Question

Question 1 1.1 If the velocity distribution of a fluid flowing over a 1m² flat plate is given by u=l+ y + y, find the m. Assume dynamic viscosity to be y=6x10*(Ns/m”). force acting on a plate at y = [5 marks] 1.2 A 2D velocity field in an incompressible flow was measured by PIV method and determined to follow the following functions u= 2x’ +2y and v=x - 4y. Check whether your measurements are correct at a point x = m based on conservation of mass. [5 marks] 1.3 Explain the difference between rotational and irrotational flow. [3 marks] 1.4 Reynolds number Re, is a measure of the relative strengths of two different forces; what are these forces? For flow in a pipe, if the inlet velocity is doubled, using Re definition, explain what happens to the Re and why. For the same forced convection experiment, what can you say about the Re of a turbulent flow when compared with the Re of a laminar flow? [6 marks] 1.5 Experiment has been conducted to measure the drag coefficient of a cylinder and a sphere and experimental results are summarised in the figure below. Find the drag coefficients of a sphere (whose diameter, Ds, is meter) and a cylinder (whose diameter, Dc, is meter and length, L, is meter) when they are flying in the air at the speed of V = m/s. Assume there is no wind. Given that the dynamic viscosity of air is 1.81 x 10-5 kg/(m.s) and the kinematic viscosity of air is 1.48 x 105 m² /s. [6 marks] 102 TO 24/Re Cylinder Co Sphere 10- Effect of roughness 10-2 10-1 10 103 102 Re 104 105 106 [Total 25 marks] (Turn Over) Page 2 of 6

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Answer 1

o u=1492+1 Eau du dy du O+29+1 -2771 dy fa = 2XA A.2142 F = M(24+1) = 6x10 (25+1 fa :0006(24+1) Newton 2 u=2x24292 vane_uy 2 for How to be incompressisle du . o antar d 41–4= 거의 1M

3 VX Vzo for Ire-tational flow And XV to for Rotational frow a Da Ito 3 + 2 x2 on z Rea 으 Puertia force riscons force fv Res VD If u'zar Réa 2 Re se case Rear (Redgursne way fow (Res griner for exemple for flow in pipe (R) Lama 2000 (Res+24000