An Introduction to Hydrodynamics and Water Waves

acceleration axis Bernoulli equation bottom boundary conditions boundary layer calculation coefficient considered constant continuity equation convective inertia coordinates cosh md cross section defined deformation density direction dx² energy external forces Figure flow pattern fluid particle free surface friction forces given gravity wave head loss Hence horizontal hydraulic jump inertia forces integral irrotational laminar flow linear mathematical mean motion method momentum equation momentum theorem Navier-Stokes equations neglected nonlinear obtained order of approximation pipe porous medium pressure distribution pressure forces Reynolds number rotational scale model shear stress similitude sinh md solution steady stream function streamlines T₁ tanh turbulent flow two-dimensional uniform flow unsteady V₁ vector velocity components velocity distribution velocity potential velocity potential function vertical void coefficient water depth water waves wave height wave motion zero δη ди ди дл др дф дх ду дх дх მა