Test: Fluid Flow Kinematics - 1 - Civil Engineering (CE) MCQ

Integrating (i), we get,

Differentiating (iii) w.r.t. y, we get,

Equating (ii) and (iv), we get,
f'(y) = 0    ....... (v)
Integrating (v), we get,
f(y) = C
where C is a numerical constant which can be treated as zero.
From (iii),. we get,
 

For two dimensional incompressible flow, :
(i) the continuity equation is' 
(ii) the equation of a stream line is vdx - udy = 0

A path-line may be defined as the line traced by a single fluid particle as it moves over a period of time, Thus a path-line will show the direction of velocity of the same fluid particle at successive instants of time. As indicated earlier a streamline on the other hand shows the direction of velocity of a number of fluid particles at the same instant of time. A fluid particle always moves tangentially to the streamline, and in the case of steady flow since there is no change in direction of the velocity vector at any point with time, the streamline is fixed in space. Therefore in steady flow the pathlines and streamlines are identical. However, in unsteady flow since the direction of velocity vector at any point may change with time, streamline may shift in space from instant to instant. A particle then follows one streamline at one instant and another at the next instant and so on, so that the path of the particle may have no resemblance to any given instantaneous streamline. In other words, in unsteady flow path-lines and streamlines are different.

at (1, 1) V_x = -2 m/s = V_y