What flow is that? From Hydraulics to Hydrology

When I look at a river or stream, I always try to guess how much water is flowing. That is, the water discharge. I’ve measured the discharge in dozens of rivers, under circumstances ranging from tranquil summertime flows to winter storms. And before I step into the water with my measuring instruments, I would always try to guess ahead of time, just for fun. You don’t really need to have experience measuring rivers to do this. Here’s the secret: the water discharge is equal to the cross-section area of the river multiplied by the velocity of the water. If water is too deep, you can possibly see the bottom, and guess depth. Then you can guess the width, and here we mean the width of the water that’s actively flowing, not the stagnant water along the edge. Finally, focus your eyes on something out of the middle, that’s floating downstream and count off the seconds it takes to move 10 feet or 10 meters, whatever you’re most comfortable with. If there’s nothing out there, throw in a stick. Then multiply depth times with times velocity, and there you have it! River flow, or more properly water discharge, is measured in units of volume over time. In the United States, discharge is measured in cubic feet per second (CFS), while in the rest of the world it is measured in cubic meters per second (CMS) or liters per second. If all of the water was moving at the same velocity in every part of the river channel, we could easily compute the water discharge as velocity multiplied by channel cross-sectional area, as I described above. But water doesn’t flow with a single, uniform velocity throughout the cross-section. We all know that water in out towards the middle of the river is moving faster than water near the edge, and water at the top surface is moving faster than water in contact with the streambed. When people measure the flow of water, they need to account for this variation, even though for wider, straighter river channels, the turbulence does tend to make the velocity more uniform across the mid section. Scientists who measure water discharge account for this variation by dividing the width of the river into 20 or more increments. In the middle of each increment, they measure the depth, and they measure the velocity with a special current meter. With the width and depth of each increment, and the local velocity, they can compute the discharge in that increment. Finally, adding all the increments together gives the discharge for the whole river. The only additional detail is where to measure the velocity. It turns out that the best place is not the surface, but a point about six tenths of the depth down from the surface. This point tends to be an average, accounting for the slowing of the water in the zone near the bottom where the friction with the bottom is stronger. So we can measure the water discharge when we visit the river. But we know that this discharge changes, from winter to summer, from storm to calm, from day to day, even from hour to hour. So what we really need, what would really be interesting, is a way to continuously measure the discharge, over days, months, years, decades. For this, we need to put in a stream gauge. A stream gauge is a device placed in the river or alongside of it which is capable of recording the level of the water surface. Usually, an electronic pressure measurement at or near the level of the streambed will suffice. Pressure is actually measured in a protected “stilling well” on the stream bank, which is connected to the river bed with a pipe. By measuring the pressure every few minutes, we can record the pattern of change in water surface elevation. And if we go out and measure the water discharge numerous times at numerous water surface elevations, we can develop “conversion chart,” called a rating curve, to estimate the water discharge at each water surface elevation. Using this rating curve, we can convert the record of water surface elevation into a record of estimated water discharge.