Cross-sectional flow area and wetted perimeter

1. Making measurements
Cross-sectional area and wetted perimeter vary uniquely at each stream or channel.  In order to calculate these values, first you must make measurements of the stream bed.  These measurements will require the use of a string, a ruler, and a level.  Unless the stream is very narrow, you will also need to wade out into the stream to take the measurements, so you should have a partner present and should practice stream safety.

First, stretch a string from the top of one bank to the top of the opposite bank.  Use the level to ensure that the string is precisely horizontal.  You may need to bring the string down from the top of one bank to level it with the lower bank.

Next, measure the distance between the string and the bottom of the channel at regular intervals.  We chose to measure the depth of our stream at every 5 inches across the channel's width.  Based on the width and cross-sectional complexity of your channel, you may choose a different measurement interval.

The depth measurements from our stream are recorded in the table below:

 Distance Depth (in.) 0 0 5 2 10 7 15 10 20 17 25 19 30 17 35 17 40 21 45 24 50 24 55 25 60 25 65 24 70 21 75 16 80 9 85 4 90 0

2. Cross-sectional flow area

The next step is to use the measured depths to draw a chart of the stream bottom.  You should draw this on a piece of graph paper, making sure that the scale is the same on the x-axis and y-axis.  I find it helpful to invert the y-axis so that my graph has the same orientation as the channel I took the data from.

Using this chart, cross-sectional flow area can be estimated by counting the number of squares in the streambed and multiplying this number by the area of each square.  On the chart above, there are 56.5 squares within the streambed.  The scale of each square is 25 in.2, so the total cross-sectional flow area is:

a = 56.5 squares  ×  25 in.2/square = 1412.5 in.2

3. Wetted Perimeter

In order to find the wetted perimeter, we must first find the wetted area between each interval at which the stream's depth was measured.  The wetted area between each measured depth is calculated using the following equation:

Where:
Aw = wetted area between two points
D1 = depth at first point
D2 = depth at second point
W = distance between measured points

In my example, "W" will always be 5 inches since I measured the depth of the channel at intervals of 5 inches.  For example, the wetted area between distances 0 and 5 is calculated as follows:

The wetted perimeter is the sum of the wetted areas, which in the case of our example is 110.1 inches.