Euler’s Equation in Different Conventional Coordinate System

Euler’s equation in different coordinate systems can be derived either by expanding the acceleration and pressure gradient terms of Eq. (12.7d), or by the application of Newton’s second law to a fluid element appropriate to the coordinate system.

Euler's Equation in Different Conventional Coordinate Systems

Coordinate System	Euler's Equation (Equation of motion for an inviscid flow)
Rectangular Cartesian coordinate	x direction y direction z direction
Cylindrical Polar Coordinate	r direction θ direction z direction
Spherical Polar Coordinate	R direction θ direction φ direction