QUESTION 2 - 12 MARKS Answer in the space provided - test booklets are available if necessary. A flat photographic film is being pulled out of a liquid bath at a velocity U at an angle away from the horizontal. A steady flow of liquid with a constant thickness is also drawn out of the bath by the film. The width of this film is very long in the z-direction (normal to the plane of the diagram) such that there is no fluid velocity in this direction and the edge effects can be ignored. The flow is fully developed in the y-direction and because everywhere above the liquid the pressure is equal to atmospheric pressure, there is no pressure gradient in the y-direction. Finally, the amount of liquid being pulled up by the film is the same as that falling back by gravity. a. List the appropriate equations for the components of the gravitational vector (gx,gy,gz) in terms of the gravitational constant (g) and the angle . (3 marks) b. Simplify the Navier-Stokes equations (given below for x& y directions - you can disregard the z direction) to yield the governing equation(s) of motion. (4 marks) (tvx+vxxvx+vyyvx+vzzvx)=xP+[x22vx+y22vx+z22vx]+gx(tvy+vxxvy+vyyvy+vzzvy)=yP+[x22vy+y22vy+z22vy]+gy c. List the appropriate boundary conditions that are needed to solve for the velocity flow field. (2 marks) d. Make a neat sketch of the expected form of the velocity profile - REMEMBER that 'the amount of liquid being pulled up by the film is the same as that falling back by gravity