In the previous lecture, we obtained an expression for the conservation of mechanical energy in a flowing system. We will like to apply the same expression between two points or location in the flow- field. Before that, let us understand ‘streamlines’ and “stream tubes”. Streamline – it represents a line drawn in the flow field such that tangent drawn at every point of it is in the direction of the local velocity vector,
(Fig. 20a)
Note that streamline will change in the unsteady-state flow field. Also, note that laminar flow is represented/ characterized by streamlines (turbulent flow is characterized by eddy, irregular, unstable flow patterns). If we inject dyes or color at a certain location in the laminar flow, we can track the path of dyes and visualize streamlines. Similarly, if we inject or sprinkle several tiny (mass-less) needles in the fluid under steady- state laminar flow conditions, the needles will align themselves along the fluid- flow path. A hypothetical line connecting the head of the needles may be considered to be ‘streamline.
Two streamlines cannot cross each other, because there will be two velocities at the point of intersection, which is not possible.
On similar note, mass cannot cross a streamline. Based on the understanding of streamlines, one can visualize a stream tube as a hypothetical 3D tube encompassing streamlines inside, whose surface also consists of streamlines.
Note that at the entry and exit of the stream tube (marked in bold lines), velocity is perpendicular to the CS.
