# Bernoulli Equation for isentropic ideal gas flow

If one derives the Bernoulli Equation for the isentropic ideal gas flow you get:

$$\frac{1}{2}v^2 + g z + \left(\frac{\kappa}{\kappa -1} \right) \frac{p}{\rho} = const.$$

Two questions:

1. Is isentropic equivalent to frictionless?

2. If the temperature stays the same during the process the quotient of pressure and density stays the same? This would lead to the very easy formula for the velocity at $t_2$. $$v_2=\sqrt{v_1^2-gz}$$

2. Nearly, it is $v_2 = \sqrt{v_1^2 - 2g \Delta z}$. But note, that constant temperature does not necessarily imply isentropicity.