QUESTION 1 [50 Marks] PART A (25 Marks) The mass conservation equation is given as: op (pu) (pv) (pw) = 0 + t + ax by + z (1) (i) Rewrite equation (1) using the material (substantial) derivative D/Dt and comment on the differences between Dp/Dt and op/t. [4 Marks] (ii) For an incompressible flow, simplify equation (1). What physical description of the flow can be concluded based on the simplified equation? [2 Marks] (iii) Consider an incompressible steady flow with constant fluid properties. The velocity components are given by: u(y)=y =(-1) (2) v=w=0 If U, hand-op/ax are constants, p=p(x) and the body force are neglected, does u(y) satisfy the Navier- Stokes equations given below? du du du +V +w |== +4 Oz + ax dx dy + Ov ov dv +v +w. ax =- + + + Ow Ow Ow www u +v +w + + Oz z Hint: You should substitute the velocity components in the above equations. [7 Marks]