If you learn only three things from your Fluid Mechanics class

I’m going to get it out in the open right now… I got a C in Fluid Mechanics. But in my own defense, it was from the University of Illinois where competition was fierce as it came from other planets. So a C wasn’t that bad on a broader scale. It was a 4-hour course and its lab looked like something out of an old Batman movie. Cool but creepy.

I hated that class and would have never dreamed I would be making a living from what I learned there. As they say, we learn from mistakes and based on that theory, I learned a lot about fluid mechanics. With over 20 years of wrestling with it, I have this advice for anyone coming out of college with a BSCE. If you learn only three things from your Fluid Mechanics class:

1. The Continuity Equation

Continuity Equation

Where:

Q = Flow (cfs)
V = Velocity (ft/s)
A = Cross-sectional area of flow (sqft)

This nifty little equation stands tall as it will never fail you. You will find it most handy when designing or analyzing storm sewers or open channels.

In my previous Hydraflow years a day rarely passed without a tech support call regarding the velocity in a storm sewer pipe. “According to Manning’s equation the velocity should be this much and my reports say that much. What gives?” the confused user would say. And of course my standard reply involved yet another lesson on the continuity equation.

Know this: No matter what, Manning’s, Shmanning’s, velocity always equals the flow divided by cross-sectional area. I’d ask them to look at the actual cross-sectional area. Divide Q by that and viola… the correct velocity. If this happens to you, it’s the Area not Velocity you should be questioning.

The continuity equation is also the basis behind the Storage Indication method used in pond routing. You see, Q is energy and energy is always conserved. You cannot create it nor destroy it. If Q goes into one end of a pipe for example, rest assured, it’s coming out the other end. Different combination of V and A perhaps, but the same Q. Consider a detention pond. The Q that enters the pond minus the Q exiting the pond is what is left over in the pond. Yup, the pond will rise at a velocity equal to that leftover Q divided by the pond’s wet contour area at that Q. In other words, V1A1 = V2A2 + V3A3.

2. The Energy equation

It’s the granddaddy of all H&H equations. There’s so much you can do with the energy equation it’s mind boggling and to explain it in its entirety is way beyond the scope of this post. But for now, let’s stick to H&H for civil engineers. Orifice equations, weir equations, Bernoulli equation, etc, all derive from the energy equation. From physics we learned that the energy, E1 at point 1 always equals the energy at point 2, E2. And that energy is made up of two parts, potential and kinetic.

Energy Equation

In our world, potential energy is elevation head in feet (Y) and kinetic energy is V2/2g.

Energy EquationHere’s an example. Let’s say you are modeling a storm sewer pipe. It’s downstream end is suspended about 5 feet from the ground and is a free outfall. You need to find the velocity of flow when it hits the ground to aid in dissipater design. Let’s call Point 1 the upstream end where kinetic energy is zero and potential energy is 5.  Point 2, the bottom, is 5 feet below so potential energy is zero. We just need to solve for kinetic energy at the bottom. If E1 = E2;

Practice using this energy equation as often as you can, even in every-day problems, and you’ll become quite skillful. For example, it doesn’t always have to involve water. If a cat fell off a 50-foot high roof it would be travelling 57 ft/s or about 39 mph when it hit the ground. Ouch!

3. Manning’s Equation

Manning's Equation

Pretty much every civil engineer, even some structurals, have seen this equation a time or two and it doesn’t need much of an introduction or explanation. Surprisingly, my fluid mechanics text book only dedicated about a half-page to its description. This post would be incomplete without it however as many civils use it daily.

Manning’s equation is used primarily to determine head or energy loss due to friction implied by the n term, roughness coefficient. The A term is the actual cross-sectional area of flow. R is the hydraulic radius which is A divided by the wetted perimeter of that A. That’s easy enough.

What puzzles many engineers is the S term. S is the slope. Slope of what? It’s not the slope of the channel bed nor is it the slope of the pipe invert. It is the slope of the energy grade line (EGL)*. Choose any two points along an open channel for example. Add up the kinetic energy, (V2/2g) and the potential energy, (Y) at each point. That sum is the total energy at that point or EGL. S is the slope of the line between those two points. The difference between the two EGLs represents the loss of energy due to friction. It’s clever of course for storm sewer designers to set the pipe slope equal to S. That way the EGL runs parallel to the top of the pipe.

Isn’t it funny that this equation was named after someone who never took a fluid mechanics class? Irishman Robert Manning did not receive any education or formal training in fluid mechanics or engineering. He had an accounting background. Read Pulp Friction for a more in-depth article.

*Some restrictions apply. Flow is constant, steady, uniform and gradually varied. Flow depth is Normal. n is constant.

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