To calculate the discharge flow rate of a Parshall Flume several pieces of information are required:

• Flume size (Parshall Flumes are sizes by throat width)
• Head at the primary (H_a) and secondary (H_b) points of measurement
• Submergence ratio (secondary point of measurement head H_b / primary point of measurement head H_a)
• Whether the flume is experiencing free or submerged flow (as determined by the submergence ratio and flume size and submergence transition)

With this information and the appropriate free or submerged flow equation, the flow rate can be quickly calculated.

Note that this assumes that the flume is experiencing good approach conditions and that the flume has not settled or shifted out of position after installation.

Correcting for poor approaching flow conditions cannot be done numerically - the flow itself must be corrected.  However, corrections for Parshall Flume settlement have been developed.

Flume Size

Parshall Flumes have an hourglass shape.  The waist - or narrowest portion of the flume - is defined as the throat.  As Parshall flumes have rigid, defined dimensions  (per ASTM D 1941 and ISO 9826).  So long as the flume conforms to these standards, the flume size can be checked by the throat width alone.

H_a and H_b Depths

Short throated flumes like the Parshall have defined locations for the primary (H_a) and secondary points of measurement (H_b).  These locations can be found on the Parshall Flume Master Dimensions drawing.

Note that the zero reference level for both H_a and H_b is the floor of the inlet / converging section (even through the inlet for the H_b location is below this level).

Submergence Ratio

The submergence ratio of a flume is defined as the ratio of the downstream level (H_b) to the upstream level (H_a).

H_b/H_a

This ratio (H_b/H_a) is used to indicate the degree to which downstream conditions limit free flow out of the flume.

Submergence Transition

As Parshall Flumes increase in size, their resistance to the effects of downstream submergence increases.

1-3 inch Parshall	50%
6 inch Parshall	60%
1-8 foot Parshall	70%
10-50 foot Parshall	80%

Flow Equations

With the above known, the flow rate in the flume can now be calculated. 

For free flow, the flow equation is:

Q = KHan

Q = free flow rate (cfs / l/s)

K = flume discharge constant (varies by flume size / units)

Ha = depth at point of measurement (feet / centimeters)

n = discharge exponent (depends upon flume size)

 

Per ASTM D1941:

Throat Width	K (Imperial)	K (SI)	n
1”	0.338	0.0479	1.55
2”	0.676	0.0959	1.55
3”	0.992	0.141	1.55
6”	2.06	0.264	1.58
9”	3.07	0.393	1.53
1’	4	0.624	1.522
1’-6”	6	0.887	1.538
2’	8	1.135	1.55
3’	12	1.612	1.566
4’	16	2.062	1.578
5’	20	2.5	1.587
6’	24	2.919	1.595
7’	28	3.337	1.601
8’	32	3.736	1.607
10’	39.38	4.709	1.6
12’	46.75	5.590	1.6
15’	57.81	6.912	1.6
20’	76.25	9.117	1.6
25’	94.69	11.32	1.6
30’	113.13	13.53	1.6
40’	150	17.94	1.6
50’	186.88	22.35	1.6

 

For submerged flow, the flow equation is:

For more information on the submergence equation.