1. Integral vs Differential Approach Fluid flows may be analysed using - 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 Differential Approach Does give a point by point description of Fluid Motion or

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. System and Control Volume System is a fixed mass of fluid, its boundaries may change with time. A Control Volume is a region in space, mass can cross its boundary

4. Conditions on Fluid Motion Systems are 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. Reynolds Transport Theorem

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. Momentum Equations (N=mV and h = v) Fs Surface force Fb Body force d Volume element dA Area element

8. Energy Equation For a steady incompressible flow one has E, Total Energy, Internal Energy, g acceleration due to gravity, , Z elevation, Qentry Rate of Heat Addition, Wentry Work done on the system. For a steady incompressible flow one has