how to understand and explain specific energy

[pinkpig]

What’s the purpose of developing the term of specific energy for open channel flow? I understand specific energy is a component of the total energy by not taking account of the vertical distance from vertical datum to channel bottom. But I don’t see any advantage of using it. If we use the total energy (total head) we can apply the conservation of energy equation (Bernoulli) and we can develop EG line, and HG line and calculate head loss from Section A to Section B. But apparently the conservation of energy does not apply to specific energy. Unless you can ignore head loss or bed slope (normal uniform flow?), specific energy is not conserved at all. I would like to be educated on what advantages we have by using specific energy particularly in a real world where we cannot ignore head loss or bed slope. Furthermore, can anyone explain the physical meaning of specific energy and how it changes with the direction of flow (increase, decrease, keep constant).

 

[beej67]

It's long and complicated, and one of the major reasons why open channel flow is one of the most complex, and often unintuitive things in the entire field of hydraulics.

The very short version is that once you grind out all the math, a flow of a given specific energy can exist at two different depths, one subcritical (high depth low velocity) and one supercritical (low depth high velocity). Whether it exists at the first depth or the second depth is a function of what happens in and around the flow itself. This creates rapids, hydraulic jumps, choking, and all sorts of flow characteristics that need to be understood if you're going to avoid massive design failures. Learning enough of the math to get an intuitive feel for the Specific Energy Diagram is pretty important.

https://en.wikipedia.org/wiki/Energy–depth_relationship_in_a_rectangular_channel

You really can't explain it intuitively without getting into the math. Any open channel flow textbook will devote an entire chapter to this. My go-to is Sturm. Chapter 2.

Do some youtube searches for hydraulic jumps in flume experiments.

https://www.youtube.com/watch?v=VU7UEiO6ijA

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[beej67]

There are also a lot of very important aspects of the Froude number that you need to get an intuition about. Froude number, although it's derived from the specific energy relationship, is in fact an expression of the ratio of the velocity of a flow to that flow's wave celerity. Any disturbance (wave) in a supercritical flow (FR>1) gets swept downstream, and can't affect the surface of the water upstream, because the velocity is greater than the wave celerity. (similar to how you can't hear a supersonic airplane approach you.) A disturbance in a subcritical flow (FR<1) will cause a wave that propagates both downstream and upstream, therefore downstream obstructions can affect upstream depth. This is important for hydraulic jumps, but also for setting the boundary conditions for a gradually varied flow calculation, such as a flood study.

You're not going to learn what you need to know about this topic from a discussion forum, unfortunately. Nor, likely, from wikipedia. You're going to need a textbook at a minimum, or to audit a senior level civil engineering fluid mechs class.


Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[LincolnPE]

"This creates rapids, hydraulic jumps, choking, and all sorts of flow characteristics that need to be understood if you're going to avoid massive design failures."

This is not correct analysis and theory application. Energy is not conserved as the OP mentions. See the diagram below.

Momentum is however conserved on closed systems, and the principles of conservation of momentum (specific force, M-y diagrams) are used to analyze conjugate depths, mitigate "massive design failures" and provide for public safety.

Alternate depths (Specific energy) are essentially valid across energy conserving devices such as sluice gates.

 

[beej67]

Energy is not conserved as the OP mentions

I never said energy is conserved, I said that the specific energy relationship in open channels means that given a known flowrate and known specific energy, that flow can exist at two different depths.

As you can see, pinkpig, this is very complicated, and you're not going to learn everything you need to know from a discussion forum.

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[SMIAH]

What’s the purpose of developing the term of specific energy for open channel flow?

The concept of specific energy was introduced by Bakhmeteff in 1912.

I like this explanation:

For short reaches of channel, changes in specific energy related to the downstream decline in bed elevation or water-surface slope (both measured with respect to an external horizontal datum) are negligible compared to that related to local changes in depth and velocity. Thus we can adopt the bed itself as a datum, greatly simplifying the energy equation and allowing us to explore the relation between the velocity and depth heads.

 

[LincolnPE]

The specific energy curve is typically used as a design aid for prismatic channels. It shows the sequent depths for your design flow, and why we design a good factor of safety away from critical depth to eliminate unstable oscillation between the two depths.