Date of this Version
When a liquid flows through a pipe in such a way that it completely fills the pipe, and as much liquid enters one end of the pipe as leaves the other end of the pipe in the same time, then the liquid is said to flow at a steady rate. At any point of the pipe, the flow of the liquid does not change with time. The path of any particle of liquid as it moves through the pipe is called a streamline. We can map the flow of liquid through the pipe by drawing a series of streamlines following the paths of the particles of liquid, as shown in Figure 9-1. The instantaneous velocity of a liquid particle is always tangent to the streamline. The rate of flow may be represented by the density of streamlines, or the number of streamlines passing through a surface of unit area perpendicular to the direction of flow. Thus the streamlines will be close together where the liquid is moving rapidly and farther apart in regions of the pipe where the liquid is moving slowly. Similar conventions were used to represent the direction and magnitude of the gravitational field intensity.