Stream tube

A number of streamlines form a stream tube. Flows can enter and leave a stream tube only through the ends. 

Finally, we come to the effects of the Lewis number. Figure 4.2.14 shows the intensified images of vortex ring combustion of lean and rich propane/air mixtures. Since the flame is curved and stretched at the head region, the mass and heat is transferred through a stream tube. 

When the energy balance on the fluid in a stream tube is written in the following form, it is known as Bernoulli s equation ... 

We will apply the steady state momentum balance to a fluid in plug flow in a tube, as illustrated in Fig. 5-6. (The stream tube may be bounded by either solid or imaginary boundaries the only condition is that no fluid crosses the boundaries other that through the inlet and outlet planes.) The shape of the cross section does not have to be circular it can be any shape. The fluid element in the slice of thickness dx is our system, and the momentum balance equation on this system is... 

Figure 5-6 Momentum balance on a slice in a stream tube.

Aw is the width of the stream tube, and Ah is the change in hydraulic head over the incremental flow path, AL. 

Fires involving liquid process streams are the most common heater loss. Most involve a ruptured process stream tube leading to a firebox fire or a pool fire under or near the heater. The two most common causes are failure of the tubes due to overheating and rupture of the tubes as the result of a fire box explosion. 

Carrier-gas is transferred from the column through a heated metal capillary, which minimizes the dead volume at the end of the column and prevents condensation of the column effluent prior to its entry into the scrubbing unit. The tube carrying the liquid stream is joined to the gas stream tube, at a T-junction that is joined to the mixing coil by a glass-to-metal seal. Furfural is transferred from the gas stream into the liquid stream and the colour develops the two phases are then separated by the debubbling unit and the liquid stream is re-sampled through the flow cell of the colorimeter. A Technicon peristaltic... 

The river can be divided into a series of longitudinal planes with no signihcant interaction, such that v = 0 and Sy = 0. (This is the assumption of the stream-tube computational models.)... 

Detonation, Rayleigh (or Mikhel son) Line and Transformation in. (Called here Rayleigh-MikheTson Line) The Chapman-Jouguet theory deals with adiabatic transformations in steady, non-viscous, onedimensional flows in stream tubes or ducts of constant cross-section. Such transformations can be called Rayleigh transformations. From the equation of continuity valid for flow of constant cross-section and from the momentum equation (Ref 1, p 117 Ref 2, p 99), with use of the formula c = y-Pv for sonic velocity in an ideal gas, can be derived the relationship ... 

For the region of the flow bounded by a stream- tube of unit sectional area, and two planes X0) X, (the former lying in the undetonated expl and the latter within the steady zone), conservation of mass, momentum, and energy within the control surface requires ... 

Mathematical formulation of Prandtl-Meyer flow is given in Ref 66, p.p 162—64, equations 5.3 1 to 5.3.25 inclusive. In Fig 34 is shown the Prandtl-Meyer flow within a steady- deton zone characteristics are solid lines and stream lines are dashed line AB is the shock front, r = ratio of radius of axial stream tube to its initial radius and c = sound speed... 

Thus, integrating the preceding equation over any cross section of a stream tube of the particle phase and using the Gauss theorem, we can obtain... 

One solution to the problem mentioned above is not to rely solely on flow symmetry, but to achieve equidistribution by pressure-loss adjustment by means of flow resistors (see Figure 4.98) [140, 141, 148). In the flow sequence consisting of a main stream tube, fluid inlet, damping tank, distribution tubes and micro device such as a micro mixer, the main pressure drop is nearly always on the last side. The separation layer mixer acts here as a pressure restrictor similar to the sparger mentioned above. This requires accurate control over structural precision of micro fabrication. 

For pumped streams, tubes of 2 mm inner diameter and 4 mm outer diameter are used. For gravity flowing streams, tubes with 8 mm inner and 10 mm outer diameter are used. These tubes are easier to use than conventional stainless steel tubes due to a larger flexibility and smaller weight. They are also better then PTFE tubes because PVDF has almost no tendency to flow under pressure as compared to PTFE and PVDF has a far better radiation resistance. 

The stream-tube method is more closely related to the Protean coordinate approach. It refers to the flow analysis introduced some yeans ago by Clermont [40,53], which may be applied to the study of two- or three-dimensional duct or free surface flows [54-56] and pure circulatory or vortex flows [57]. In this analysis, the unknowns of the problem are, in addition to the pressure p, a one-to-one transformation between the physical flow domain D (or a subdomain D of D)... 

The main features of the stream-tube method in 2D and 3D flows, discussed more extensively elsewhere [40,53,55], are now summarized for two-dimensional situations. Flows with open streamlines are considered. The main flow region D of the physical domain D (D 2 D ) is mapped into a domain D such that the transformed streamlines are straight and parallel to an assumed main direction Oz of the flow. An example corresponding to 2D flows is illustrated in Fig 11. 

Viscoelastic constitutive equations in the stream-tube method... 

Figure 12. Stream tube B and its complementary domain B(. considered for the global momentum conservation equation.

The stress equations are considered together with the dynamic equations, leading to a set of equations involving the primary variables /, g and the pressure p or a mixed formulation with the stress components Tij. Both cases were considered in nTunerical applications of the stream-tube method. 

When considering an elementary stream-tube, the numerical computation of the unknowns for a stream tube may thus be related to the following problem... 

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