Bernoulli and the Energy Equation

Bernoulli and the Energy Equation

1. Bernoulli's Equation related the pressure head, velocity head, and elevation head at one point to the pressure head, velocity head, and elevation head at another point in a system.

   • However, this does not help much for real life problems; the energy equation is more useful and stems from the Bernoulli Equation

2. The Energy Equation is similar to Bernoulli's Equation. It related two points by their pressure, velocity, and elevation head. However, the energy equation also accounts more pumps, turbines, and minor losses, such as bends, contractions, expansions, friction, etc.

   • • You can see the similarities to Bernoulli!!!
     • Note: In this class, we assume flow is turbulent, so alpha = 1.0
   • To find the pump head, you use the following:
   • To find turbine head you use the following:
     • • Most of the time you will be told what these are (for PEGN 251)
   • One of the new additions is head losses, hl. This includes hm, minor losses, and hf, friction losses
     • Minor losses include bends, contractions, expansions, etc.
       • • K is the minor loss coefficient; these are found on charts given or found in the book.
     • Friction losses are due to fluids moving in pipes. It is affected by the length, diameter, and roughness of the pipe, as well as how fast the fluid id moving.
       • • Friction losses are also affected by f, the friction coefficient. This is found by using a Moody Diagram, but first you need the Reynolds Number and the equivalent roughness
           • • Reference [1] McFarland, Michael J. "Appendix F: Minor Losses in Pipes and Appurtenances." On GlobalSpec. IHS, Web. 29 Apr. 2014.
             • Figure 1: A moody diagram that can be used to determine f.
           • The equivalent roughness is found by charts given or found in the book.

3. Assumptions you must have in order to use these equations:

   • a. flow is steady
   • b. the fluid density is the same throughout all spatial locations
   • c. the system you are looking at is a controlled volume with only one inlet and one exit port.

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