This, however, is not true due to the fact that the relaxation time involved relates to different aspects of the scattering mechanism. Consequently, we may suspect that the electron component of the viscosity should behave similarly to the thermal conductivity. In appearance it is similar to the expression for thermal conductivity with the exception that the specific heat per particle in the thermal conductivity is being replaced by the particle mass. Viscosity is expressed in units of g/cm/sec, which is also called poise. Where n is the molecular density, m the mass of each molecule, υ ― the average thermal velocity of the molecules, and τ the relaxation time. This error can be minimized by using a “Boundary Layer probe” to reduce the distance between the center of the tube and the solid boundary surface. Integrating the velocity gradient at the pressure probe’s nose will result in a higher stagnation pressure value than the stagnation pressure calculated from the square of the average velocity. The second error results due to the stagnation pressure being proportional to the square of the velocity. A solution to minimize this measurement error is to use a flattened tip probe (called a “Boundary Layer probe” in Fig. 3.12b) to measure the stagnation pressure provided the flow direction is known. This deflection will cause the pressure probes to show a higher than normal stagnation pressure. This results in the streamlines deflecting to a region of lower velocities. The first measurement error results when the pressure probes are exposed to a high stagnation pressure gradient field, which is seen when measuring inside the boundary layer or near solid boundaries. There are two measurement errors that can result. The transverse velocity gradient, which is the difference in velocity between adjacent boundary layers, will result in a measurement error of the stagnation pressure measurements ( Schlichting, 1979). Kim, in Application of Thermo-Fluidic Measurement Techniques, 2016 3.3.5 Velocity Gradient Effect Pneumatic Measurements for Pressure, Velocity, and Flow-direction = LF such materials have both “solid-like” and “liquid-like” characteristics). The response functions of rate-dependent materials (e.g., viscoelastic materials) involve both F and L (through F. Therefore, as we shall see, the response functions (e.g., the relations between stress and strain) for a “solid” involve deformation measures like F, and the response functions for a “fluid” involve deformation measures like L. Loosely, the response of a “solid” depends on the deformation of the continuum away from some reference (usually stress-free) configuration, whereas the response of a “fluid” depends only on the flow configuration at that instant. This is in contrast to the deformation measures F, F −1, C, B, c, E, and e of Section 3.3, which all describe some feature of the present configuration relative to a reference configuration. Note that the velocity gradient L, the rate of deformation tensor D, and the vorticity tensor W depend only on the present configuration, and have no connection to any reference or previous configuration. Motions for which W (or w) are zero are called irrotational motions. It is seen from ( 3.64) that the axial vector w is the angular velocity of the line element that is along an eigenvector of D, so W has the physical significance of being the rate of rotation of the small neighborhood.
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