Flow.Consider the flow with velocity vector v=yi. Show that this flow is incompressible.Show that the particles that at time t=0 are in the cube bounded by the planes.x=0, x=1, y=0, y=1, z=0, z=1 occupy at t=1 the volume 1

Q1: The volume flow rate (Q) over a rectangular duct depends on the head H over the đuct, acceleration due to gravity g. length of duct L, height of the duct Z and the kinematic viscosity v of the liquid. (1) Derive the relationship between the above variables and the volume flow rate by using Buckingham's I-theorem. (2) Explain the physical meaning of the obtained dimensionless groups.

Section 4.3 and 4.4 Control Volume and System Representations and the Reynolds Transport Theorem 4.32 Water flows through a duct of square cross section as shown in Fig. P4.32 with a constant, uniform velocity of V = 20 m/s. Consider fluid particles that lie along line A-B at time t = 0. De- termine the position of these particles, denoted by line A'-B', when t = 0.20 s. Use the volume of fluid in the region between lines A-B and A'-B' to determine the flowrate in the duct. Re- peat the problem for fluid particles originally along line C-D and along line E-F. Compare your three answers. V - 20 m/s B B' A A' C C FIGURE P4.32 D 45° E 0.5 m

Consider a fluid of viscosity μ between two circular parallel plates radie 'R' separated by a distance h upper plate is rotated at an angular velocity w where as bottom plate is held stationary. The velocity profile between two plate is linear. The torque experienced by the bottom. plate is?