Equation of Motion in Streamline Coordinates

Euler’s equation expresses the relationship between the velocity and the pressure fields in inviscid flow. Written in terms of streamline coordinates, this equation gives information about not only about the pressure-velocity relationship along a streamline (Bernoulli’s equation), but also about how these quantities are related as one moves in the direction transverse to the streamlines. The transverse relationship is often overlooked in textbooks, but is every bit as important for understanding many important flow phenomena, a good example being how lift is generated on wings. A streamline is a line drawn at a given instant in time so that its tangent is at every point in the direction of the local fluid velocity (Fig. 1). Streamlines indicate local flow direction, not speed, which usually varies along a streamline. In steady flow the streamline pattern remains fixed with time; in unsteady flow the streamline pattern may change from instant to instant.