim, and the only honest test is to catch the water and weigh it. THE CALIBRATION. Run the pump at a fixed setting and let the flume settle for a full minute — the level takes time to stabilise and reading it early is the commonest error. Read Ha in the upstream stilling well. Then divert the flume outlet into a bucket on a scale for a timed interval of at least 30 seconds, and weigh. Mass divided by time divided by density gives you the true discharge. Repeat at eight or ten pump settings across the range. Plot measured discharge against Ha on log-log axes. WHAT YOU SHOULD SEE, and it is the satisfying part: a straight line. The published free-flow equation for a 3-inch Parshall flume is Q equals 0.1771 times Ha raised to the power 1.55, with Q in cubic metres per second and Ha in metres. On log-log axes that is a straight line of slope 1.55, and your measurements should lie on it within a few percent. If your slope is right but the line is offset, your datum is wrong — you are measuring Ha from the wrong reference and the fix is arithmetic. If the SLOPE is wrong, your geometry is wrong, and no amount of arithmetic will save it. NOW DROWN IT, which is the part that distinguishes this instrument from every other one in the sibling group. The free-flow equation assumes the flume is in control — that critical depth occurs in the throat and nothing downstream can influence the upstream level. Raise the tailwater by putting a weir or a partial blockage in the outlet channel, and at some point the downstream water backs up far enough to drown the control. Measure the submergence ratio, Hb divided by Ha, and raise the tailwater in steps while holding the pump setting constant. At low submergence, Ha does not change at all as you raise the tailwater — the flume is genuinely independent of what happens downstream, which is a remarkable property and the reason it is trusted. Then, above a threshold, Ha begins to rise even though the flow has not changed. That threshold is around 0.5 for a 3-inch flume, 0.6 for the small sizes generally, and 0.7 for larger ones. Find yours and record it. Beyond it, a single reading of Ha OVERSTATES the flow, and to get a correct answer you must read both heads and apply a submergence correction. This is worth doing because submerged flumes in the field are extremely common — a downstream channel silts up, a pump station backs water up — and a flume reading high for a reason nobody has noticed will quietly misreport a works' flow for years.