## How big does that ditch have to be anyway? That depends on how fast the water flows….

Engineers use a formula called “The Manning’s Equation” to calculate how fast water moves in a ditch.  This formula also works for pipes when they are not flowing full.

Velocity = B x C x D

B is one divided by a number we find in charts that accounts for the roughness of the channel surface.  It is commonly referred to as “Manning’s n”.  Manning’s n for concrete is about .012.  So the value of B for a concrete pipe or channel is 1/.012 or 83.  Manning’s n gets higher the rougher the channel surface is; which results in a lower value for B.  You know that.  The smoother the surface….the faster the flow.

C is related to the “hydraulic radius” of the channel; which is the ratio of the channel surface to its area.  You determine the “hydraulic radius” by dividing the length of water touching the channel by the area of the water.  You know that.  The channel bottom and sides drag on the water.  The less water touching the channel; the faster it goes.

D is the square root of the slope.  You know that.   Steeper channels flow faster.  However, that “square root” has a big impact.  The square root of nine is three.  So a channel nine times as steep only flows three times as fast.

And how much water you need to move…..

Engineer’s use a formula called the continuity equation to relate the amount of water flowing to the size of the channel and the velocity of the water in the channel.

Q = A x V

Q is “how much water you need to move” and is usually discussed in gallons per minute or cubic feet per second.

A is the area of the channel that is full of moving water.  For example, if the channel is a rectangle, the area is the width of the channel times the depth of the water.  The key to this value “A” is that it doesn’t matter how big the channel is; only how much of the channel actually has water in it.

V is the velocity of the water in the channel that we talked about earlier.

Recap

Most of this seems pretty obvious, doesn’t it?

Steeper      ==>   Faster
Smoother  ==>   Faster
Bigger        ==>   More

But, you have to keep in mind….

…..only the part of the ditch that is filled with moving water counts!  Water in the bottom that does not drain out 100% when flow is stopped does not count.  Digging a ditch deeper does not always help!

….shape matters.  A ditch two feet wide and one foot deep can move more water than a ditch one foot wide and two feet deep.  The area is the same but the water in the one foot wide ditch is touching 5 feet of channel and the water in the two feet wide ditch is only touching 3 feet of channel.  What do you think is the most efficient shape for a channel?  No engineers please.

These two versatile equations, Manning’s Equation and the Continuity Equation, are used to size swales on farm fields and back yards, estimate flood elevations in creeks, and determine what size storm sewer pipes are needed.  Engineer’s use many equations that are what I call “very approximate”.  These two equations are “very accurate” if you get the information right.

Let me know if you have any questions or would like to suggest a topic for discussion! 