Enter the head and the throat width of the Parshall flume into the calculator to determine the flow rate. This calculator assumes free-flow (unsubmerged) conditions and supports nominal throat widths from 1 inch to 72 inches (6 ft).
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Parshall Flume Flow Rate Formula
The Parshall flume flow calculator estimates open-channel discharge from the measured upstream head and the flume throat width. Under free-flow conditions, the discharge follows a power-law relationship, which is why even a small change in head can noticeably change the computed flow rate.
Q = K H_a^n
For the generalized free-flow relationship used in this calculator with U.S. customary units:
Q = 4W^{1.026}H_a^{\left(1.522W^{-0.026}\right)}- Q = flow rate in cubic feet per second (cfs)
- W = nominal throat width in feet (ft)
- Ha = upstream head in feet (ft)
- K and n = discharge constants that vary with flume size
What a Parshall flume measures
A Parshall flume is a specially shaped hydraulic structure used to measure flow in an open channel. As water passes through the converging section and throat, the geometry creates a predictable relationship between water depth and discharge. That makes the flume useful for irrigation channels, stormwater systems, plant outfalls, and wastewater applications where direct flow measurement may be difficult.
| Calculator Field | Meaning | How to Use It |
|---|---|---|
| Head (Ha) | The upstream water depth used for the rating equation | Measure at the proper upstream head location and reference it to the flume floor datum |
| Throat Width (W) | The nominal width of the flume throat | Enter the actual flume size, not a rough channel width estimate |
| Flow Rate (Q) | The computed discharge through the flume | Read the output in cfs, m³/s, or L/s as needed |
How to calculate Parshall flume flow
- Measure the upstream head Ha.
- Identify the nominal throat width W of the flume.
- Convert both values to feet if solving manually with the generalized equation.
- Substitute the values into the discharge formula.
- Convert the result to the desired output units if necessary.
This calculator is intended for free-flow, or unsubmerged, operation. If downstream water backs up enough to influence the throat, upstream head alone is no longer sufficient and the free-flow result should not be used without a submergence correction.
Unit conversion reference
If you need to move between output units, the following relationship is useful:
1\text{ cfs} = 0.0283168\text{ m}^3/\text{s} = 28.3168\text{ L/s}Example calculation
If the measured upstream head is 6 inches and the flume throat width is 12 inches, first convert both values to feet:
H_a = 6\text{ in} = 0.5\text{ ft}W = 12\text{ in} = 1\text{ ft}Now substitute into the generalized free-flow equation:
Q = 4(1)^{1.026}(0.5)^{\left(1.522(1)^{-0.026}\right)} \approx 1.39\text{ cfs}The same result is approximately 0.0394 m³/s or 39.4 L/s.
When the result is most reliable
- The flume is operating under free-flow conditions.
- The head is measured at the correct upstream location.
- The flume is reasonably clean, level, and free of excessive sediment or debris buildup.
- The entered throat width matches the flume’s nominal size.
- The water surface is calm enough to obtain a stable reading.
Common input mistakes
- Using the wrong head reference: The reading should be tied to the flume datum, not estimated from a random point in the channel.
- Entering channel width instead of throat width: The formula depends on the flume throat size, not the overall channel width.
- Ignoring submergence: Backwater conditions can invalidate a free-flow-only calculation.
- Mixing units manually: If you solve by hand, keep head and throat width in feet for the generalized equation shown above.
Why throat width matters
The throat width affects both the coefficient and the exponent in the discharge relationship. Smaller flumes respond more sharply to changes in measured head, while larger flumes can pass more water at the same depth. That is why selecting the correct nominal flume size is just as important as taking an accurate head reading.
Practical note for field use
If your calculated value seems unusually high or low, first verify the head measurement location, then confirm the throat width, and finally check whether downstream conditions may be causing submergence. In many field situations, those three issues account for most flow calculation errors.
