You are working for a glider manufacturer and have been asked to analyse the laminar boundary layer at a certain point on the smooth wing. The velocity profile at this point, u(y), is given by: us 3 3³ (²) ² − ² (²) ²³ + +A ¹ (²5). + B where 8 is the boundary-layer thickness and us is the velocity at the edge of the boundary layer. A and B are constants.

Is Bernoulli equation valid only for rotational flows or it is also valid for irrotational flow? Explain your answer.

A pitot tube is a simple device used to experimentally determine the velocity of a flow, see the figure below. U, ليا و السهر To manometer (b) d D > 1 P01 -P02 (c) (a) FIG. 6.4 Pitot probes. (a) Simple pitot tube; (b) front view of tube with flattened open- ing for boundary-layer work; (c) pitot probe in supersonic flow. = For a supersonic flow, determine an analytic relation for the ratio poz/p1 = f(M) that will allow you to find the incoming Mach number.

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(a) Use the y-momentum equation to show that the pressure gradient across the boundary layer is approximately zero i.e. = 0 . Assume the boundary layer to be a two-dimensional ду steady and incompressible flow. Neglect gravitational forces. State clearly all assumptions made. Use the Bernoulli's equation to prove that the pressure difference is given by (b) P2-P1 = -4pU? for a fluid with constant density p flowing from point 1 to point 2 where pi, U1, A1 are the pressure, velocity and flow cross-section area at point 1 and p2, U2, A2 are the pressure, velocity and flow cross-section area at point 2 respectively. The ratio of the cross-section area A1 = 3.

Consider an airflow over the surface of a flat plate with a temperature Ts = 220 °C. At a certain point from the origin, the temperature profile of the airflow is given by the following y function: q/A As, Ts dA, T(y) = T, - (T. - T)exp afuido The airflow at atmospheric pressure has a free flow velocity u = 0,08 m/s and a temperature T, = 20°C. The thermal diffusivity of the fluid is afluid = 3,65E-05 m?/s and its fluid thermal conductivity Aquid = 0,0329 W/(m K). For the position that corresponds to the temperature profile above, 1. Determine the heat flux over the surface of the plate. 2. Determine the convection coefficient of the airflow.

In what way is the Euler equation an approximation of the Navier–Stokes equation? Where in a flow field is the Euler equation an appropriate approximation?

In this era of expensive fossil fuels, many alternativeshave been pursued. One idea from SkySails, Inc., shownin Fig.  is the assisted propulsion of a ship by a largetethered kite. The tow force of the kite assists the ship’spropeller and is said to reduce annual fuel consumptionby 10–35 percent. For a typical example, let the ship be120 m long, with a wetted area of 2800 m2. The kite areais 330 m2 and has a force coefficient of 0.8. The kite cablemakes an angle of 258 with the horizontal. Let Vwind =30 mi/h. Neglect ship wave drag. Estimate the ship speed(a) due to the kite only and (b) if the propeller delivers1250 hp to the water. [Hint: The kite sees the relativevelocity of the wind.]

Question 4: (10) Marks a) What is boundary layer separation? What are forces acting on it and effect of pressure gradient in the direction of flow? b) What are methods of controlling separation of boundary layer?

The air-cushion vehicle in Fig.  brings in sea-levelstandard air through a fan and discharges it at high velocitythrough an annular skirt of 3-cm clearance. If the vehicleweighs 50 kN, estimate ( a ) the required airflow rate and( b ) the fan power in kW.