Notes #8 MAE 533, Fluid Mechanics
نویسنده
چکیده
1 One-dimensional Unsteady Inviscid Flows We consider now the problem of unsteady flow in one-dimension under the inviscid assumption. We have a rigid tube with cross-sectional area A(x), and we assume that all the variables (x-component of velocity u and all the thermodynamic state variables) are functions of x and t only. The governing equations are: A Dρ Dt + ρ ∂(uA) ∂x = 0, (1a) ρ Du Dt + ∂p ∂x = 0, (1b) Ds Dt = 0, (except across shocks) (1c) Under the one-dimensional assumption, the substantial derivative is: D Dt = ∂ ∂t + u ∂ ∂x. (2) We assume the fluid is in thermodynamic equilibrium in the sense that an equation of state exists of each glob of fluid (e.g. given two state variables, any other state variables can be computed).
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