Friction expansion factor

In comparison with metallic materials, the use of plastics is limited to relatively moderate temperatures and pressures (230°C is considered high for plastics). Plastics are also less resistant to mechanical abuse and have high expansion rates, low strengths (thermoplastics), and only fair resistance to solvents. However, they are lightweight, are good thermal and electrical insulators, are easy to fabricate and install, and have low friction factors. 

For individually finned tubes as shown in Fig. 17.14a, flow expansion and contraction take place along each tube row, and the magnitude is of the same order as that at the entrance and exit. Hence, the entrance and exit losses are generally lumped into the core friction factor. Equation 17.65 for individually finned tubes then reduces to... 

This equation is an inverted form of the core pressure drop in Eq. 17.65. For the isothermal pressure drop data, p, = p = l/(l/p)m. The friction factor thus determined includes the effects of skin friction, form drag, and local flow contraction and expansion losses, if any, within the core. Tests are repeated with different flow rates on the unknown side to cover the desired range of the Reynolds number. The experimental uncertainty in the/factor is usually within 5 percent when Ap is measured accurately within 1 percent. 

The temperature ratio on the LHS of the above equation indicates how close an expansion is to being perfectly adiabatic (LHS = 0) vs. being perfectly isothermal (LHS = 1.0). Inserting typical values of the friction factor and L/D for the archetypical cases of the plain orifice and the long capillary we obtain the following ... 

For the fluid to expand, the channel must be convergent (Dz < 0) under subsonic conditions (Ma < 1) and divergent (Dz > 0) under supersonic conditions (Ma > 1). Note that Eq. (31) has a singularity at Ma = 1 and changes its sign when the flow speed u z) crosses the speed of sound Msnd- Because Dz = 0 in a cylindrical channel, an adiabatic expansion must be driven by friction (or else the trivial solution dp/dz = 0 is obtained). The friction factor / in Eq. (30) is always positive thus, if one starts at subsonic conditions, flow can never be accelerated beyond the speed of sound inside a cylindrical duct. Flow that attains exactly the speed of sound at the exit of the duct is called choked flow. As we... 

As we found for separation performance described above, i e-similarity is not critical for the pressure drop, either. In Chap. 4 we found that many of the empirical models for cyclone pressure drop only contain the ratio of inlet to outlet areas, implying that Eu will be the same between geometrically similar cyclones, irrespective of f e-similarity. Obviously, as was the case for separation efficiency, this is only valid when Re is high enough that the friction factor is essentially independent of Re. This should come as no real surprise since the same situation holds true for most flow devices (such as pipes, elbows, orifices, contractions and expansions, etc.) that operate in fully developed turbulent flow. In such cases, pressure loss can be characterized by the formula ... 

The viscous or frictional loss term in the mechanical energy balance for most cases is obtained experimentally. For many common fittings found in piping systems, such as expansions, contrac tions, elbows and valves, data are available to estimate the losses. Substitution into the energy balance then allows calculation of pressure drop. A common error is to assume that pressure drop and frictional losses are equivalent. Equation (6-16) shows that in addition to fric tional losses, other factors such as shaft work and velocity or elevation change influence pressure drop. 

The discharge head of a pump is the head measured at the discharge nozzle (gauge or absolute), and is composed of the same basic factors previously summarized 1. static head 2. friction losses through pipe, fittings, contractions, expansions, entrances and exits 3. terminal system pressure. 

The pressure drops throughout the cyclone owing to several factors (1) gas expansion, (2) vortex formation, (3) friction loss, and (4) changes in kinetic energy. The total pressure drop can be expressed in terms of an equivalent... 

The gas expansion factor Yg in Equation 4-68 depends only on the heat capacity ratio of the gas y and the frictional elements in the flow path 2 K. An equation for the gas expansion factor for choked flow is obtained by equating Equation 4-68 to Equation 4-66 and solving for Yg. The result is... 

The calculation to determine the expansion factor can be completed once y and the frictional loss terms 2 Kf are specified. This computation can be done once and for all with the results shown in Figures 4-13 and 4-14. As shown in Figure 4-13, the pressure ratio ( f - P2)/Pi is a weak function of the heat capacity ratio y. The expansion factor Yg has little dependence on y, with the value of Yg varying by less than 1 % from the value at y = 1.4 over the range from y = 1.2 to y = 1.67. Figure 4-14 shows the expansion factor for y = 1.4. 

This relation applies from the initial expansion of the bed until transport of solids takes place. There may be some discrepancy between the calculated and measured minimum velocities for fluidisation. This may be attributable to channelling, as a result of which the drag force acting on the bed is reduced, to the action of electrostatic forces in case of gaseous fluidisation—particularly important in the case of sands—to agglomeration which is often considerable with small particles, or to friction between the fluid and the walls of the containing vessel. This last factor is of greatest importance with beds of small diameters. Leva et al.<4 introduced a term, (GF — GE)/ GF, which is a fluidisation efficiency, in which GF is the minimum flowrate required to produce fluidisation and G / is the rate required to produce the initial expansion of the bed. 

Bj = correction factor in Eq. (30) to account for friction due to sudden contraction, sudden expansion, and reversal of flow direction, dimensionless... 

Construct the dry-pressure-drop line on log-log coordinates (optional). For turbulent flow, the gas-phase pressure drop for frictional loss, contraction and expansion loss, and directional change loss are all proportional to the square of the superficial F factor. For the dry packing the pressure drop can be calculated from the equation... 

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