# Bernoulli Equation, Energy Balance, and Stagnation Temperature

1. May 9, 2012

### Red_CCF

Hi

I was trying to derive the equation h0 = h + v^2/2, which is the definition of the stagnation temperature and I ran into a conceptual problem. I set up a control volume where fluid with velocity v and enthalpy h enters and fluid with v = 0 and enthalpy h0 exits. Using the general energy balance Q + W = ΔEcv + ΔH + ΔKE + ΔPE, and the assumptions that the process is adiabatic/isentropic, no work, steady state, and negligible PE change (from http://en.wikipedia.org/wiki/Stagnation_temperature), I was able to get to the above equation by cancelling things out.

I did something similar using a modified Bernoulli equation, which is the same as the ideal Bernoulli equation with a a loss term where loss = u2-u1-qin where u is specific internal energy of incoming/exiting flow and added to the exiting flow. This also yielded the above equation.

My question is, when I used the ideal bernoulli equation without a head loss term, I do not get the enthalpy term. I only get P0 = P + density*V^2/2 and since uin does not equal uout, I can't add it to get h0 and h. Does this mean that the ideal bernoulli equation inherently assume that the internal energy of the inlet and exit are the same?

Also, I'm wondering what work means in fluid flow; how do I do work on a fluid? How come a turbine can do work but a nozzle can't?

Thanks

Last edited: May 10, 2012