Enlargements and contractions

The first part of this chapter was devoted to the steady flow of a fluid in a part of a circular pipe,) well downstream from the pipe entrance. However, in each of the examples there were places where the flow entered and left a pipe. In Examples 6.1, 6.3, and 6.4, the fluid flowed from the first reservoir into a pipe and left the pipe to enter a second reservoir. Friction losses are associated with these transitions jsee Fig. 6.15. 

For the enlargements we can calculate the friction effect on the basis of some simple assumptions (the calculation, made by means of the momentum balance, is given in Sec. 7.3. The results of that calculation can be put in the form I 

From Fig. 6.16 it is clear that the larger the change of diameter, the greater the pressure losses. The reasons for the losses are as follows  

Resistance due to sudden enlargements and contractions. The resistance coefficient K is defined in Eq, 6.28. (From Crane Technical Paper No. 410. Reproduced by permission of the Crane Company.) 

In a sudden contraction, the flow does not come into the pipe entirely in the axial direction. Rather, it comes from all directions, as sketched in Fig. 6.15. On entering the pipe, the flow follows the pattern shown in Fig. 6.17. 

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For sudden pipe system contractions as represented in Figure 2-12A through 2-16, the values of the resistance coefficient, K, can be read from the charts. For more details for various angles of enlargements and contractions, see References [3] and [2]. 

Osada et al. [52] have also grafted PMAA to a porous substrate in order to achieve an environmentally sensitive membrane. This sensitivity was termed a chemical valve function because mechanochemical forces caused the pores to enlarge and contract. PMAA was grafted onto poly(vinyl alcohol) (PVA) films which had a mean pore radius of 4 pm. The water permeation of the membrane was strongly affected by the conformational state of the PMAA grafts. At low pH the chains were contracted and the water permeability was... 

P. Maijanovic, V. Djordjevic, On the compressible flow losses through abrupt enlargements and contractions, J. Fluids Eng. Trans ASME 116 (1994) 756-762. 

Threads notch the pipe and cause loss of strength and fatigue resistance. Enlargement and contraction of the flow passage at threaded joints creates turbulence sometimes corrosion and erosion are aggravated at the point where the pipe has already been thinned by thread... 

Similar to the phenomenon that highway air patrol pilots observe after a driver slows suddenly, then speeds up. From the airplane, the spacing between cars looks like the side pleats of an accordion—gradually enlarging and contracting waves. 

In automatic shifting period, it process the integral times enlarging and contracting... 

The values of a are the same as those found previously. He also examined the pressure losses in commercial screw type elbows and observed a large increase in resistance due to the enlargement and contraction of section. 

FIG. 6-13 Contractions and enlargements (a) sudden contraction, (h) rounded contraction, (c) sudden enlargement, and (d) uniformly diverging duct. 

It is the purpose of this chapter to describe a number of ring enlargement and simultaneous ring enlargement-ring contraction procedures which should be of general use. Recommended illustrative experimental procedures are given. 

For higher resistance valves, such as globes and angles, the losses are less than sudden enlargements or contractions situations. For these reduced seat valves the resistance coefficient EL, can be calculated as [3] ... 

P = ratio of small to large diameter orifices and nozzles and contractions or enlargements in pipes... 

Figure 2-38C. Critical Pressure Ratio, r, for compressible flow through nozzles and venturi tubes. By permission, Crane Co., Technical Paper 410, 1957. Also see 1976 edition. See note at Figure 2-18 explaining details of data source for chart. Note P = psia p= ratio of small-to-large diameter in orifices and nozzles, and contractions or enlargements in pipes.

Friction losses occurring as a result of a sudden enlargement or contraction in the cross-section of the pipe, and the resistance of various standard pipe fittings, are now considered. 

For flow at right angles to the axes of the tubes, the cross-sectional area is continually changing, and the problem may be treated as one involving a series of sudden enlargements and sudden contractions. Thus the friction loss would be expected to be directly proportional to the number of banks of pipes j in the direction of flow and to the kinetic energy of the fluid. The pressure drop - APf may be written as ... 

The reaction of oxime 323 with concentrated aqueous HCl proceeded with a ring contraction and afforded pyridazine 324 as a single product (equation 140) . On the contrary, the rearrangement of pyrrol-3-one oxime in the presence of hydrazine proceeded with ring enlargement and led to l//-pyridazin-4-one oxime . ... 

A variety of mono- and bi-cyclic heterocycles undergo ring interconversions leading to (5,5)-fused heterocycles. Both thermal and photolytic, and acid- and base-catalyzed, rearrangements, ring enlargements and ring contractions are known. 

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