In the limit of nearness to this quantity, Chaplygin's equation can be simplified to the linear PDE u-sub-x-x minus x times u-sub-y-y equals zero, which is hyperbolic for x less than zero, elliptic for x greater than zero, and called the Euler-Tricomi equation. A flow nears this quantity as it progresses towards the throat of a De Laval nozzle. The Prandtl-Glauert transfor
In the limit of nearness to this quantity, Chaplygin's equation can be simplified to the linear PDE u-sub-x-x minus x times u-sub-y-y equals zero, which is hyperbolic for x less than zero, elliptic for x greater than zero, and called the Euler-Tricomi equation. A flow nears this quantity as it progresses towards the throat of a De Laval nozzle. The Prandtl-Glauert transformation has a (*) singularity at this value. The wavefronts of a travelling object lag behind the object, forming a cone whose edge is a shock wave, when the object is moving faster than this quantity. It can be defined as the square root of quantity specific heat ratio times ideal gas constant times temperature, or as bulk modulus over density. For 10 points, name this quantity that's the speed at which a disturbance propagates through a fluid medium, sometimes known as Mach 1.
In the limit of nearness to this quantity, Chaplygin's equation can be simplified to the linear PDE u-sub-x-x minus x times u-sub-y-y equals zero, which is hyperbolic for x less than zero, elliptic for x greater than zero, and called the Euler-Tricomi equation.
speed of sound [or: obvious equivalents; until it is read, accept: Mach 1; prompt on: c]