Internal frictional losses

We finally observe that delayed response phenomena akin to creep and relaxation occur in other areas of Mechanics and Physics, and are attributable to the same fundamental cause, namely (usually internal) frictional losses. The mathematical techniques used for analyzing such phenomena are similar to those used in analyzing the properties of the viscoelastic functions. Such a close analogy exists between certain phenomena in the theory of Dielectrics and Linear Viscoelasticity, as emphasized by Gross (1953). 

In materials with high internal friction losses, it often happens that inertial effects, namely those depending on q, the density of the material, may be neglected compared with viscous effects. This is analogous to the approximation in the... 

This formula is another variation on the Affinity Laws. Monsieur s Darcy and VVeisbach were hydraulic civil engineers in France in the mid 1850s (some 50 years before Mr. H VV). They based their formulas on friction losses of water moving in open canals. They applied other friction coefficients from some private experimentation, and developed their formulas for friction losses in closed aqueduct tubes. Through the years, their coefficients have evolved to incorporate the concepts of laminar and turbulent flow, variations in viscosity, temperature, and even piping with non uniform (rough) internal. surface finishes. With. so many variables and coefficients, the D/W formula only became practical and popular after the invention of the electronic calculator. The D/W forntula is extensive and eomplicated, compared to the empirieal estimations of Mr. H W. 

When rubber is deformed the difference between the energy input and output is known as hysteresis. The loss of energy is consumed in internal friction and results in heat build-up. See Hysteresis Loop and Resilience. 

Measurements of <5 yield direct information about the magnitude of the energy dissipation and the phase angle. 0 measures the fractional energy loss per cycle due to the anelasticity and is often termed the internal friction. According to the discussion above, 8 will be a function of the frequency, to should approach zero at both low and high frequencies and will have a maximum at some intermediate frequency. The maximum occurs at a frequency that is the reciprocal of the relaxation time for the re-population of the point defects. 

Illers and Jenckel have discussed the internal frictions peak in the region of the crystal disordering transition. They analyzed the shape of the loss peak at various frequencies in terms of two different distributions of relaxation times existing above and below the transition. Nagamatsu, Yoshitomi, and Takemoto have also discussed this change in the distribution of relaxation times as revealed by measurements of stress relaxation. 

The linear model of Equation (4) gives a representation of damping of vibrations by internal friction 2J. When a steady sinusoidal excitation is involved, the internal friction causes a phase delay in the transmission of signals through the material which can be expressed as a loss-tangent, tan 5, which is related to i6, y and the frequency w, of the signal by... 

The mechanical loss, represented by the imaginary part of Eq. (16.102) or by the decaying exponential in Eq. (16.103), is obviously caused by the internal friction due to the viscoelastic character of the material. 

Pressure relief devices must be properly sized (capacity), and discharge location is critical. These devices are generally sized for the most likely pressure increasing event, e.g., external fire or internal process upset such as an uncontrolled exothermic reaction. The engineer must calculate the temperature and pressure increases associated with the event as well as the expected release volume. He or she must also account for pressure drops across the relief device as well as for friction losses in the lines. A decision must also be made about whether to discharge to the atmosphere or to a closed system that includes a scrubber, a flare, or even as simple as a water tank, such as is sometimes used for venting anhydrous ammonia. Some of these design decision issues are addressed in more detail by Crowl and Louvar. ... 

In dielectric property measurements, MAE manifests as a loss minimum and the magnitude of the loss minimum can be as high as 1 order of magnitude. Rather dramatic changes occur in the mixed alkali regions in the internal friction behaviour. Shown in Figure 6.08 is the... 

Equations 11.8 and 11.9 are isomorphous to equations 9.9 and 9.10 which define the storage and loss components of the complex dielectric constant . Similar equations are also used to define the complex bulk modulus B, the complex shear modulus G, and the complex Poisson s ratio v, in terms of their elastic and viscous components. The physical mechanism giving rise to the viscous portion of the mechanical properties is often called "damping" or "internal friction". It has important implications for the performance of materials [8-15],... 

For a steady flow of an incompressible fluid in a uniform pipe, the only property that varies along the pipe is pressure. However, for a compressible fluid when the pressure varies (i.e., drops), the density also drops, which means that the velocity must increase for a given mass flow. The kinetic energy thus increases, which results in a decrease in the internal energy and the temperature. This process is usually described as adiabatic, or locally isentropic, with the effect of friction loss included separately. A limiting case is the isothermal condition, although special means are usually required to achieve constant temperature. Under isothermal conditions for an ideal gas. 

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