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#1 |
New Member
Join Date: Jul 2009
Location: near Marseille, France
Posts: 7
Rep Power: 17 ![]() |
Hello
I'd like to calculate the pressure variation between the inlet and the outlet of a heating channel. The causes of this variation are well known : - Friction, because of viscosity and turbulence : IRREVERSIBLE - Fluid Acceleration, either because of density change (heating for instance!) or because of cross section change : REVERSIBLE - Gravity, if z coordinate changes : REVERSIBLE Now I want to give an expression for these different components, but my two methods are not in agreement... 1) First Method: 1D Navier-Stokes 1D Momentum equation: ![]() ![]() From which we define: ![]() where ![]() It comes: ![]() Then integration of a small portion of my channel gives: ![]() - When density is constant (no heating) and cross section varies: First term is zero, so that leaves us with ![]() - When density changes but cross section is constant: G is also constant so that both terms are finally equal, and we obtain for the pressure drop ![]() 2) Second Method: Generalized Bernoulli's law Let's define hydraulic head, which represents the energy necessary to the fluid motion through piping: ![]() Generalized Bernoulli's law yields in: ![]() We recognize: a) ![]() b) ![]() But then, what is ![]() CONCLUSION: My opinion is that Bernoulli's law is applicable only for incompressible flows. Yet, when the fluid is heated, ![]() Do you see any mistake in my formulas or reasoning? Thank you for reading me. Jérôme |
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