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## Assumptions

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**Inviscid: no term in Navier-Stokes**Non-rotating, uniform density atmospheric pressure constant and uniform. Shallow Water Equations Equation of Continuity: Depth Integration: Assumptions**Equation of Continuity**m = density( ) * h* dx Dx = u*dt m = *h*u*dt**Pressure increases with depth according to overhead mass**per unit area. Pressure at depth h-z: Integrating Hydrostatic Balance**But,**=> Therefore Net Force => F = Fs + F1 – F2 Thus we get, Depth Integration**=> (h)tx= -**(uh)xx => (u)tt = - g(h)tx Eliminating (h)tx on both sides, (uh) xx - 1/g*u tt = 0. (u)xx – (1/gh)*utt=0 (Hyperbolic PDE) Wave Equation -> c2(u)xx – utt = 0 Thus, c=root(gh); - Tushar Athawale. Shallow Water Equation