When I say flow, what I really mean is ‘volumetric flow rate’. In layman’s terms, flow is the volume of water that passes a certain point in a set period of time and it’s generally expressed as either gallons per minute (gpm) or cubic feet per second (cfs). The equation for flow is:
Q = V * A
Where Q is flow, V is velocity of the flow, and A is the area of the flow.
For instance, say you have a square ditch running by your house. You know it is three feet wide and five feet deep, but the water in it is currently three feet deep. That makes your area 3 ft * 3ft = 9 square feet. You measure the velocity of the water and determine it’s moving about 2 ft per second. That means the flow rate in that ditch is: Q = 2 * 9 = 18 cubic feet per second.
The numbers themselves aren’t that important. The most important thing to take away from this discussion is how the variables affect each other. If Q goes up, V or A must go up. If A goes down then V goes up, and so on.
Let’s continue our example above. The neighbor wants to slope his yard so it also drains into our ditch. His yard is about the same size as ours, so we’ll assume he’s going to have about the same amount of water. Suddenly the Q in our ditch doubles from 18 to 36. Do we let him do it?
If our Q is going up, then V and/or A are also going to have to go up. Velocity depends on what the ditch is made out of and how steep it is, and the neighbor isn’t going to change those so we’ll assume our velocity stays the same as before, but the ditch is 5 ft high and our water is only 3 ft deep so area can increase when the flow does. But is it enough? To figure that out we’ll calculate the maximum flow the ditch can hold. We do that by using the entire ditch height rather than just the 3 ft of depth.
A= width * height = 3 ft * 5 ft = 15
Q = 15 ft * 2 ft/sec = 30
So our ditch will hold 30 cubic feet per second without overflowing. We calculated the flow in our yard to be 18 cfs and we think the neighbors will be about the same. So if we let the neighbor do what he wants there will be 18 + 18 = 36 cfs of water in our ditch. But the max is only 30 cfs. So we tell the neighbor no, because it will make our ditch overflow.
Another way to use our new found knowledge…. Maybe you decide to put in a flower bed next to the creek and want to make it more narrow. You can can do the same calculations with a smaller area and see how that works out. Or if you’re afraid your kids are going to fall down the five foot vertical wall and want to make it a shallow slope instead, you can figure out the best way to do that.
I’ve simplified it quite a bit, but now you know the foundation of hydraulic engineering, so we can build on that. Later I’m going to talk about bridges and levees and how they affect flow.