Water flows at a velocity of 1.2 m/s over a flat plate 1.2 m long. Assume 1/7th power law and determine the boundary layer thickness and displacement thickness. Compare the values with values calculated using laminar flow correlations. v = 1 x 10-6m²/s.

An incompressible viscous flow is contained between two parallel plates separated from each other by distance b. as shown in Figure 1. The flow is caused by the movement of the upper plate which has a velocity U, while the bottom plate is fixed. If U =7 m/s and b= 1 cm, and there is no pressure gradient in the flow direction. A.) Start with Navier-Stokes equations and determine the velocity at the point x = 3 cm and y= 0.41 cm. The value of the velocity is.B.) Calculate the magnitude of the vorticity at the same point. The magnitude value of vorticity. C.) Calculate the rate of angular deformation at the same point. The angular deformation value

(a) A wing section with a chord of c and a span of b is mounted at zero angle of attack in a wind tunnel. A pitot probe is used to measure the velocity profile in the viscous region downstream of the wing section as shown in the figure. The measured velocity profile is u(z) = U∞ - (U/2) cos[TZ/(2w)] for -w ≤ z ≤w. Here, w = 0.02c. Assuming a constant pressure p = po along the streamlines (dashed lines in the figure) and across the wake where the velocity was measured, calculate the friction drag coefficient Cp, of the wing section. U Streamlines u = U_ -- cos 22 2W² +w Viscous wake = -W (b) Consider a thin flat plate at zero angle of attack in an airflow at P∞ = 1.225 kg/m³, T∞ = 288 K and μ∞ 1.7894 x 10-5 kg/m/s. The length of the plate is 2 m and the span is 0.5 m. Assume the boundary layers on the plate are laminar throughout (on the upper and lower surfaces both) where LBL(x)/x = 0.664/√√/Rex applies. The freestream velocity is 100 m/s. Calculate the friction drag (Df) of the first…

A simple parallel flow with constant velocity shear σ is given byu = σy v = w = 0 Evaluate the five components of motion (e.g. translation, divergence, vorticity,shearing and stretching deformation.)

Rain water is flowing through an inclined plane under gravity as shown in figure. A thin layer of thickness h is formed over the plate. An upward wind flow that exerts a shear stress on the upper surface (y = h) of the liquid layer. The wind flow tends to push the rain layer upward while gravity pulls the layer downward Write continuity and and Navier-Stokes equations to model this flow field. (Assume the flow is fully developed) Obtain expressions for the liquid velocity profile, the shear stress distribution, the volume flow rate, and the the expression for the thickness h of the liquid layer for which there is no net volume flow along the roof

Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.