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1. Integral vs Differential Approach

1. Integral vs Differential Approach. Fluid flows may be analysed using -. Differential Approach Does give a point by point description of Fluid Motion. Integral Approach will not give a point by point description of Fluid Motion. Gives only the overall effect of fluid motion

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1. Integral vs Differential Approach

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  1. 1. Integral vs Differential Approach Fluid flows may be analysed using - Differential Approach Does give a point by point description of Fluid Motion Integral Approach will not give a point by point description of Fluid Motion. Gives only the overall effect of fluid motion on a structure or body or

  2. 2. Lagrangian vs Eulerian Methods Lagrangian Method A system approach to track of a fixed mass of fluid. Complicated Eulerian Method Studies what happens at a point or within a Control Volume Convenient y (x0,y0,t) a b Pa = Pa(t) Pb = Pb(t) Pc = Pc(t) x c P=P(x,y,t)

  3. 3. System and Control Volume Systemis a fixed mass of fluid, its boundaries may change with time. AControl Volumeis a region in space, mass can cross its boundary

  4. 4. Conditions on Fluid Motion • Systemsare subject to • Law of Conservation of Mass : • Newton’s Second Law of Motion: • First and Second Laws of Thermodynamics: • To calculate a flow we need in addition • Equation of State • A formula/Equation for Viscosity • Boundary Conditions

  5. 5. Reynolds Transport Theorem

  6. 6. Continuity Equation (N = m, h = 1) v2 v1 dA2 dA1 2 1 Steady Flow- Which for a stream tube becomes Incompressible flow: For an incompressible flow

  7. 7. Momentum Equations (N=mV and h = v) FsSurface force FbBody force dVolume element dAArea element

  8. 8. Energy Equation E, Total Energy, Internal Energy, gacceleration due to gravity, , Zelevation, Qentry Rate of Heat Addition, WentryWork done on the system. For a steady incompressible flow one has

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