  How to Calculate Average Stream Depth, Average Stream Velocity,  and Stream Flow

When stream width, depth, and velocity measurements are submitted to the IOWATER database, average stream depth and velocity, and total flow are automatically calculated for you.  Below are the calculations for those three parameters:

SD = stream depth (meters; SD1 is the stream depth at spot 1)
1, 2, etc = spots along the stream transect
n = number of spots along the transect
W = width of box at each spot; 1 meter is used
SV = stream velocity (1 meter divided by seconds measured; meters per second)
* = multiplier
¸ = divider

Average Stream Depth (meter)

Average Stream Depth = [SD1 + SD2 + SDn] ¸ n

NOTE: The transparency tube can be used to measure stream depth at each spot. Be sure to convert the measurement from centimeters to meters.

Total Flow (cubic meters per second or m3/s)

For total flow, imagine a box placed around each spot on your stream transect. A flow is determined for each box and summed for all boxes. Flow associated with each box is calculated by multiplying the width of the box at each spot (1 meter) by stream depth (which you measure) by the velocity of the spot (in the field you measure the number of seconds it takes for the tennis ball to travel one meter; velocity is one meter divided by the number of seconds). The flow of each box is in cubic meters per second (m3/s). The flow of each box is added together to give total flow.

Total Flow = (W1*SD1*SV1) + (W2*SD2*SV2) + (Wn*SDn*SVn)

Average Stream Velocity (meters per second or m/s)

Average stream velocity is calculated by dividing total flow by the cross-sectional area of your transect. The cross-sectional area is determined by calculating a cross-sectional area for the box at each spot of your transect and then summing the cross-sectional areas.

Average Stream Velocity = Total Flow ¸ [(W1*SD1) + (W2*SD2) + (Wn*SDn)]

EXAMPLE: Sally and Bill measure stream width, depth, and velocity for Jack Creek. Jack Creek is 4.2 meters wide.

 Stream Depth (meters) Stream Velocity (meters/seconds) Spot 1 0.21 1 meter/8 seconds (0.125) Spot 2 0.45 1 meter/4 seconds (0.25) Spot 3 0.62 1 meter/3 seconds (0.33) Spot 4 0.35 1 meter/7 seconds (0.143)

Average Stream Depth = (0.21 m + 0.45 m + 0.62 m + 0.35 m) ¸ 4 = 0.41 m

Total Flow = (1 m * 0.21 m * 0.125 m/s) + (1 m * 0.45 m * 0.25 m/s) + (1 m * 0.62 m * 0.33 m/s) + (1 m * 0.35 m * 0.143 m/s) = 0.39 m3/second

Average Stream Velocity = Total Flow ¸ Cross-Sectional Area

Average Stream Velocity = 0.39 m3/second ¸ [(1 m * 0.21 m) + (1 m * 0.45 m) + (1 m * 0.62 m) + (1 m * 0.35 m)] = 0.24 m/s Cross-sectional view of a stream.