The following formulas are commonly used by engineers to predict the lift and drag of an airfoil: where L and Dare the lift and drag forces, V is the airspeed, S is the wing span,  is the air density, and CL and CD are the lift and drag coefficients. Both CL

01: The drag force (F) of an aircraft during flight depends upon the length of aircraft flow velocity air viscosity density p. and bulk modulus of air K. (1) Derive the relationship between the above variables and the drag force by using Buckingham's II theorem . (2) Explain the physical meaning of the obtained dimensionless groups .

2. Casson model was discussed in class in the context of blood rheology. This phenomenological model is often used to describe the shear stress vs. shear rate relationship in colloidal suspensions where particle aggregation might cause the measured viscosity to increase at low shear rates. In an experiment, data for the shear stress and the applied shear rate S were fitted to the Casson model written below (in a slightly different form compared to that given in the lecture notes): √t = √²₁+√as. (1) The best least square fit parameters to the experimental data were found to be 40 mPa for the yield stress to and 2.5 mPa s for the parameter a, which is referred to as the plastic viscosity. a. Using Eq. (1), derive an expression for the fluid viscosity u as a function of S. b. Plot the viscosity of the fluid as a function of S for 0.1s¹ ≤S≤ 10 s¹. c. Based on class discussion on fluid classification, how would you characterize this fluid?

The following equation may be used to estimate the take-off ground run for an aircraft: Equation has been attached as an image. Calculate the take-off ground run, from a runway at ISA-SL conditions, for a twin engine aircraft for which the following data may be assumed Aircraft lift-off speed 155 knots Max take-off gross weight 220 tonnes Wing planform area (S) 358 m Wing CL (t/o flaps deployed, a = 0) 1.1 Wing span 53.18 m Oswald efficiency factor, e 0.7 KGE = CD(IGE) / Co(OGE) 0.4 Co sum (fuselage, wing, tailplane and nacelle) 0.015 Co for undercarriage 0.021 Co for flaps at taking-off setting 0.0073 Coefficient of rolling friction, u 0.02 Engine thrust (assumed constant) 310 kN per engine It may be assumed that 1knot = 0.51444 m/s   It may be assumed that 1knot = 0.51444 m/s

Convert the following using the conversion table attached.

In a supersonic flow, the force on a body, F, depends on the length of the body, L, its diameter, D, flow velocity, V, fluid density, p, and bulk modulus of elasticity, E. Derive an expression for force, F, using Buckingham Pi theorem. If a model is being constructed with a model to prototype ratio of 1:10, what would be the velocity ratio of model to prototype? (Ambient fluid for both model and prototype is air)

20 4. An airship is to operate at 20 m/s in air at standard conditions (p 1.225 kg/m³, p 101,300 Pa). A model is constructed to scale and tested in a variable-pressure wind tunnel at the same air temperature to = determine the drag. GOOD YEAR The Goodyear Blimp is an example of an airship. (a) What criterion should be used to determine dynamic similarity? (You may assume that roughness is not important for this problem.) (b) If the model is tested at 20 m/s, what pressure should be used in the wind tunnel? (c) If the model drag force is found to be 250 N, what will be the drag of the full-scale airship?

An airplane wing model is designed with a similarity test. the sustaining force is a function of speed, chord, density, viscosity, speed of sound and angle of attack. determine the dimensionless numbers

L. y X VA A VB PLANE OF CONTACT BY UBC Engineering On an air hockey table, two pucks of identical mass collide in the middle of the rink. Puck A had an initial m velocity vA 1.9? and puck B had an initial velocity vB = 3.2j The plane of contact can be thought of as a line angled 0 = 34° above the x-axis. If the coefficient of 0.5 between the pucks, what are the velocities of the pucks after the impact? || m according to the x-y axis shown. restitution is e =

8.1. An airplane wing of 3 m chord length moves through still air at 15°C and 101.3 kPa at a speed of 320 km/h. A !:20 scale model of this wing is placed in a wind tunnel, and dynamic similarity between model and prototype is desired. (a) What velocity is necessary in a tunnel where the air has the same pressure and temperature as that in flight? (b) What velocity is necessary in a variable-density wind tunnel where absolute pressure is 1 400 kPa and temperature is 15°C? (c) At what speed must the model move through water (15°C) for dynamic similarity?