Determine the stream function and plot the streamlines ?=1 and 2.

Question 1

(a) The x and y components of fluid velocity in a two-dimensional flow field are u=x and v= -y respectively

(i) Determine the stream function and plot the streamlines ?=1 and 2

(ii) If a uniformed flow defined by ?=y is superimposed on the above flow, determine the stream function and the velocity potential for this combined flow.

(b) Explain the meaning of:

i) vorticity

ii) irrotational flow

iii) streamline

iv) stream function

v) velocity potential

Question 2

(a) Air with a free stream velocity of 40 ms-1 flows past a smooth plate which is 3 m wide and 10 m long in the flow direction. Assuming that air density is equal to 1.2 kg m-3 and kinematic viscosity is equal to 1.49 10-5 m2s-1, determine

(i) The shear stress acting by the flow on the plate 6 m from the leading edge

(ii) The laminar sublayer thickness 6 m from the leading edge

(iii) The boundary layer thickness 6 m from the leading edge

(b) Explain the meaning of:

i) Reynolds stress tensor

ii) Reynolds stress model

iii) averaged value

iv) turbulent kinetic energy