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FLUID FLOW CONCEPTS Section 1 Flow of Matter
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angle approaches zero axes body boundary conditions boundary layer Cauchy-Riemann equations circle closed curve complex number complex potential constant cosh differential direction cosines distance doublet dx dy dy dz element elliptic cylinder equipotential lines expressed finite flow pattern fluid flow fluid particles free streamlines ft per sec given gradient Hence ideal fluid infinite fluid infinity irrotational irrotational flow kinetic energy Laplace equation line integral mass modulus Navier-Stokes equations normal stresses obtained origin parallel plane plate polygon positive pressure intensity pure imaginary radius real axis region respect Reynolds numbers rotation satisfied shear stress shown in Fig singular points sinh solution sphere stagnation point steady flow Stokes stream function stream surface Substituting Sx Sy Sz symmetry theorem tion to-plane transformation two-dimensional flow uniform flow velocity components velocity distribution velocity potential viscosity vortex ring vortex tube vortices x-axis x-direction z-plane