1. A compressible flow of a gas occurs in a pipeline. Assume uniform flow with the x-direction along the pipe axis and state the simplified continuity equation.
2. An incompressible steady flow of a fluid, such as a stratified flow of salt water (as in the isthmus between a fresh body of water and a body of salt water), flows in a channel with a sudden change in the height of the channel bottom (this allows for nonzero u and v). Assume no variation in the z-direction and write the two equations that result from the continuity equation. (Experiments show that a stagnant region of fluid exists in front of a sudden increase in the height of the bottom of a channel in a stratified flow. This phenomenon causes the buildup of smog in Los Angeles when air flows toward the city, but substantial smog does not appear in the more densely populated New York City. There are mountains east of Los Angeles but not west of New York.)