(Book: 5.9)
The energy equation in words: the change of energy of a material region is the net work done on the region and heat added to the region.
Lagrangian formulation:
|
(15) |
Note: we will account for gravity as an external force doing work, rather than including gravitational potential energy in the energy.
An expression for the heat flowing in was given in the previous section (with a minus sign, since the previous section gave outflow instead of inflow.)
Work done per unit time equals force times velocity, or to be precise, the scalar product of the velocity and force vectors. The total work on the fluid region is therefor:
 |
(16) |
For an inviscid fluid, and in vector notation, this simplifies to:
 |
(17) |