Figure 2.39 shows viscous incompressible fluid between three plates. Plates (a) and (b) are stagnant, while plate (c) moves downward with constant velocity V. Due to the movement of plate (c), the...

Figure 2.39 shows viscous incompressible fluid between three plates. Plates (a) and (b) are stagnant, while plate (c) moves downward with constant velocity V. Due to the movement of plate (c), the fluid is subject to flow. There is a parabolic distribution of the velocity component in the x-direction, and it vanishes at plates (a) and (c).

(a) Determine the expressions for the velocity components in the flow= domain when the distance between plates (a) and (c) is h.

(b) Determine the expression for the stream function in the domain.

(c) Calculate the variation of the discharge flowing between plates (a) and (c) as a function of time and x-coordinate.