Question 3 a) Neglecting freestream turbulence, the decelerating freestream velocity profile over a flat plate is given by, u = u₁ (1-x/L)", with L=10m. i) Estimate the point where the separation occurs, for n = 1,2,3,4. ii) Consider the case when n = 2 and estimate the momentum thickness at the separation point by the Walz-Thwaites's method. iii) Use Michel's method (after 1 iteration) to predict transition when u₁ = 10 m/s and obtain an equation for the location of the transition point, x,,. State the assumption that was made to obtain the result. iv) Is x,, upstream or downstream of the point where separation occurs? b) If uo is unknown, using Michel's formula for transition, find the value of u₁ = uo_col such that both separation and transition occur at the point of separation. (i.e. the two points are co-located.) When, u>0_col" state whether the transition point x, is upstream (towards the leading edge) or downstream (towards the trailing edge) of the point where separation occurs? Take the kinematic viscosity to be: v=1.5×105 m²/s.

Question 3 a) Neglecting freestream turbulence, the decelerating freestream velocity profile over a flat plate is given by, u = u₁ (1-x/L)", with L=10m. i) Estimate the point where the separation occurs, for n = 1,2,3,4. ii) Consider the case when n = 2 and estimate the momentum thickness at the separation point by the Walz-Thwaites's method. iii) Use Michel's method (after 1 iteration) to predict transition when u₁ = 10 m/s and obtain an equation for the location of the transition point, x,,. State the assumption that was made to obtain the result. iv) Is x,, upstream or downstream of the point where separation occurs? b) If uo is unknown, using Michel's formula for transition, find the value of u₁ = uo_col such that both separation and transition occur at the point of separation. (i.e. the two points are co-located.) When, u>0_col" state whether the transition point x, is upstream (towards the leading edge) or downstream (towards the trailing edge) of the point where separation occurs? Take the kinematic viscosity to be: v=1.5×105 m²/s.