First law over constricting pipe section
So i am trying to get a sense of the change in internal energy for a fluid that flows through a constricting pipe ($\displaystyle d_{out}<d_{in}$). Bernouilli won't do since the flow is turbulent, hence it contains irreversibilities which will affect the internal energy.
First law:
$\displaystyle U_{in} + \frac{p_{in}}{\rho}+\frac{u_{in}^2}{2} = U_{out} + \frac{p_{out}}{\rho}+\frac{u_{out}^2}{2}$
$\displaystyle \dot{m}$ remains constant, so using conservation of mass combined with the diameters yields $\displaystyle u_{in}$ and $\displaystyle u_{out}$.
Furthermore, I assume that the system is adiabatic and isolated. $\displaystyle \rho$ is assumed remain constant.
I am looking to get a value for $\displaystyle p_{out}$ and $\displaystyle U_{out}$, two unknowns from one equation...
Am I overlooking another equation? Or how am I to solve this.
thanks in advance!
