Aula Teórica 17 Equação de Evolução da Energia Mecânica

Equação de Transporte de Energia Cinética Forma da Equação: Termo de Conversão de energia Mecânica em Energia interna (Calor)

Transport equation fo kinetic Energy Aimed rate of change: It can be obtained using other equations: Dissipation term. Conversion of mechanical energy into internal energy

How is mechanical energy dissipated? Shear stress has the same value on both sides of the surface sides. The work done is not the same because the velocity is not the same. The difference of work is the energy dissipated. In fact the work done on the side where velocity is higher is negative thus the difference between both sides is always negative. One can say that energy is dissipated wherever there is a velocity gradient and is maximum where that gradient is higher and not necessarily over a solid surface. τ τ ∆u

Injector pump The figure represents schematically the flow of air in a injector pump. The jet entrains surrounding air creating a pressure low that pumps the atmospheric air into the pipe. Assuming that the air enters intro the pipe at 5 m/s and the jet velocity is 30 m/s and that the pipes’ diameters are 20 e 40 mm: Where is the region of maximum shear stress ? If the entrance profile was exactly how is show in the figure, what would be the maximum shear stress? Draw a more realistic velocity profile and the corresponding shear stress profile. Compute the fluxes of (i) volume (ii) momentum, (iii) kinetic energy at the entrance section and in the section where the profile is fully developed. Compute the pressure at the entrance section assuming that viscous effects are negligible Compute the pressure in the section where the profile is fully developed assuming that the average shear along the wall is 0.05N/m 2 and that it is 1 m apart from the other section. Draw the stream lines that are passim by points A (axis) and B taking into attention the distances to the wall and to the center line. How thus the convective term vary along those lines? A B

Flow entering into a pipe