Confirmation of the First Law of Thermodynamics in Theory and Extended Bernoulli Equation

The internal energy change of ideal gas does not depend on the volume and pressure. The internal energy change of real gas has not any relation with the volume and pressure, which had been proved. If the internal energy change had not any relation with the volume and pressure, we could confirm the first law of thermodynamics in theory. Simultaneously, the internal energy change is the state function that shall be able to be proved in theory. If the internal energy change depended on the volume and pressure, we could not prove that the internal energy change is the state function and the chemical thermodynamics theory is right. The extended or modified Bernoulli equation can be derived from the energy conservation law, and the internal energy change, heat, and friction are all considered in the derivation procedure. The extended Bernoulli equation could be applied to the flying aircraft and mechanical motion on the gravitational field, for instance, the rocket and airplane and so on. This paper also revises some wrong ideas, viewpoints, or concepts about the thermodynamics theory and Bernoulli equation.

THE EXTINCTION BEHAVIOR OF THE SOLUTIONS FOR A CLASS OF REACTION-DIFFUSION EQUATIONS

The methods of L-p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boundary values partial derivativeu/partial derivativet = Deltau - lambda \u\(gamma-1) u - betau ((x, t) is an element of Omega x (0, + infinity)), u(x, t) \(partial derivativeOmegax (0, +infinity)) = 0, u(x, 0) = u(0) (x) is an element of H-0(1) (Omega) boolean AND L1+gamma(Omega) (x is an element of Omega). Sufficient and necessary conditions about the extinction of the solutions is given. Here lambda > 0, gamma > 0, beta > 0 are constants, Omega is an element of R-N is bounded with smooth boundary partial derivativeOmega. At last, it is simulated with a higher order equation by using the present methods.

Recurrent formula of Bernoulli numbers and the relationships among the coefficients of beam,Bernoulli numbers and Euler numbers

Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying the linear load is generalized,and then it is expanded into the corresponding Fourier series.With the obtained summation results of the infinite series,it is found that they are related to Bernoulli num-bers and π. The recurrent formula of Bernoulli numbers is presented. The relationships among the coefficients of the beam,Bernoulli numbers and Euler numbers are found,and the relative mathematical formulas are presented.

Effect of compressibility on the hypervelocity penetration

We further consider the effect of rod strength by employing the compressible penetration model to study the effect of compressibility on hypervelocity penetration.Meanwhile, we define different instances of penetration efficiency in various modified models and compare these penetration efficiencies to identify the effects of different factors in the compressible model. To systematically discuss the effect of compressibility in different metallic rod-target combinations, we construct three cases, i.e., the penetrations by the more compressible rod into the less compressible target, rod into the analogously compressible target, and the less compressible rod into the more compressible target. The effects of volumetric strain, internal energy, and strength on the penetration efficiency are analyzed simultaneously. It indicates that the compressibility of the rod and target increases the pressure at the rod/target interface. The more compressible rod/target has larger volumetric strain and higher internal energy. Both the larger volumetric strain and higher strength enhance the penetration or anti-penetration ability. On the other hand, the higher internal energy weakens the penetration or anti-penetration ability. The two trends conflict, but the volumetric strain dominates in the variation of the penetration efficiency, which would not approach the hydrodynamic limit if the rod and target are not analogously compressible. However, if the compressibility of the rod and target is analogous, it has little effect on the penetration efficiency.

Analysis of Water Transport inside a Plant Xylem Vessel with Pitted Thickening

In this article,computational fluid dynamics(CFD)are used to explore the dynamics of water transport inside the pitted thickening of a plant xylem vessel.A pitted thickening model combined with the Bernoulli equation is used to analyze the influence of various factors(namely,the inner diameter,thickening width,thickening height,thickening spacing,number of laps and adjacent pit axial rotation).The pressure drop and the flow resistance coefficient are the variable parameters for our analysis.The results show that these two parameters are proportional to the thickening height and thickening width,and inversely proportional to the inner diameter,thickening spacing and number of laps.Three different wall thickening structures of the vessel are compared and the pitted thickening vessel is shown to provide the largest structural flow resistance,the annular thickening vessel has the second largest resistance and the helical thickening vessel corresponds to the smallest resistance of the three structures.

Wind Power Potential in Interior Alaska from a Micrometeorological Perspective

The wind power potential in Interior Alaska is evaluated from a micrometeorological perspective. Based on the local balance equation of momentum and the equation of continuity we derive the local balance equation of kinetic energy for macroscopic and turbulent systems, and in a further step, Bernoulli’s equation and integral equations that customarily serve as the key equations in momentum theory and blade-element analysis, where the Lanchester-Betz-Joukowsky limit, Glauert’s optimum actuator disk, and the results of the blade-element analysis by Okulov and Sorensen are exemplarily illustrated. The wind power potential at three different sites in Interior Alaska (Delta Junction, Eva Creek, and Poker Flat) is assessed by considering the results of wind field predictions for the winter period from October 1, 2008, to April 1, 2009 provided by the Weather Research and Forecasting (WRF) model to avoid time-consuming and expensive tall-tower observations in Interior Alaska which is characterized by a relatively low degree of infrastructure outside of the city of Fairbanks. To predict the average power output we use the Weibull distributions derived from the predicted wind fields for these three different sites and the power curves of five different propeller-type wind turbines with rated powers ranging from 2 MW to 2.5 MW. These power curves are represented by general logistic functions. The predicted power capacity for the Eva Creek site is compared with that of the Eva Creek wind farm established in 2012. The results of our predictions for the winter period 2008/2009 are nearly 20 percent lower than those of the Eva Creek wind farm for the period from January to September 2013.

On the Maximum of Wind Power Efficiency

In our paper we demonstrate that the filtration equation used by Gorban’ et al. for determining the maximum efficiency of plane propellers of about 30 percent for free fluids plays no role in describing the flows in the atmospheric boundary layer (ABL) because the ABL is mainly governed by turbulent motions. We also demonstrate that the stream tube model customarily applied to derive the Rankine-Froude theorem must be corrected in the sense of Glauert to provide an appropriate value for the axial velocity at the rotor area. Including this correction leads to the Betz-Joukowsky limit, the maximum efficiency of 59.3 percent. Thus, Gorban’ et al.’s 30% value may be valid in water, but it has to be discarded for the atmosphere. We also show that Joukowsky’s constant circulation model leads to values of the maximum efficiency which are higher than the Betz-Jow-kowsky limit if the tip speed ratio is very low. Some of these values, however, have to be rejected for physical reasons. Based on Glauert’s optimum actuator disk, and the results of the blade-element analysis by Okulov and S&oslashrensen we also illustrate that the maximum efficiency of propeller-type wind turbines depends on tip-speed ratio and the number of blades.

Asymmetric and Moving-Frame Approaches to MHD Equations

The magnetohydrodynamic （MHD） equations of incompressible viscous fluids with finite electrical conductivity describe the motion of viscous electrically conducting fluids in a magnetic field. In this paper, we find eight families of solutions of these equations by Xu＇s asymmetric and moving frame methods. A family of singular solutions may reflect basic characteristics of vortices. The other solutions are globally analytic with respect to the spacial variables. Our solutions may help engineers to develop more effective algorithms to find physical numeric solutions to practical models.

Structure optimization of cam executive component and analysis of precisely applying deep-fertilization liquid fertilizer

Since there are some problems in the previous cam of deep-fertilization liquid fertilizer applicator,such as poor precision and low-fertilization performance,a method of the contour line of a cam was proposed based on Matlab GUI development platform.Bernoulli’equation between the liquid fertilizer and the pressure valve of the fertilizer-spraying needle was founded.Moreover,the motion angles of a rise travel and return travel were corrected and the corresponding parameters of the contour line of the cam were obtained.Equations of cam moving from rise travel to return travel were derived according to the simple harmonic motion.In addition,3D model of cam was established by applying the Pro/E software and the rationality of the cam design was verified.The static analysis of the cam was carried out under working conditions and the corresponding dynamics analysis was performed based on D’Alembert’s principle.And then relationships between the binding force and the drag torque were obtained.A bench test indicates that when the pressure of a hydraulic pump is 0.5 MPa and the velocity of a output shaft is 50 r/min,the average consumption of the fertilizer is 19.7 mL for each measurement,which meets the corresponding agronomic requirement,i.e.20 mL.When the rotation angle of the cam is 8.6°and the rise displacement of a plunger is 0.84 mm,the mouth of the fertilizer-spraying needle sprayed liquid fertilizer as soon as it got into the soil and stopped spraying as soon as it got out of the soil.The results show that the designed contour line of the cam meets the requirement,that is,the mouth of the fertilizer-spraying needle should spray liquid fertilizer as soon as it gets into the soil and stop spraying as soon as it gets out of the soil,which meets the agronomic requirements,that is,fertilizer should be sprayed deeply and precisely.And this study lays a theoretical foundation for designing the cam of intermittent type distributor and provides relevant parameters.