Contraction and expansion losses

The consideration of the pressure drop over the monoliths containing a variety of CPSI (cells per in ) for the modeling of honeycomb reactor may be required, since Ap of the reactor strongly depends on CPSI of monolith. Eqn. (7) for the pressure drop of the honeycomb was employed to develop the reactor model describing the performance of the honeycomb fabricated in the present work [8]. and Ke indicate contraction and expansion loss coefficient at the honeycomb inlet and outlet, respectively and o is the ratio of free flow area to frontal area. 

The pressure drop due the contraction and expansion losses through the ports in the plates must be added to the friction loss. Kumar (1984) suggests adding 1.3 velocity heads per pass, based on the velocity through the ports. 

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... 

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. 

This is 1 percent of the 761bf/in previously calculated. In this example the pipe was long (several thousand feet). If the pipe were short, the contraction and expansion losses would be just as large, but the percentage error in neglecting them would be much greater. 

The friction losses are associated with the flow in a 75 m length of 50 mm pipe including one gate valve, one globe valve, two short curvature elbows, a contraction (at A) and an expansion at B. At this stage, neglecting the contraction and expansion losses, one can express the loss term in terms of the unknown velocity V as ... 

Let subscript 1 refer to the bypass subscript 4 refer to bypassed section From Eq, (5.73), since 2 - Z, and fittings losses and contraction and expansion losses are neglected/... 

The head required for flow of continuous phase he includes losses due to (1) friction in the down spout, which should be negligible, (2) contraction and expansion upon entering and leaving the down spout, and (3) two abrupt changes in direction. These total 4.5 velocity heads ... 

Determine or assume losses through orifice plates, control valves, equipment, contraction and expansion, etc. 

Pressure drop on the tube-side of a shell and tube exchanger is made up of the friction loss in the tubes and losses due to sudden contractions and expansions and flow reversals experienced by the tube-side fluid. The friction loss may be estimated by the methods outlined in Section 3.4.3 from which the basic equation for isothermal flow is given by equation 3.18 which can be written as ... 

Alternate exposures of resins to high and low concentrations of electrolytes can cause cracking and breakage due to alternate contraction and expansion. Eventually there may be significant reduction in particle size, causing increased resistance to flow and subsequent resin losses. 

The definition of A" (i.e., Kj= 2efW) involves the kinetic energy of the fluid, V /2. For sections in which the flow area changes (e.g., pipe entrance, exit, expansion, contraction, etc.), the entering and leaving velocities will be different. Since the value of the velocity used with the definition of Kp is arbitrary, it is very important to know which velocity is implied when values of the loss coefQcient are used from various sources (e.g., handbooks, manuals, texts, etc.). In most cases it is the largest velocity, through the smallest flow area, but the values in Table 5.6 for contractions and expansions are all used with the upstream velocity. 

Finally, a third possible effect in causing the capacity decline is the isolation of some of the IC electrode particles within the composite positive membrane, due to losses of electrical contact resulting from the repeated volume contractions and expansions associated with the intercalation-deintercalation cycles. 

Dudgeon, C. R. and J. E. Hills, Head Losses in Pipe Fittings with Stepped Contractions and Expansions, Proc. 9th Australian Fluid Mechanics Conf., Auckland, 105-108 Dec. 8-12 (1986). 

A venturi meter is shown in Fig. 3.2-2 and is usually inserted directly into a pipeline. A manometer or other device is connected to the two pressure taps shown and measures the pressure difference Pi — Pz between points 1 and 2. The average velocity at point 1 where the diameter is D m is m/s, and at point 2 or the throat the velocity is V2 and diameter >2. Since the narrowing down from Di to D2 rid the expansion from D, back to Z i is gradual, little frictional loss due to contraction and expansion is incurred. 

It is tricky to avoid errors with the use of capillary effect viscometers. A particular source of errors is the end effect. At the entrance exit of the tube, contraction and expansion of the flow cause additional pressure losses. 

Friction losses also occur due to turbulence caused by branch entries, elbows and contractions and expansions in duct diameter. For example, when the diameter of a duct is contracted, the static pressure in the larger diameter duct... 

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 ... 

Contraction and expansion of flow paths of the coolant while entering and leaving cooling chaimels result in pressure losses that depend on flow rate, channel geometry and dimensions of the end boxes. 

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