By Milton Van Dyke
Over four hundred appealing black-and-white pictures, gathered from world wide, illustrate the nice range of fluid movement. Flows starting from creeping to hypersonic speeds, in either the laboratory and Nature, are saw at once, or made noticeable utilizing smoke, ink, bubbles, debris, shadographs, schlieren, interferometry, and different concepts. Succinct captions describe the fundamental positive factors of every stream.
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Additional resources for Album of Fluid Motion
11), we still need to calculate cr∗ . Noting that cr = cr∗ , we will use a new coordinate system (x , y , z ) with the x axis aligned with the direction of cr and y on the reference plane, as shown in Fig. 3. In the new coordinate system (x , y , z ) shown in Fig. 24) Its components in the (x, y, z) coordinate system can be obtained by using the direction cosines. 25) X is a second order tensor with components being the direction cosines of the primed coordinate system. 3 Collision coordinate system.
6) 50 Chapter Four For a binary elastic collision, the mass, momentum, and the kinetic energy of the particle remain unchanged. Now let Q be the collision invariants, m, mc, and 12 m |c|2 , respectively. 7) where the summation convention has been used. 8) where the momentum ﬂux tensor can be written as the sum of the contribution from the average motion and that from the thermal ﬂuctuation, ρcc = ρ( c¯ + c )( c¯ + c ) = ρ c¯ c¯ + ρc c The pressure tensor ρc c or ρci cj can be written in terms of the viscous stress tensor τi j .
The limit given here as L, a local characteristic length scale, is about ten times as large as the side of a cubic element that contain 1000 molecules, which correspond to statistical ﬂuctuations with a standard deviation of approximately three percent. Note that ρ0 and n0 represent the mass density and the number density under standard conditions of 1-atm pressure and 0◦ C temperature. Typically, microﬂows have a characteristic length scale between 100 and 1 µm (10−4 and 10−6 m). It can be seen from Fig.
Album of Fluid Motion by Milton Van Dyke