Parshall Flume Calculator

Introduction to Parshall Flumes

A Parshall flume is a standardized hydraulic structure used to measure the flow rate of water in open channels, such as irrigation canals, wastewater treatment plant streams, and sewer systems. Designed by Ralph L. Parshall in the early 20th century, the flume uses a contracting neck or throat to accelerate water flow, creating a critical-flow state. This allows the flow rate to be accurately determined by measuring the water depth at a single designated upstream point.

The Parshall Flume Flow Formula

Under free-flow conditions (where the downstream water level does not restrict the flow through the throat), the relationship between flow rate and upstream head (depth) is defined by the empirical equation:

$$Q = 4 \cdot B^{1.026} \cdot h_1^{1.522}$$

Where:

• $Q$ is the volumetric flow rate in cubic feet per second (cfs).
• $B$ is the throat width of the flume in feet (ft).
• $h_1$ is the upstream head or water depth in feet (ft), measured at the standard gauge point (located $2/3$ of the converging section length upstream from the throat).

Solving for Other Variables

Depending on your application, you may need to solve for the throat width or upstream depth. This calculator automatically performs these inverse calculations:

Solving for Throat Width ($B$)

If you know the target flow rate and acceptable upstream depth, the required throat width is:

$$B = \left( \frac{Q}{4 \cdot h_1^{1.522}} \right)^{\frac{1}{1.026}}$$

Solving for Upstream Depth ($h_1$)

To predict the water level upstream for a given flow rate and flume size:

$$h_1 = \left( \frac{Q}{4 \cdot B^{1.026}} \right)^{\frac{1}{1.522}}$$

Free Flow vs. Submerged Flow

The calculations in this tool assume **free-flow conditions**, which occur when the ratio of downstream depth ($h_2$) to upstream depth ($h_1$) is below the submergence limit (typically $0.70$ for throat widths of 1 to 8 feet). If the submergence ratio exceeds this limit, tailwater backs up into the throat, and a submergence correction must be applied to determine the true flow rate.