To understand the continuity equation. Streamlines represent the path of the flow of a fluid. You can imagine that they represent a time-exposure photograph that shows the paths of small particles carried by the following fluid. The figure (Figure 1) shows streamlines for the flow of an incompressible fluid in a tapered pipe of circular cross section. The speed of the fluid as it enters the pipe on the left is v_1. Assume that the cross-sectional areas of the pipe are A_1 at its entrance on the left and A_2 at its exit on the right. Find Q_1, the volume of fluid into the pipe per unit of time. This quantity is also known as the volumetric flow rate. Because the fluid is assumed to be incompressible and mass is conserved, at a particular moment in time, amount of fluid that flows into the pipe must equal the amount of fluid out. This fact is embodied in the continuity equation. Using the continuity equation, find the velocity c_2 of the fluid flowing out of the right end of the pipe.