Parshall Calculator
The Parshall flume consists of a rigid structure with a flat-bottomed converging section at the inlet, a short throat section with a positive slope of 3:8, and a diverging section with an adverse slope of 1:6 at the outlet.
The Parshall flume is a type of critical gauge. Its design causes the flow to transition from a subcritical to a supercritical condition through a critical flow point. This principle allows the flow rate to be related to the water level in a predictable manner. It combines a hydraulic phenomenon that occurs due to a change in regime from subcritical (F<1) to supercritical (F>1), given by the Froude number, with a level measurement to determine the channel's flow rate. It is recommended to have a Froude number less than 0.6 before the flume.
Why measure flow without knowing the velocity?
Normally, when we talk about measuring flow or discharge in a channel, it is usually done using the Area-Velocity method. However, in this case, it is not necessary to measure the velocity directly. By forcing the flow to pass through a critical section, the need to measure velocity is eliminated; only the depth or depth needs to be measured. At the critical depth point, the relationship between depth (water height) and discharge is unique (for a given section), allowing the height to be used simply as an input variable.
We can make an example of a calculation for a flow in a Parshall canal:
Where:
Q is the flow rate (m³/s).
hₐ is the head or depth (m).
C is the adjustment coefficient.
m is the adjustment exponent.
According to the Parshall table:
Since the throat (b) is 0.152 m or 6 inches, the values are as follows:
hₐ = 0.15 m (a random depth within the Parshall's reach)
C = 0.381 m
m = 1.580 m
In the event that the Parshall gauge does not match the throat sizes listed in the regulations, it can be calculated, however it must be remembered that these are theoretical interpolations and precision is lost, especially in throats smaller than 6 inches or 0.15 m:
If you need to know the constants C and m of the formula you can visit our other articles:
Parshall flume flow equation
Under free-flow conditions, the flow through a Parshall flume depends only on the head H measured in the converging section, at 2/3 of its length upstream of the throat:
Q = K · Hⁿ
K and n depend on the throat width W. For 1 to 8 ft throats, the classic imperial form is the following, with W and H in feet and Q in ft³/s:
Q = 4 · W · H^(1.522 · W^0.026)
The K and n values for every standard size are in the AxoTek Parshall constants calculator.
Worked example
A 1 ft (0.305 m) throat flume with a head of 0.30 m (0.984 ft): Q = 4 × 1 × 0.984^1.522 = 3.90 ft³/s = 0.110 m³/s, about 110 L/s.
Free flow and submerged flow
The equation is valid only if the submergence ratio Hb/Ha stays below the limit for each size; above it, the flow must be corrected:
1 to 3 in throat: maximum submergence 0.50
6 to 9 in throat: maximum submergence 0.60
1 to 8 ft throat: maximum submergence 0.70
10 to 50 ft throat: maximum submergence 0.80
Frequently asked questions
Where is the head measured?
In the converging section, at 2/3 of its length before the throat, with a staff gauge or an ultrasonic level sensor.
What is the typical error of a Parshall flume?
Well built and in free flow, between ±3 and ±5 %. Construction errors in the throat or poor leveling increase it considerably.
Parshall flume or area-velocity method?
The Parshall flume is ideal for continuous measurement in wastewater channels. For rivers and channels without a structure, use the area-velocity method (NMX-AA-179), also available on AxoTek.