Chapter Overview and Goals In the previous chapter, we considered global forms of the basic equations governing fluid mechanics. In many cases, these are sufficient for obtaining information of engineering interest. However, there are important occasions where a full threedimensional local description of the flow is necessary to the engineer. A local description means that it is presented in the form of differential equations valid at an arbitrary point in the fluid. In this chapter, we derive the basic equations governing flows whose pressure, velocity, and density can vary in three space directions, and also possibly in time.