With the governing equations for the flow of the power-law fluid in annulus with the inner cylinder executing a planetary motion being transformed by using the undetermined coefficient method, the formula of pressure ...With the governing equations for the flow of the power-law fluid in annulus with the inner cylinder executing a planetary motion being transformed by using the undetermined coefficient method, the formula of pressure gradient for this flow under the given flow rate and the relevant numerical calculation method are given in this article. Through the experiments on the flow of Hydrolyzed Polyacrylamide （HPAM） aqueous solution which can be regarded as a power-law fluid, the calculated results of the pressure gradient values are compared with measured data, the mean relative error between them is smaller than 5%, which verifies the results presented in this article.展开更多
New Reynolds' mean momentum equations including both turbulent viscosity and dispersion are used to analyze atmospheric balance motions of the planetary boundary layer. It is pointed out that turbulent dispersion ...New Reynolds' mean momentum equations including both turbulent viscosity and dispersion are used to analyze atmospheric balance motions of the planetary boundary layer. It is pointed out that turbulent dispersion with r 0 will increase depth of Ekman layer, reduce wind velocity in Ekman layer and produce a more satisfactory Ekman spiral lines fit the observed wind hodograph. The wind profile in the surface layer including tur-bulent dispersion is still logarithmic but the von Karman constant k is replaced by k1 = 1 -2/k, the wind increasesa little more rapidly with height.展开更多
Tycho Brahe was known for his comprehensive and remarkably accurate astronomical observations,and was considered one of the greatest astronomers before the invention of the telescope.However,Johannes Kepler,using coni...Tycho Brahe was known for his comprehensive and remarkably accurate astronomical observations,and was considered one of the greatest astronomers before the invention of the telescope.However,Johannes Kepler,using conic sections,formulated three laws of planetary motion based on Tycho’s observations.The formulas for circles and ellipses thus derived,and the traditional formula for ellipses based on a single focus of an elliptical orbit,were impractical and led to large and small errors.Because astronomy at that time was based on observations and mathematical formulas derived from them,these laws are still considered valid today.Unfortunately,Kepler’s laws are not really“laws”of the laws of physics,but rather trends that Kepler noticed and calculated using astronomical observations of the planets.This paper describes the eccentricity,amplitude,phase shift,angular momentum,polarization,radial path,and orbital energy of two-body orbital mechanics simultaneously,and then presents a wave function formula that avoids the above-mentioned difficulties.The results are in good agreement with the observational data.This paper contains 26 new equations and 11 figures,and it is hoped that the findings and results will contribute to the progress of the theory of celestial mechanics.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.50374018)
文摘With the governing equations for the flow of the power-law fluid in annulus with the inner cylinder executing a planetary motion being transformed by using the undetermined coefficient method, the formula of pressure gradient for this flow under the given flow rate and the relevant numerical calculation method are given in this article. Through the experiments on the flow of Hydrolyzed Polyacrylamide （HPAM） aqueous solution which can be regarded as a power-law fluid, the calculated results of the pressure gradient values are compared with measured data, the mean relative error between them is smaller than 5%, which verifies the results presented in this article.
文摘New Reynolds' mean momentum equations including both turbulent viscosity and dispersion are used to analyze atmospheric balance motions of the planetary boundary layer. It is pointed out that turbulent dispersion with r 0 will increase depth of Ekman layer, reduce wind velocity in Ekman layer and produce a more satisfactory Ekman spiral lines fit the observed wind hodograph. The wind profile in the surface layer including tur-bulent dispersion is still logarithmic but the von Karman constant k is replaced by k1 = 1 -2/k, the wind increasesa little more rapidly with height.
文摘Tycho Brahe was known for his comprehensive and remarkably accurate astronomical observations,and was considered one of the greatest astronomers before the invention of the telescope.However,Johannes Kepler,using conic sections,formulated three laws of planetary motion based on Tycho’s observations.The formulas for circles and ellipses thus derived,and the traditional formula for ellipses based on a single focus of an elliptical orbit,were impractical and led to large and small errors.Because astronomy at that time was based on observations and mathematical formulas derived from them,these laws are still considered valid today.Unfortunately,Kepler’s laws are not really“laws”of the laws of physics,but rather trends that Kepler noticed and calculated using astronomical observations of the planets.This paper describes the eccentricity,amplitude,phase shift,angular momentum,polarization,radial path,and orbital energy of two-body orbital mechanics simultaneously,and then presents a wave function formula that avoids the above-mentioned difficulties.The results are in good agreement with the observational data.This paper contains 26 new equations and 11 figures,and it is hoped that the findings and results will contribute to the progress of the theory of celestial mechanics.
