Presentation on theme: "Introduction to Fluid Mechanics"— Presentation transcript:
1 Introduction to Fluid Mechanics Chapter 5Introduction to Differential Analysis of Fluid Motion
2 Main Topics Conservation of Mass Motion of a Fluid Particle (Kinematics)Momentum Equation
3 IntroductionIn Chapter 4, integral equations for finite control volumes are derived, which reflect the overall balance over the entire control volume under consideration -- A top down approach.However, only information related to the gross behavior of a flow field is available. Detailed point-by-point knowledge of the flow field is unknown.Additionally, velocity and pressure distributions are often assumed to be known or uniform in Chapter 4. However, for a complete analysis, detailed distributions of velocity and pressure fields are required.A bottom-up approach is needed.
5 Conservation of Mass Rectangular Coordinate System The net mass flow rate out of the CV in x direction is:Differential control volume herein vs. finite control volume in Chapter 4. The differential approach has the ability to attain field solutions. The basic equations from Chapter 4 are still applicable here but with infinitesimal CV in conjunction with coordinate system.
6 Conservation of MassRectangular Coordinate System
7 Conservation of Mass Rectangular Coordinate System “Continuity Equation”
8 Conservation of MassRectangular Coordinate System“Del” Operator
9 Conservation of Mass Rectangular Coordinate System Incompressible Fluid:Steady Flow:
10 Conservation of MassCylindrical Coordinate System
11 Conservation of MassCylindrical Coordinate System
12 Conservation of MassCylindrical Coordinate System“Del” Operator
13 Conservation of Mass Cylindrical Coordinate System Incompressible Fluid:Steady Flow:
26 Navier-Stokes Equations where p is the local thermodynamic pressure, which is related to the density and temperature by the thermodynamic relation usually called the equation of state. Notice that when velocity is zero, all the shear stresses are zero and all the normal stresses reduce to pressure under hydrostatic condition.