Transport terms neglected
 

I have heard that in the equation for mechanical energy, it is known from experiments that the transport terms can be neglected.

I would like to understand why, by fail to identify the transport terms. What are these transport terms also called, and how do they look/what are they?

Re: Transport terms neglected
 

Maybe I should elaporate a bit:

I have heard that in the equation for mechanical energy (derived from NS eq. by multiplying NS with velocity), it is known from experiments that the transport terms can be neglected.

I would like to understand why, but fail to identify the transport terms, i.e. I have difficulties in identification of the terms in the equation. What are these transport terms also called (so I can compare with my text books and thereby identifying all the terms), and how do they look (if you could write the transport term for me, please)/what are they (again a help to me for identifying the terms in the mechnical energy equation)?

Re: Transport terms neglected
 

If the differential linear momemtum equation is written as

d/dt(rho vec_V) + div dot (rho vec_V)

= - grad(p) + div dot tensor_tau + rho F_body

where

vec_V = velocity vector

tensor_tau = viscous stress tensor

Then the mechanical energy equation is typically obtained by taking the dot product of above vector equation with the velocity vector vec_V to obtain the scalar equation

d/dt(rho V^2/2) + div dot (rho V^2/2)

= -vec_V dot grad(p) + vec_V dot (div dot tensor_tau) + rho F_body dot vec_V

where the 2nd term on right-hand-side containing the viscous stress tensor would represent the work done by viscous forces to increase the fluid kinetic energy.