Question 2 a) A laminar boundary layer profile may be assumed to be approximately of the form u/Ue = f (n)=f(y/8) i) Use an integral analysis with the following two-segment velocity profile, ƒ (n)=(n/6)(10–3n−n³), for 0≤n≤0.293 and ƒ (n) = sin(лn/2) for 0.293≤ŋ≤1, to find expressions for the displacement thickness &*, the momentum thickness 0, the shape factor H, the skin-friction coefficient of, and the drag coefficient CD. ii) Derive an expression for the velocity normal to the stream wise direction given that, u/U₂ = f(n). iii) Hence obtain the velocity normal to the stream wise direction for the above two- segment velocity profile.

A fighter aircraft is to operate at 200 m/s in air at standard conditions ( = 1.2 kg/m3). Amodel is constructed to 1/20 scale (length ratio) and tested in a wind tunnel at the sameair temperature (same air viscosity) to determine the drag force. The drag force FD is afunction of the air density  and viscosity , the velocity V and the cross section length ofthe airplane D.

e. b. C. d. a. EME3026 Question 2 A dimensionless velocity profile, u* = u/U = Co + C₁-C₂y, where, y = y/8, is proposed to approximate the laminar boundary layer solution for flow around a corner. The outer flow velocity can be expressed as, U = C²x, where, C, is constant. Boundary layer has the thickness of, 8, where, Co. C₁, and C₂, are the constants to be determined in order to match the boundary conditions in the boundary layer, including the no slip condition, match the outer flow velocity and zero shear stress at the edge of the boundary layer. Apart from that, an additional boundary condition is proposed. a²u dyz y=0 Given the fluid kinematic viscosity, v = 1.46 x 10-5 m²/s and the constant, C² = 0.09 s-¹. Validate the proposed additional boundary condition. FLUID DYNAMICS U (dU Find the velocity profile, u", by evaluating the constant, Co, C₁, and C₂. = --- Determine the displacement thickness and momentum thickness in term of boundary layer thickness. Show that the general…

A model of the Airbus 320 is tested in a wind tunnel using air at standard conditions. If the tunnel airspeed is 50m/s, calculate the water speed if the same model is to be tested in a water tunnel atdynamically similar conditions. Take mair=1.73 x 10-5Pa.s, mwater=10-3Pa.s, rair=1.225kg/m3 andrwater=1000 kg/m3.

(b) A Formula 1 team tests their car in a wind tunnel at a scale of 50%, at a speed of Vwinarunnet = 50 m/s. The measured downforce at this speed is Foownforce.WT = 3000 N and the model reference area is Aref wT = 0.5 m?. 1. Find the downforce magnitude on the full-scale race car at the same Reynolds number. Assume constant air density p = 1.2 kg/m. II. It is said that F1 cars could travel upside down, as shown below. At what speed should the full-scale car travel to achieve this, if its mass is m = 740 kg? The acceleration of gravity is g = 9.81 m/s?. Downforce Weight

Q1, ): A particular laminar boundary layer velocity profile is given by 2 и(у) = 1+ A Um 서-() y Where y denotes the distance from the center of the channel. a) Determine the expression for the shear stress T(y) as a function of y and other given parameters assuming that d and Um are constant. Find the value of A from table 1 at the end of the questions. b) If A = 0, find the shear stress value at the center of the channel (i.e., at y = 0).

the appropriate characteristic length and velocity scales for B.L. analysis are L and u., respectively. This gives x y = ²₁ y² = ²₁ I' y* L x* = U∞o du* L Əx* ?u* əx* u* = + Rearranging and substituting into conservation of mass yields du əv ə(u*u…) ð (v*ux) + + =0-> ?х ду a(x*L) a(v*L) U U oo Uoo dv* L Əy* } = 0 dv* + = 0 Əy* v* = = 0 v U oo Replicate this process for conservation of momentum and energy to derive the dimensionless B.L. equations.

(a) You would like to measure wind speed with a cup anemometer on a sailboat trip across the Atlantic Ocean. The measure of the rotational speed of the axle of the device has a precision of +/-0.2 rotations/s and was calibrated in a steady wind-tunnel flow at 20m/s with 10 rotations/s. Define for the below-given situations, 1 to 4, the type of error (random or systematic) and explain how to overcome or reduce this error. 1 Bearing of the axle is old 2 Turbulent flow 3 Icing on the cups 4 Strong tumbling of the sailboat You would like to use it for a measure of the in-cabin air flow a quiet environment. Discuss why the measurement system is not well posed for this purpose.

A 5 m of ship model is towed in the water of kinemetic viscosity 1x10^-6 m^2/s at 3.5 m/s. The wetted hull area is 1.4 m^2. What i_s the skin fric_tion drang

A- Womersley number (a) of a human aorta is 20 and for the rabbit aorta is 17, the blood density is approximately the same across the species. The values of viscosity were 0.0035 Ns/m² for the human and 0.0040 Ns/m² for the rabbit. The diameter of the aorta is 2.0 cm for the man, and 0.7 cm for the rabbit, estimate the heart rate beats per minute (bpm) for both species