Contraction ratio

Discharge Coefficients and Gas Discharge A compressible fluid, upon discharge from an orifice, accelerates from the puncture point and the cross-sec tional area contracts until it forms a minimum at the vena contracta, If flow is choked, the mass flux G, can be found at the vena contrac ta, since it is a maximum at that point, The mass flux at the orifice is related to the mass flux at the vena contracta by the discharge coefficient, which is the area contraction ratio (A at the vena contracta to Ay at the orifice) ... 

The modulus term in this equation can be obtained in the same way as in the previous example. However, the difference in this case is the term V. For elastic materials this is called Poissons Ratio and is the ratio of the transverse strain to the axial strain (See Appendix C). For any particular metal this is a constant, generally in the range 0.28 to 0.35. For plastics V is not a constant. It is dependent on time, temperature, stress, etc and so it is often given the alternative names of Creep Contraction Ratio or Lateral Strain Ratio. There is very little published information on the creep contraction ratio for plastics but generally it varies from about 0.33 for hard plastics (such as acrylic) to almost 0.5 for elastomers. Some typical values are given in Table 2.1 but do remember that these may change in specific loading situations. 

In a small mechanism, a polypropylene spring is subjected to a fixed extension of 10 mm. What is the initial force in the spring and what pull will it exert after one week. The length of the spring is 30 mm, its diameter is 10 mm and there are 10 coils. The design strain and creep contraction ratio for the polypropylene may be taken as 2% and 0.4 respectively. 

If the spring is subjected to a 50% overload for 1 day, estimate the percentage increase in the extension over the normal 1 day extension. The shear stress in the material is given by 16 WR/d. Use the creep curves supplied and assume a value of 0.4 for the lateral contraction ratio. 

The experimental setup sketched in Figure 5.2.3 comprises a burner with ad = 22 mm nozzle exit diameter and a driver unit (loudspeaker) fixed at its base. The burner body is a cylindrical tube of 65 mm inner diameter containing a set of grids and a honeycomb followed by a convergent nozzle with an area contraction ratio of cr= 9 1. 

The fluidization quality significantly decreased when the reaction involving a decrease in the gas volume was carried out in a fluidized catalyst bed. In the present study, we carried out the hydrogenation of CO2 and used relatively large particles as the catalysts. Since the emulsion phase of the fluidized bed with these particles does not expand, we expected that the bed was not affected by the gas-volume decrease. However, we found that the fluidization quality decreased and the defluidization occurred. We studied the effects of the reduction rate of the gas volume and the maximum gas contraction ratio on the fluidization behavior. 

FCB using these catalyst particles. We investigated the effects of the gas-volume reduction rate and the maximum contraction ratio on the fluidization behavior during the reaction. 

The simplest and most common device for measuring flow rate in a pipe is the orifice meter, illustrated in Fig. 10-7. This is an obstruction meter that consists of a plate with a hole in it that is inserted into the pipe, and the pressure drop across the plate is measured. The major difference between this device and the venturi and nozzle meters is the fact that the fluid stream leaving the orifice hole contracts to an area considerably smaller than that of the orifice hole itself. This is called the vena contracta, and it occurs because the fluid has considerable inward radial momentum as it converges into the orifice hole, which causes it to continue to flow inward for a distance downstream of the orifice before it starts to expand to fill the pipe. If the pipe diameter is D, the orifice diameter is d, and the diameter of the vena contracta is d2, the contraction ratio for the vena contracta is defined as Cc = A2/A0 = (d2/d)2. For highly turbulent flow, Cc 0.6. 

The burner in the test facility, shown in Fig. 18.1, is an axisymmetric nozzle, which is concentrically placed into the circular suction collar. To achieve a top-hat velocity profile with laminar boundary layer at the nozzle exit, a fourth order polynomial with a large contraction ratio of 31.6 1 and an exit diameter of D = 10.16 mm is used in the design. The suction collar assembly is connected to a vacuum pump through a series of solenoid valves so that a counterflow, which is in the opposite direction of the fuel-air mixture flow, can be established... 

Note 5 Poisson s ratio is also sometimes called the lateral contraction ratio and is sometimes used in cases of non-linear deformation. The present definition will not apply in such cases. 

As illustrated in Fig. 17.6, opposed, high-contraction-ratio, nozzles can be used as an alternative to opposed porous plates. The contraction nozzles, which have been developed and applied by Law and colleagues, also establish the uniform exit-velocity profile that is required to support the mathematical similarity behavior [109,130,131,227,353,384, 387]. 

The effect of the thickness of gel film on the contraction response time is shown in Fig. 8. When the thickness was 10 pm the contraction response time was about 0.2 s which is almost the same speed as the contraction of skeletal muscle in animals. The typical curve of contraction is also shown. Figure 9 shows the result of contraction ratio vs load for gels made under different conditions. The higher the elasticity the higher is the contraction ratio under loading. Perpendicular type gels showed a comparatively high contraction ratio, and Parallel ... 

Fig. 9. Mechanical active properties of amphoteric PVA gels. Contraction ratio vs load...

Fig. 10. Contraction curves for A, B and C (see Sect. 3.1) under several loading conditions. The data are limited to 7/8 of the final contraction ratio...

Calculated orbital contraction ratio R / NR as a function of atomic number Z. 

Reservoir (width X denth) Die land (width X depth) Aspect ratio (width / depth) Contraction ratio Ref... 

Experiments were conducted in the newly built High Temperature Supersonic Jet Facility at the Fluid Mechanics Research Laboratory of the Florida State University in Tallahassee. A schematic of the facility can be seen in Fig. 3.2. In the present experiments, a converging axisymmetric nozzle having an exit diameter of 50.8 mm Wcis used. The nozzle profile was designed using a fifth-order polynomial with a contraction ratio of approximately 2.25. The stagnation pressure and temperature were held constant to within 0.5% of its nominal value during the experiment. 

Stagnation Zone. A jet issuing from a fully developed tube flow without a terminating nozzle will also be turbulent for Rerf > 4000, where Rerf is based upon Vn. The manifolding and piping systems that supply liquid to nozzles are often turbulent, and, unless the nozzle has a very large contraction ratio, this turbulence will be carried into the jet formed. Stagnation... 

Figure 29.2 shows the schematic diagram of a low-speed, sucfion-type wind tunnel used to simulate the crossflow field at the University of Oklahoma. Overall lengfh of fhe wind tunnel was 1130 cm (38 ), and the test section was 250 cm (8.2 ) long, 58 cm (1.9 ) wide, and 53 cm (1.7 ) high. The inlet section was designed with a contraction ratio of 10. Both side walls of the test section were constructed with 13-mm thick Pyrex glass panels for optical access. The top and bottom panels... 

S23 occur in expressions for the contraction ratios and S55 and S<,6 represent torsional deformations. 

Creep contraction ratios, which are time dependent functions analogous to the Poisson s ratios of elastic theory can be defined. 

So far the parameters defined, compliances, moduli and contraction ratios, are in forms which can be rigorously interpreted for infinitesimal time dependent deformation under constant stress, thus creep moduli E 9, r) are functions of angle and time. Extension to accommodate nonlinear behaviour at finite strain is obtained by allowing the quantities to become also functions of stress or strain. Thus modulus has the form E 6,t,%) and compliance functions Si/t.t). Such an extension is not rigorous but is useful. 

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