This is Volume 4 of the book series of the Body and Soul mathematics education reform program, and presents a unified new approach to computational simulation of turbulent flow starting from the general basis of calculus and linear algebra of Vol 1-3. The book puts the Body and Soul computational finite element methodology in the form of General Galerkin (G2), up against the challenge of computing turbulent solutions of the inviscid Euler equations and the Navier-Stokes equations with small viscosity. The book shows that direct application of G2 without any turbulence or wall modeling, allows reliable computation on a PC of mean value quantities of turbulent flow such as drag and lift. The book demonstrates the power of G2 by resolving classical scientific paradoxes of fluid flow and uncovering secrets of flying, sailing, racing and ball sports. The book presents new aspects on both mathematics and computation of turbulent flow, and challenges established approaches.