Question

Advanced Fluid Mechanics

For an inviscid fluid we have Euler's equation (vectors are denoted by bold characters) )= Vp - Vgx + V xu at and whether or not the fluid is incompressible, we also have the conservation of mass Dp +pv u 0. Dt Show that x Vp Dt Deduce that, if p is a function of palone, the vorticity equation is exactly as in the incompressible, constant density case, except that ois replaced by ap.

Answer 1

Auweys Page 0 Given LVP-y t D.S 2 DE From equalion (1) +WXut botherdes by dhidiny 1 Cwru) Du then Now, from aguation 2 -V.u DS -) Dt both sides Swfagrating

Noc from euation Pagel DE pt f Taking w.7 SO Dt SAX . Jaxfi)as tHonce proved ela