# PE Thermal & Fluid Sys: Energy Equation



## Minipett (Mar 20, 2021)

Morning, I need major help!!! Preping for PE Thermal & Fluid Sys exam for AUG 2021. Using the MERM for the CBT edition (latest one). I will not go into how much I hate the amount of errors I am finding in this book.

I need help understanding when and why to use the different "Mechanical Energy Equations in terms of Energy per Unit Mass, Volume, and Weight" Sec. 9.6 in the NCEES reference manual v1.2 (latest at this post date).

Going through problems in the MERM Practice Book and they use these equations to solve problems but are bouncing from "per Unit Mass" for one solution and the next use "per Unit Weight"?

Any feedback would help. PS: Why are these equations in HVAC section? They could've at least repeated in Fluids.


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## Slay the P.E. (Mar 20, 2021)

Minipett said:


> Morning, I need major help!!! Preping for PE Thermal & Fluid Sys exam for AUG 2021. Using the MERM for the CBT edition (latest one). I will not go into how much I hate the amount of errors I am finding in this book.
> 
> I need help understanding when and why to use the different "Mechanical Energy Equations in terms of Energy per Unit Mass, Volume, and Weight" Sec. 9.6 in the NCEES reference manual v1.2 (latest at this post date).
> 
> ...



Typically in hydraulics/incompressible fluids problems one would use the so-called "Extended Bernoulli Equation" with terms of energy per unit weight, so that the terms have dimensions of length (dynamic head, elevation head, pressure head, pump head, friction head loss, minor head losses, etc). 

It's really the same thing, though. The energy equation per unit mass (page 483, section 9.6.1) is the first law of thermodynamics for a control volume with one inlet and one outlet and an incompressible fluid. In thermo, we typically work per unit mass, so that's why that equation is presented in that form. From there, you take that equation and divide by gravity, g, to obtain the form per unit weight, which is what hydraulics/civil engineers typically use.

The conclusion is that per unit weight or per unit mass, it shouldn't matter as its all the same thing (for incompressible liquids).


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## Minipett (Mar 22, 2021)

Thanks for the clarification. I am going to work these units to get an understanding.


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