Bernoullis Equation for Gases

Bernoulli s equation, as we have written it, is exactly correct for constant-density fluids and practically correct for all flows in which the density changes are unimportant. For liquids this includes almost all steady flows. We show here that it also is practically correct for low-velocity gas flows. 

Example 5.1. The tank in Fig. 5.4 is full of air at 70°F, The air is flowing put at a steady rate through a smooth, frictionless nozzle to the local atmosphere. What is the flow velocity for various tank pressures  

At point 1 the velocity is negligible, and, as discussed in Sec, 5.5, the pressure at point 2 is equal to the local atmospheric pressure, if the flow is subsonic. Making these insertions in Bernoulli s equation, we find 

Which value of the density should we use here It is obviously different at the two states, because the pressure is not the same at the two states. However, if the pressure chang e is small, the two densities will be practically the same. Let us use the upstream density (but see Prob, 5.5). This is given by substituting the perfect-gas law p = MPJ RT ) into Eq. 5,16  

Using this equation, we can calculate V2 for various values of Pj. For example, if P, is Pgtjjj + 0.01 Ibf/in, then 

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