ux = U{1 y /a*) ) t CD p! = Po (2»U/a*) (x Ut)j It can be shown that Eqs. (1) are a nontrivial solution only if y = 1.5. I t seems likely that this solution is part of a more general solution which has other terms involving {y — 1.5). We shall assume that the more general solution is of the form: V = [u(y, z, t), 0, 0], p = const. Under this assumption, the continuity equation is satisfied identically and the remaining Navier-Stokes equations reduce to
x = U{1 y /a*)) t CD p!= Po (2 * U/a*) (x Ut)j。(1)是一个非平凡解，只有当y = 1.5。这个解似乎是一个更一般的解的一部分，它有其他涉及{y - 1.5)的项。我们假定更一般的解是这样的形式:V = [u(y, z, t)， 0,0]， p = const。在此假设下，连续性方程被完全满足，剩余的Navier-Stokes方程约化为
{"title":"An Exact Solution of the Navier-Stokes Equations","authors":"H. Hunter","doi":"10.2514/8.7984","DOIUrl":"https://doi.org/10.2514/8.7984","url":null,"abstract":"ux = U{1 y /a*) ) t CD p! = Po (2»U/a*) (x Ut)j It can be shown that Eqs. (1) are a nontrivial solution only if y = 1.5. I t seems likely that this solution is part of a more general solution which has other terms involving {y — 1.5). We shall assume that the more general solution is of the form: V = [u(y, z, t), 0, 0], p = const. Under this assumption, the continuity equation is satisfied identically and the remaining Navier-Stokes equations reduce to","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115511727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Comment on Asymptotic Eigenfunctions for Turbulent Heat Transfer in a Pipe","authors":"L. S. Dzung","doi":"10.2514/8.9638","DOIUrl":"https://doi.org/10.2514/8.9638","url":null,"abstract":"","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121413344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Minimum Runway Length for an STOL Aircraft","authors":"E. Shoemaker","doi":"10.2514/8.7854","DOIUrl":"https://doi.org/10.2514/8.7854","url":null,"abstract":"","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122628350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Comparison of Flow-Direction Probes at Supersonic Speeds FRANK W. BARRY 750 I HAS BEEN SHOWN 1 tha t transverse magnetic fields of practica strengths exert considerable influence on liquid-metal, freeconvection, vertical, flat-plate and parallel-plate flow fields. The extent of influence was determined by the magnitude of a nondimensional parameter A which is the ratio of the Hartmann number to the fourth root of the Grashof number, and is a measure of the relative influence of the magnetic and buoyant forces. In this note the steady, fully developed, laminar, freeconvection flow of a fluid of electrical conductivity
{"title":"Magnetohydrodynamic Free-Convection Pipe Flow","authors":"K. Cramer","doi":"10.2514/8.9158","DOIUrl":"https://doi.org/10.2514/8.9158","url":null,"abstract":"Comparison of Flow-Direction Probes at Supersonic Speeds FRANK W. BARRY 750 I HAS BEEN SHOWN 1 tha t transverse magnetic fields of practica strengths exert considerable influence on liquid-metal, freeconvection, vertical, flat-plate and parallel-plate flow fields. The extent of influence was determined by the magnitude of a nondimensional parameter A which is the ratio of the Hartmann number to the fourth root of the Grashof number, and is a measure of the relative influence of the magnetic and buoyant forces. In this note the steady, fully developed, laminar, freeconvection flow of a fluid of electrical conductivity <TQ through a fully submerged, open-ended, constant-temperature, vertical pipe located in a transverse magnetic field of strength B0 is analyzed in terms of the same parameter. The magnitude of its influence on the velocity and temperature profiles, the surface shear and heat transfer, and the volumetric flow rate is determined.","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117104874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Means and Examples of Aeronautical Research in France at ONERA: The Twenty-Second Wright Brothers Lecture","authors":"M. Roy","doi":"10.2514/8.8013","DOIUrl":"https://doi.org/10.2514/8.8013","url":null,"abstract":"","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130583787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
rpHE HYDROSTATIC GAS BEARING lias been used in in•*• dustry for many years. On the other hand, while the principle of the hydrodynamic gas bearing has also been known for many years, it has only recently been applied. Not surprisingly, its first application has been in the nuclear field, where bearing lubricants would be adversely affected by radiation. Possibly even more significant has been the application of the hydrodynamic gas bearing in the gyromotor field, where the fantastic accuracies required have led to experimentation with everything from "atomic" to cryogenic gyros. It is quite likely that the current interest in, and work on, the spherical gas bearing will lead to other applications because of its inherently high stability and long life. The gyro motors being developed for air and space applications are, by the nature of these applications, limited in size and, thus, power. Aside from initially bringing the gyro wheel up to synchronous speed, power is necessary to overcome the windage loss of the motor and the viscous loss in the gas-bearing gap. I t can be readily seen how important it is to determine accurately the power requirements in such a small motor. The purpose of this paper is to show how to calculate viscous torque in a spherical gas bearing when the bearing eccentricity e is taken into account. For a high value of eccentricity—i.e., above 0.5—the error introduced by neglecting the eccentricity effect is large, and should not be neglected. An expression for the percentage of this error, which is introduced into the cal-
{"title":"Viscous Torque in a Spherical Gas Bearing","authors":"T. Yeh","doi":"10.2514/8.9356","DOIUrl":"https://doi.org/10.2514/8.9356","url":null,"abstract":"rpHE HYDROSTATIC GAS BEARING lias been used in in•*• dustry for many years. On the other hand, while the principle of the hydrodynamic gas bearing has also been known for many years, it has only recently been applied. Not surprisingly, its first application has been in the nuclear field, where bearing lubricants would be adversely affected by radiation. Possibly even more significant has been the application of the hydrodynamic gas bearing in the gyromotor field, where the fantastic accuracies required have led to experimentation with everything from \"atomic\" to cryogenic gyros. It is quite likely that the current interest in, and work on, the spherical gas bearing will lead to other applications because of its inherently high stability and long life. The gyro motors being developed for air and space applications are, by the nature of these applications, limited in size and, thus, power. Aside from initially bringing the gyro wheel up to synchronous speed, power is necessary to overcome the windage loss of the motor and the viscous loss in the gas-bearing gap. I t can be readily seen how important it is to determine accurately the power requirements in such a small motor. The purpose of this paper is to show how to calculate viscous torque in a spherical gas bearing when the bearing eccentricity e is taken into account. For a high value of eccentricity—i.e., above 0.5—the error introduced by neglecting the eccentricity effect is large, and should not be neglected. An expression for the percentage of this error, which is introduced into the cal-","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133882756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
T HAS BEEN STATED by some authors1 that the maximum stiff ness of a beam for a given weight is attained when the strain energy is a minimum or when the stress is constant. It can be shown that this condition does not, generally, result in maximum stiffness; however, it closely approximates the optimum condition in some cases. The optimum distribution of material for torsional stiffness of tubular beams is such that the thickness is constant around any cross section, and, for positions along the axis of the tube, the wall thickness should be proportional to the square root of the torsional moment and inversely proportional to the enclosed area. For maximum bending stiffness, the effective flange thick ness should be proportional to the square root of the bending moment or the square root of the product of the moment and the axial length on the beam, depending on whether angular or linear deflections are being considered. For the case of torsion, stiffness is measured by the amount of angular rotation, and, if t is independent of s, is given by:
{"title":"A Note on the Optimum Distribution of Material in a Beam for Stiffness","authors":"B. Saelman","doi":"10.2514/8.7614","DOIUrl":"https://doi.org/10.2514/8.7614","url":null,"abstract":"T HAS BEEN STATED by some authors1 that the maximum stiff ness of a beam for a given weight is attained when the strain energy is a minimum or when the stress is constant. It can be shown that this condition does not, generally, result in maximum stiffness; however, it closely approximates the optimum condition in some cases. The optimum distribution of material for torsional stiffness of tubular beams is such that the thickness is constant around any cross section, and, for positions along the axis of the tube, the wall thickness should be proportional to the square root of the torsional moment and inversely proportional to the enclosed area. For maximum bending stiffness, the effective flange thick ness should be proportional to the square root of the bending moment or the square root of the product of the moment and the axial length on the beam, depending on whether angular or linear deflections are being considered. For the case of torsion, stiffness is measured by the amount of angular rotation, and, if t is independent of s, is given by:","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130936925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hypersonic approximation of the minimum semiapex angle giving subsonic flow behind an attached shock
在附带激波后产生亚音速流动的最小半顶点角的高超声速近似
{"title":"HYPERSONIC APPROXIMATION OF THE MINIMUM SEMIAPEX ANGLE GIVING SUBSONIC FLOW BEHIND AN ATTACHED SHOCK","authors":"E. S. Love","doi":"10.2514/8.9709","DOIUrl":"https://doi.org/10.2514/8.9709","url":null,"abstract":"Hypersonic approximation of the minimum semiapex angle giving subsonic flow behind an attached shock","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133306916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Errata—\"Free Molecular Flow Forces and Heat Transfer for an Infinite Circular Cylinder at Angle of Attack\"*","authors":"L. Talbot","doi":"10.2514/8.7932","DOIUrl":"https://doi.org/10.2514/8.7932","url":null,"abstract":"","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114072309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
TEMPERATURE DISTRIBUTION The governing equation of the temperature T(x) in a thin rectangular fin is dT/dx (e
矩形薄翅片温度T(x)的控制方程为dT/dx (e
{"title":"On Minimum-Weight Rectangular Radiating Fins","authors":"Chen-Ya Liu","doi":"10.2514/8.8784","DOIUrl":"https://doi.org/10.2514/8.8784","url":null,"abstract":"TEMPERATURE DISTRIBUTION The governing equation of the temperature T(x) in a thin rectangular fin is dT/dx (e<x/kb)T* = 0 (0 < x < L) (1) where e is the emissivity of the fin material, <r is the StefanBoltzmann constant, k is the conductivity, and 2b and L are the fin width and length. The boundary conditions are T = To dT/dx = 0 T = TL Note that the boundary-value problem is completely defined by Eqs. (1), (2), and (3). The additional condition, Eq. (4), is merely used as a parameter which will be uniquely determined. By direct integration of Eq. (1) with boundary conditions, Eqs. (3) and (4), the solution for the temperature distribution along the fin can be written as","PeriodicalId":336301,"journal":{"name":"Journal of the Aerospace Sciences","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114720634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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