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fundamental equation
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  基本方程
    APPROXIMATION OF WATER HAMMER FUNDAMENTAL EQUATION
    水击基本方程的近似牲
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    Introduced the structure, the principle and the fundamental equation of TOPMODEL model.
    介绍了TOPMODEL的结构、原理和基本方程
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    In this paper, the authors consider that whether the equation of motion or the Continuity equation in the fundamental equation of water hammer they were derived under the assumption ……=0(……=0) and……=0(……=0) .
    本文认为水击基本方程中无论是运动方程或是连续方程都是在假定情况下取得的。
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    In accordance with the similarities between waves and hydraulic jumps , the expressions for estimating wave decay and energy dissipation in the surf zone are derived based on the fundamental equation of fluid mechanics .
    本文从流体力学的基本方程出发,利用破波现象和明渠水跃现象的相似性,推求了破波的能量损失和波高在破波区的衰减规律;
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    According to the two-dimensional tidal wave fundamental equation,the tides and tidal current in the bight of Fengcheng harbour were computed by using finite difference method. The results basically reveal the characteristics of motion of tidal current in the bight of Fengcheng harbour in view of the comparison between the measured values and the calculated values.
    根据二维潮波基本方程,采用有限差分方法,计算了防城港湾的潮汐和潮流.由实测值与计算值的比较可知,该项计算结果较好,基本能揭示防城港湾的潮流运动规律.
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  “fundamental equation”译为未确定词的双语例句
    Under the geomagnetic dipolar coordinate system, a partial differential equation of electric potential is deduced from the ionospheric dynamo theory and taken as the fundamental equation for the electric
    然后,为了验证这个新的思路,我们建立了一个中低纬度电离层电场理论模式,利用该理论模式模拟发现了中低纬度电离层电场具有明显的半年变化现象,并提出沿磁力线南北半球耦合效应可能是电场半年变化现象的重
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    Based on the theory of fluid mechanics, the fundamental equation of single stage liquid-gas jet pump and a simplified formula are deduced and then verified by the experimental results.
    应用流体力学的基本原理,推导并初步验证了单级液气射流泵的基本性能方程及其简化式;
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    Based on the fundamental equation for unsteady flow in open channel the Preissman method is applied to establish the model for simulating the hydraulic transient in long distance conduit water transfer system with retaining weirs.
    为研究大型调水工程的水力瞬变过程,采用明渠非恒定流方程及Preissiman方法模拟无压管涵非恒定流、有压管涵水击和明满交替流,提出了设置保水堰的长距离管涵输水系统的水力学仿真模型。
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  fundamental equation
The temperature dependence of the investigated properties is analyzed on the basis of the activated complex theory and of the fundamental equation of A.I.
      
The fundamental equation is obtained that relates the critical radius of a nucleus and reaction parameters, such as temperature, metal particle oversaturation by carbon, the work of metal adhesion to graphite, and the metal-carbon bond energy.
      
The fundamental equation of a compressible discrete vortex method is derived.
      
For prediction of gradient retention times of analytes, the fundamental equation of gradient elution was numerically solved.
      
We consider the dissipative Landau-Lifshitz equation as the fundamental equation of motion and present a complete local bifurcation analysis in 1+1 dimensions.
      
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The use of the method of charaeterictics to solve super-critical flow problems has been previously established by several authors.In most cases,frictional resistance and bottom slope have been neglected.Taking into consideration the above two factors(Fig.1),the equation of continuity and the equations of motion are respectively (hu)_x+(h_v)_y=0.(1) uux+vu_y=g sin i-((g/2h))(h~2osi)_x-τu/ρhq.(2) uv_x+vv_y=-((g/2h))(h~2cos i)_y-τv/ρhq.(3) Where the subscripts denote the variables with respect to which...

The use of the method of charaeterictics to solve super-critical flow problems has been previously established by several authors.In most cases,frictional resistance and bottom slope have been neglected.Taking into consideration the above two factors(Fig.1),the equation of continuity and the equations of motion are respectively (hu)_x+(h_v)_y=0.(1) uux+vu_y=g sin i-((g/2h))(h~2osi)_x-τu/ρhq.(2) uv_x+vv_y=-((g/2h))(h~2cos i)_y-τv/ρhq.(3) Where the subscripts denote the variables with respect to which partial differentiations are made. Making use of the condition of irrotational flow v_x-u_y=O,(4) the energy equation can be obtained d((q~2/2))+gcosidh=gsinidx+(1/2)gh sin i·i_xdx-(τqdz)/(ρhu) =(gusini+(1/2)guh sin i·i_(τq)/(ρh))(dx/u).(5) The above are the fundamental equations for the type of flow discussed. It can be shown that the two systems of characteristics in the physical plane and the u v plane(Fig.2)are represented by C~+:dy~+=ξ~+dx~+.(21a) Γ~+ξ~-(dv~+)/(du~+-Gdx~+)=-1.(21b) and C~-:dy~-=ξ~-dx~-.(22a) Γ~-:ξ~+.(dv~-)/(du~-)-Gdx~-=-1.(22b) Where ξ~±=(15) G=(gu sin i+(1/2)guh sin i·i_x+(τq/ρh))/(u~2-ghcosi).(23) The superscripts + and- refer to the pertinent system of characteristics. For flat-bottom,frictionless channels,G=0;(21b)and(22b)indicate that at cor- responding points the tangents of C~+ and C~- are perpendicular to those of Γ~- and Γ~+ respectively and the Γ characteristics are systems of epicycloids. Taking into consideration the varying bottom slope along the x-direction and the bottom friction τ,it can be shown that the velocity vector still bissets the C characteristics(Fig.2) and both A~+ and A~- are given by q~2sin~2A=ghcosi.(20) With G different from zero,(21b)(22b)can no longer be integrated to give analytic forms and the angles between the tangents,φ~+ and φ~-,no longer equal to π/2.How- ever,based on these two equations,a graphical method is proposed,as illustrated in Fig. 6.

本文从基本方程式出发,导演了明渠急流在有底坡和摩阻力情形下的特性线方程式及沿特性线的关系式,根据各式说明任何一点流速方向、特性线方向及特性线在速度平面内的对应曲线方向之间的关系,最后建议近似的图解法并举例说明其应用.

The authors divide the effect of the shape of a valley cross-section on the earthquake hydrodynamic pressures into two parts: one due to the solidity ratio s=A/Bh, or the cross-sectional area A divided by the free-surface width B and the depth h, and the other due to the width-depth ratio w=B/H. As the ordinary cross-sections of valleys are essentially symmetric, three basic shapes, namely, rectangle, semi-circle, and isosceles right triangle, are chosen for analysis. Earthquakes in both the longitudinal and...

The authors divide the effect of the shape of a valley cross-section on the earthquake hydrodynamic pressures into two parts: one due to the solidity ratio s=A/Bh, or the cross-sectional area A divided by the free-surface width B and the depth h, and the other due to the width-depth ratio w=B/H. As the ordinary cross-sections of valleys are essentially symmetric, three basic shapes, namely, rectangle, semi-circle, and isosceles right triangle, are chosen for analysis. Earthquakes in both the longitudinal and the laterally transverse direction with respect to the valley axis are treated. The fundamental equations and hypotheses used follow those of Westergaard and Werner, and also borrowed from the two authors are the expressions for pressures on rectangular and semicircular dam surfaces due to longitudinal earthquake. Equation (8) gives a definition of the wave number c per unit length as related to the density ρand the bulk elastic modulus K of the water, the velocity ν_s, of sound in the water, and the circular frequency ω and the period T of the assumed simple harmonic seismic waves. In Eqs. (9) and (10) are introduced for the pressures and moments on dam surfaces the pressure coefficient C_p, the total pressure coefficient C_p, the coefficient of moment about the water line C_(MZ) due to longitudinal earthquake; and the corres ponding C'_p, C'_p, and C'_(MZ) and the coefficient of moment about the center line C'_MY due to transverse earthquake. In these equations, the symbol α denotes the acceleration coefficient; γ, the specific weight of water; A'=A/2, half the symmetric area; and b=B/2, the half width. Equations (11a) to (11c) and (12a) to (12d) are the derived expressions of the various coefficients for rectangular surface; Eqs. (13a) to (13c) and (14a) to (14d) are the ones for semi-circular surface, with the reduced Eqs. (14'a) to (14'd) in the condition c=0; and Eqs. (15a) to (15c) and (16a) to (16c), and also the reduced Eqs. (16'a) to (16'c) for c=0, are for isosceles right triangular surface. Figure 2 shows the effect of s on the conditions of resonances, for which the upper and the lower two curves correspond respectively to the case of transverse and longitudinal earthquake. Here the units of h and T refer respectively to meter and second.In Fig. 5 is shown the effect of s on the magnitudes of the various pressure and moment coefficients when the compressibility of water is ignored. Although this figure is for ω=2, it is considered that C_p and C_(MZ) for longitudinal earthquake depend on s only,and Fig. 5 alone is sufficient for their estimation whatever be the value w. Figure 6 shows the effect of ω on the various coefficients for transverse earthquakes when c=0 and s=1. Because C' is influenced by both s and w, it is suggested that when a C' is to be estimated, it is first obtained from Fig. 5 for the given s and then multiplied by the corresponding one obtained from Fig. 6 for the given w and again divided by C' for ω=2 from Fig. 6.

本文研究了河谷断面形式对铅直坝面上地震动水压力的影响。断面形式包括矩形、半圆形和二等边直角三角形,地震方向包括沿河谷的纵向和垂直于河谷的横向。给出了相应的压力分布、总压力和力矩的表示式,并进行了计算。引入了河谷断面充实比数和宽深比数来作为河谷断面形式的代表,并绘出了总压力和力矩系数随此二比数变化的曲线组,以供设计参考。

The design criteria for protecting a spillway surface from cavitation erosion are discussed. The spillway profile first of equal cavitation number and then of equal safety pressure are analyzed, and two corresponding curves for the protecting purpose obtained. Although the fundamental equations derived for their expressions come to be identical, the constants contained therein are different. A numerical integration method for solving the equations is given, which simple in form gives accurate results,...

The design criteria for protecting a spillway surface from cavitation erosion are discussed. The spillway profile first of equal cavitation number and then of equal safety pressure are analyzed, and two corresponding curves for the protecting purpose obtained. Although the fundamental equations derived for their expressions come to be identical, the constants contained therein are different. A numerical integration method for solving the equations is given, which simple in form gives accurate results, and is expected to be common in use for calculating spillway profiles.Finally, demonstrative calculations are made for two actual spillway profiles, both of high dams. Evidently, the profiles calculated are very effective even with large unit-width overflow discharges in avoiding erosion from cavitation, because the cavitation number of the overflow can be raised by 40~49% and the effective drop of head diminished by 24~40% by the profiles.

本文对溢流面减蚀体型的设计准则进行了探讨.对等空穴数及等安全压力两种减蚀概念的体型进行了分析,得到了两类减蚀体型曲线,但其基本方程的形式却完全相同,只是其中的设计常数不同.文中提出的数值积分法精度较高,计算简便,可期具有一定的普遍适用意义.文末对两项大型工程的泄水建筑物所作的分析计算表明:在大单宽流量下减蚀曲线的效果显著,空穴数可提高40~69%左右,有效落差可降低24~40%.

 
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