Advanced fluid mechanics 2014

1. Given:A one-dimensional flow , non-uniform density cos =e t ρ. Initial velocity 1

m/s for t=π/2 (s),x=0 m . Find u(x,t).

2. Use N-S equation find Bernoulli eqution: 2u ()2p z C g g

ψρ++=,ψ is streamline function.

3. Consider a steady ,two-dimensional ,incompressible flow of Newonian ideal fluid

with velocity field 222,u ,0x y z u xy y x u =-=-=

(1) Is the flow irrotational?

(2) Does the flow satisfy conservation of mass?

(3) Find the pressure field P(x,y) if the pressure at point (x=0,y=0) is equal to P a .

4. For a given flow with the velocity potential function 23=3xy x φ-

(1) Determine the corresponding stream function

(2) Sketch the streamlines for this flow field, indicate the direction of flow along

the streamlines

(3) Determine the acceleration of a fluid particle at the point (1,2)

5. Given : 23,u 3,24x y z u y z z x u x y =+=+=+, 0.008Pa s μ=?.Find:

stress tensor and stess vector at the point (-1,1,2) on the plane 2-1x y z +-=

6. Enclosed container, incompressible fluid.

,According to k equation to

prove: