It can be shown that for supersonic flow of a fluid in a nozzle, the flow velocity increases as the area of the nozzle increases in the direction of flow, which is the opposite of what occurs for incompressible flow. What must be true of the density in a supersonic flow for this to be the case? Does it increase, decrease, or stay the same as the fluid moves through the expanding nozzle? Write down a simple algebraic relationship for the density ratio as a function of the velocity and area ratios.