2.3.2 Infinitesimal fluid element approach Definition of infinitesimal fluid element an infinitesimally small fluid element in the flow Wi的 a differentia/ volume It contains huge large amount of molecules Fixed and moving infinitesimal fluid element o Focus of our investigation for fluid flow
2.3.2 Infinitesimal fluid element approach Definition of infinitesimal fluid element: an infinitesimally small fluid element in the flow, with a differential volume. It contains huge large amount of molecules Fixed and moving infinitesimal fluid element. Focus of our investigation for fluid flow
Volume dv dv The fluid element may be fixed in space with fiuid moving through it, or it may be moving along a streamline with velocity V equal to the flow velocity at each point as well
The fluid element may be fixed in space with fluid moving through it, or it may be moving along a streamline with velocity V equal to the flow velocity at each point as well
23.3 Molecule approach A Definition of molecule approach The fluid properties are defined with the use of suitable statistical averaging in the microscope wherein the fundamental laws of nature are appllied directly to atoms and molecules In summary although many variations on the theme can be found in different texts for the derivation of the general equations of the fluid flow the flow model can be usually be categorized under one of the approach described above
2.3.3 Molecule approach Definition of molecule approach: The fluid properties are defined with the use of suitable statistical averaging in the microscope wherein the fundamental laws of nature are applied directly to atoms and molecules. In summary, although many variations on the theme can be found in different texts for the derivation of the general equations of the fluid flow, the flow model can be usually be categorized under one of the approach described above
23. 4 Physical meaning of the divergence of velocity ◆ Definition of V.p: Vv is physically the time rate of change of the volume of a moving fluid element of fixed mass per unit volume of that element. o Analysis of the above definition Step 1. Select a suitable model to give a frame under which the flow field is being described. a moving control volume is selected
2.3.4 Physical meaning of the divergence of velocity Definition of : is physically the time rate of change of the volume of a moving fluid element of fixed mass per unit volume of that element. V V Analysis of the above definition: Step 1. Select a suitable model to give a frame under which the flow field is being described. a moving control volume is selected
Step 2. Select a suitable model to give a frame under which the flow field is being described a moving control volume is selected. Step 3. How about the characteristics for this moving control volume? volume control surface and density will be Changing as it moves to different region of the flow Step 4. Chang in volume due to the movement of an infinitesimal element of the surface ds over At △V=V2t·nS= IVAt).dS
Step 2. Select a suitable model to give a frame under which the flow field is being described. a moving control volume is selected. Step 3. How about the characteristics for this moving control volume? volume, control surface and density will be changing as it moves to different region of the flow. Step 4. Chang in volume due to the movement of an infinitesimal element of the surface dS over . V (V t) ndS (V t) dS = = t