Divergent section

The shape of the converging section is a smooth trumpet shape similar to the simple converging nozzle. However, special shapes of the diverging section are required to produce the maximum supersonic-exit velocity. Shocks result if the divergence is too rapid and excessive boundary layer friction occurs if the divergence is too shallow. See Liepmann and Roshko (Elements of Gas Dynamic.s, Wiley, New York, 1957, p. 284). If the nozzle is to be used as a thrust device, the diverg-... 

Orifice plates. Either the concentric orifice, eccentric orifice, or segmented orifice-type. Choice depends on the quality of the fluid handled. Venturi tubes. These consist of a well-rounded convergent section at the entrance, a throat of constant diameter, and a divergent section. Their accuracy is high however, installation, unless planned for in advance, is very difficult in the field. 

It has been shown above that when the pressure in the diverging section is greater than the throat pressure, subsonic flow occurs. Conversely, if the pressure in the diverging section is less than the throat pressure the flow will be supersonic beyond the throat. Thus at a given point in the diverging cone where the area is equal to At the pressure may have one of two values for isentropic flow. 

The gas continues to expand isentropically and the pressure ratio w is related to the flow area by equation 4,47. If the cross-sectional area of the exit to the divergent section is such that >r 1 = (10,000/101.3) = 98.7, the pressure here will be atmospheric and the expansion will be entirely isentropic. The duct area, however, has nearly twice this value, and the flow is over-expanded, atmospheric pressure being reached within the divergent section. In order to satisfy the boundary conditions, a shock wave occurs further along the divergent section across which the pressure increases. The gas then expands isentropically to atmospheric pressure. 

Equation 6.100 shows that in a diverging section (d5/5 > 0) the velocity must decrease for subsonic flow (Ma< 1) and increase for supersonic flow... 

A nozzle used for a rocket is composed of a convergent section and a divergent section. The connected part of these two nozzle sections is the minimum cross-sectional area termed the throat The convergent part is used to increase the flow velocity from subsonic to sonic velocity by reducing the pressure and temperature along the flow direction. The flow velocity reaches the sonic level at the throat and continues to increase to supersonic levels in the divergent part. Both the pressure and temperature of the combustion gas flow decrease along the flow direction. This nozzle flow occurs as an isentropic process. 

FIG. 14-127 Prediction of venturi-scrubber cut diameter for hydrophobic particles as functions of operating parameters as measured by Calvert [Calvert, Goldshmid, Leith, and Mehta, NTIS Puhl PB-213016, 213017, 1972 and Calvert, J. Air Pollut. Control Assoc., 24, 929 (1974).] uG is the superficial throat velocity, and AP is the pressure drop from converging to diverging section. To convert meters per second to feet per second, multiply by 3.281 to convert liters per cubic meter to cubic feet per cubic foot, multiply by 10-3 and to convert centimeters to inches, multiply by 0.394. 

One example, although not yet for optimization, is the shift of the catalytic lysine from one /3 strand to a neighboring strand catalytic competency is maintained despite spatial reorganization of the active site with respect to substrate this case could cover a) or b) (Wymer, 2001). Duplication and divergence (Section 16.4.2) and circular permutation (Section 16.3.4) are covered below. 

In converging or diverging sections of annular dies, the fluid elements are subjected to axial and radial accelerations. Neglecting the radial special accelerations (for small tapers), the -component equation of motion reduces to... 

It is also true that in the converging section of a converging/diverging nozzle the maximum obtainable fluid velocity is the speed of sound, reached at the throat. This is because a further decrease in pressure requires an increase in cross-sectional area, i.e., a diverging section. The explanation for this is as follows. At the relatively high pressures in the converging section, a given pressure drop... 

The speed of sound is attained at the throat of a converging/diverging nozzle only when the pressure at the throat is low enough that the critical value of P-JP is reached. If insufficient pressure drop is available in the nozzle for the velocity to become sonic, the diverging section of the nozzle acts as a diffuser. That is, after the throat is reached the pressure rises and the velocity decreases this is the conventional behavior for subsonic flow in diverging sections. The relationships between velocity, area, and pressure in a nozzle are illustrated numerically in Example 7.3. 

Keep sections of multipart tables at similar widths. Widely divergent section widths within a table waste space and detract from general appearance. 

Supersonic velocities are readily attained in the diverging section of a properly designed convergingldiverging nozzle (Fig. 7.1). With sonic velocity reached at the throat, a further decrease in pressure requires an increase in cross-sectional area, a diverging section in wliich the velocity continues to increase. The transition occurs at the throat, where dA/dx = 0. The relationships between velocity, area, and pressure in a convergingldiverging nozzle are illustrated numerically in Ex. 7.2. 

The value of Cd depends on conditions of flow and shape of the constriction. For a well-shaped constriction (notably circular cross section), it would vary between 0.95 and 0.99 for turbulent flow. The value is much lower in laminar flow because the kinetic energy correction is larger. The return of the fluid to the original velocity by means of a diverging section forms a flow-measuring device known as a Venturi meter. 

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