Question

For the velocity field given by

u=Vcosθ and v=Vsinθ and w=0 , where V and θ are constant, the stream lines are:
A. Straight
B. Parabolic
C. Elliptical
D. None of above

Answer 1

In a velocity field defined by u=Vcosθ, v=Vsinθ, and w=0, where both V and θ are constants, the streamlines are straight lines because the velocity is constant in both magnitude and direction. correct option is C. Elliptical

Step-by-step explanation:

For the velocity field given by u=Vcosθ and v=Vsinθ with w=0, where V and θ are constants, the streamlines describe the path that a fluid element will follow in a flow field.

Since both parts of the velocity are proportional to V and only vary with the angle θ, which is constant, the velocity is constant in magnitude and direction, the streamlines in this case are straight lines.

There is no component of the velocity that would cause the streamlines to curve, such as a velocity component that changes with position. Therefore, the streamlines for this velocity field are straight lines.

The velocity field given by u=Vcosθ and v=Vsinθ and w=0, where V and θ are constant, represents an incompressible fluid flow. The streamlines of this velocity field are straight lines.

This is because the velocity components in the x-direction (u) and y-direction (v) are constant, meaning that the fluid particles move in straight lines along these directions.

Therefore correct option is C. Elliptical