Empirical Equations Jor the Thrust Generated by an Ideal Supersonic Nozzle

1957 ◽  
Vol 61 (564) ◽  
pp. 830-831
Author(s):  
P. N. Rowe
Keyword(s):  
Supersonic Flow ◽  
Pressure Ratio ◽  
Supersonic Nozzle ◽  
Empirical Equations ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Flow Through ◽  
Image Position ◽  
The Relationship

The dimensionless thrust generated by supersonic flow through a convergent-divergent nozzle is given by Ref. 1,1which takes its optimum value, bmax when pe = pa.For ideal one-dimensional flow, the relationship between Ae and pe is given by2and the optimum dimensionless thrust by3Where4From equations (2) and (3), the constant D in equation (1) can be evaluated and thence the thrust of an ideal nozzle at any pressure ratio provided that no separation occurs.Equations (2) and (3) are tedious to evaluate and it is not easy to estimate the effect of changes in γ.

Rarefied Gas Flow Through a Circular Orifice and Short Tubes

1984 ◽  
Vol 106 (4) ◽  
pp. 367-373 ◽  
Author(s):  
Tetsuo Fujimoto ◽  
Masaru Usami
Keyword(s):  
Knudsen Number ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Pressure Ratio ◽  
Diameter Ratio ◽  
Empirical Equations ◽  
Rarefied Gas Flow ◽  
High Pressure Ratio ◽  
Circular Orifice ◽  
Flow Through

Rarefied gas flow through a circular orifice and short tubes has been investigated experimentally, and the conductance of the aperture has been calculated for Knudsen number between 2 × 10−4 and 50. The unsteady approach was adopted, in which the decay of pressure in an upstream chamber was measured as a function of time. For flow with high pressure ratio, empirical equations of the conductance are proposed as a function of Reynolds number, or Knudsen number, and length-to-diameter ratio of the apertures.

Iterative Solutions of the Equations Jor Plane Oblique Shock Waves

1959 ◽  
Vol 63 (587) ◽  
pp. 669-672 ◽  
Author(s):  
A. R. Collar
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Free Stream ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Two Dimensional ◽  
Iterative Solutions ◽  
Flow Through ◽  
Image Position

If a plane oblique shock wave, inclined to the free stream at the angle ε, is produced in two-dimensional supersonic flow of Mach number M by (for example) a wedge which deflects the flow through an angle δ, the equation connecting these quantities may be writtenIn this form, δ is given explicitly when M, ε are fixed. Similarly, we may obtain M explicitly when ε, δ are fixed; equation (1) may be written (see, for example, Liepmann and Puckett, Equation 4.27)

Network model for hydraulic conductivity of sand-bentonite mixtures

2004 ◽  
Vol 41 (4) ◽  
pp. 698-712 ◽  
Author(s):  
Tarek Abichou ◽  
Craig H Benson ◽  
Tuncer B Edil
Keyword(s):  
Hydraulic Conductivity ◽  
Unit Area ◽  
Network Models ◽  
Element Model ◽  
Sand Particle ◽  
Particle Interactions ◽  
One Dimensional ◽  
Flow Through ◽  
Sand Particles ◽  
The Relationship

A network formulation was used to model the hydraulic conductivity of sand–bentonite mixtures (SBMs) as a function of bentonite content. The sand particles were assumed to be spheres, and their arrangement was defined using a discrete element model simulating sand particle interactions. Pores between the spheres were approximated as a network of straight capillary tubes. The space defined by the spheres was divided into a collection of neighboring tetrahedrons, and the geometry of the tetrahedrons was used to define tube diameters and lengths in the network. Hydraulic heads throughout the network were computed by solving a system of equations describing flow through the tubes. Hydraulic conductivity of the network was calculated as the rate of flow per unit area for a given network of tubes driven by a one-dimensional hydraulic gradient. Bentonite was introduced into the network in several schemes to simulate SBMs. SBMs prepared with powdered bentonite were modeled as a packing of sand, where the sand particles are coated with bentonite (grain coating model and pipe blocking model), whereas SBMs prepared with granular bentonite were modeled as a packing of sand with bentonite occupying pores between the sand particles (junction blocking model). The relationship between hydraulic conductivity and bentonite content obtained from the grain coating model was similar to that measured on sand – powdered bentonite mixtures. A comparable relationship was also obtained for hydraulic conductivities predicted with the junction blocking model using a size-based filling approach and hydraulic conductivities measured on sand – granular bentonite mixtures.Key words: sand–bentonite mixtures, network models, hydraulic conductivity, degree of bentonation, bentonite distribution.

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