1. Math
  2. Advanced Math
  3. 4 the velocity field in an unsteady moving fluid is...

Question: 4 the velocity field in an unsteady moving fluid is...

Question details

4 The velocity field in an unsteady moving fluid is given by V ui +vj+wk where u u(x, y,z,t),v (i) v(x,y,z,t) and w(x,y.z,t) By considering the density, ρ(x, y, z,t), an infinitesimal control volume, δν. in the fluid moving from a point (x1ふ,21) at time 11 to a point (X2,Y2,z) at time 12 then derive the substantial (or total) derivative of ρ and interpret the meanings of the first two terms on the right-hand side of this latter expression. (12 marks) (i) Given that the divergence of V is defined by au w 1 D(8V) -= lim then, by considering the mass of the moving control volume, δι_pSV derive the equation of continuity (that is, of mass conservation) for a compressible fluid and show that this can be rearranged in conservative form as (8 marks)

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution