Stream flow, also known as discharge, represents the volume of water moving past a specific point in a stream or river over a fixed period of time. This measurement is typically expressed in cubic feet per second (cfs) or cubic meters per second. Quantifying stream flow is fundamental to hydrology, as the data is relied upon by resource managers for assessing water availability for human consumption and agriculture. Accurate discharge measurements are also foundational for engineering projects like bridge design and for predicting flood levels to protect communities.
Understanding the Fundamental Stream Flow Equation
The calculation of stream flow is based on the continuity equation for fluid dynamics. This principle states that the discharge (Q) is the product of the water’s average velocity (V) and the cross-sectional area (A) of the channel it occupies, expressed as Q = V x A. This formula allows for an indirect measurement of the total volume of water passing through a specific point.
The area-velocity method separates the problem into measuring these two distinct physical properties because directly measuring the total volume of water flow is impractical in a natural setting. Velocity (V) refers to the speed of the water, while area (A) represents the two-dimensional shape of the stream channel. By isolating the measurement of the static channel profile (A) and the dynamic water speed (V), hydrologists can determine the total discharge (Q).
Determining Cross-Sectional Area
The first step in applying the area-velocity method is to accurately determine the cross-sectional area (A) of the stream channel. Site selection is paramount, requiring a straight, uniform section of the stream where the flow is relatively stable, avoiding areas with large rocks, sharp bends, or back-eddies. After selecting a stable reach, a measuring tape must be stretched perpendicular to the flow, from one water’s edge to the other, to establish the total width of the stream.
Because natural stream channels rarely have a simple rectangular or trapezoidal shape, the cross-section must be divided into a series of smaller, vertical subsections. The most common practice is to establish measurement points at regular intervals across the width, often every one to two feet for smaller streams, or into at least 15 to 20 sections for larger rivers. This segmentation strategy, known as the mid-section method, allows the irregular channel shape to be approximated by a series of adjacent, simpler rectangles. At the center of each of these defined segments, the water depth is carefully measured using a wading rod or a weighted line.
The cross-sectional area (A) is then calculated by summing the area of each individual subsection. The area of a single subsection is approximated by multiplying its measured depth by its designated width. Combining the areas of all the defined segments provides an accurate representation of the total wetted cross-sectional area.
Measuring Water Velocity
With the cross-sectional area established, the next phase focuses on obtaining the water’s average velocity (V). While professional hydrologists often use highly specialized equipment like propeller current meters or Acoustic Doppler Current Profilers (ADCPs), the “Float Method” is a practical and accessible technique for field measurements. This method requires establishing a known measurement reach, which is a straight section of the stream, typically 50 to 100 feet long, with clearly marked start and end points.
A buoyant object, such as a partially submerged orange or a weighted bottle, is released upstream of the starting point and timed as it travels the measured distance. The float must be timed multiple times, usually three to five runs, to account for surface turbulence and variability in flow paths. The average surface velocity is then calculated by dividing the measured distance by the average travel time. This surface velocity, however, is generally faster than the average velocity of the entire water column due to friction along the streambed and banks.
To correct for friction, a velocity correction factor (C) must be applied to the calculated surface velocity. This factor is usually in the range of 0.8 to 0.9 for natural streams. A commonly accepted value for general use is 0.8, which adjusts the surface reading downward to estimate the average velocity of the entire cross-section. This adjusted velocity, calculated as \(V_{average} = V_{surface} \times C\), provides the representative speed for the final discharge equation.
Synthesizing Data and Final Calculation
The final step of the area-velocity method brings the two independent measurements, the total cross-sectional area (A) and the corrected average velocity (V), together to calculate the stream flow (Q). This is achieved by performing the final multiplication: Q = V x A. The units used in the calculation must be consistent to yield the correct result.
If the area (A) was measured in square feet (sq ft) and the velocity (V) was measured in feet per second (ft/s), the resulting discharge (Q) will be in cubic feet per second (cubic ft/s), or cfs. For example, if a stream has a total cross-sectional area of 15 square feet and the corrected average velocity is 2 feet per second, the calculation is Q = 2 ft/s x 15 sq ft, resulting in a discharge of 30 cfs. The cfs unit represents the volume of water flowing through the channel every second.