Exercise Problems  -  Chapter 3

1. The velocity field for a steady flow in a rectangular cartesian system is given by  What is the path line of the particle which is at (5, 3, 4) at t = 1s ?

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2. Verify whether the following flow fields are rotational. If so, determine the components of rotation about the coordinate axes

           (i)  ,         (ii)
           (iii)

                               [(i) ; (ii) irrotational; (iii) ]

3. For a steady two-dimensional incompressible flow through a nozzle, the velocity field is given by where x is the distance along the axis of the nozzle from its inlet plane and L is the length of the nozzle. Find

           (i)  an expression of the acceleration of a particle flowing through the nozzle and

          (ii)  the time required for a fluid particle to travel from the inlet to the exit of the nozzle

                                                                           [ (i) , (ii) ]

4. The velocity field for a steady two-dimensional flow in a cartesian coordinate system is given by , where a and b are constants. Find the equation of stream line passing through the point . Find also the condition for irrotationality of the flow.

                                                                             [ ]

5. Show that the velocity field given by  of a fluid represents a rigid body motion.

6. For a flow field  is given by . (a) Find , if it vanishes on   (b) Also find the stream function that will give these velocity components

[ (a)   (b)  ]

7. A two-dimensional flow field is given by . Find the velocity and acceleration in flow field at point A ( )

Velocity =
Acceleration=