Lecture 3 - 1. Simple solution for laminar viscous incompressible fluid.pdf - 6.9.1 Simple Solutions for Laminar Viscous Incompressible Fluids of Navier

Lecture 3 - 1. Simple solution for laminar viscous incompressible fluid.pdf

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6.9.1 : Simple Solutions for Laminar, Viscous, Incompressible Fluids of Navier Stokes Equation May 2020 FLUID MECH II Dr Mior Azman Meor Said
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Introduction: Why desire simple solutions to NSE? Recall The final form of Navier Stokes Equation (NSE): y-direction: x-direction: z-direction: Convective acceleration terms Convective acceleration terms Convective acceleration terms
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Refer to NSE, Nonlinearity arises due to the presence of convective acceleration terms. (refer previous slide) No general analytical scheme to solve nonlinear partial differential equation However, there are special cases where the convective acceleration terms can be zero. In these cases, exact solution are possible. The special cases have conditions: (1) Steady State (2) Laminar flow Introduction: Why desire simple solutions to NSE?
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Navier Stokes Equation on x-direction: Case 1: Steady, Laminar flow between fixed parallel plates Steady State , du/dt =0 No velocity in y-direction, v = 0 No velocity in z-direction, w = 0 As continuity equation is du/dx + dv/dy + dw/dz = 0. As v = 0, w =0; Hence du/dx = 0 ._ velocity, u does not varies with x, du/dx =0 velocity, u does not varies with z, du/dz =0 No gravity force on x- direction, ρ g x = 0
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Navier Stokes Equation on y-direction: Case 1: Steady, Laminar flow between fixed parallel plates Steady State , dv/dt =0 No velocity in y-direction, v = 0 no velocity in y- direction, v =0
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Navier Stokes Equation on z-direction:
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