استمرارية المائع، طاقة الضغط والتدفق اللزج
GRE Subject Test · GRE Physics الموضوع 28 5:29 سرد باللغة الإنجليزية · ترجمة مدمجة بالإنجليزية + الصينية
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A narrow pipe carries the same steady flow as the wide pipe feeding it, yet the pressure inside it depends on both the faster speed and the viscous losses.
细管中的稳定流量与给它供水的粗管相同，但管内压强既取决于更快的流速，也取决于黏性损失。
This topic combines continuity with pressure, height and kinetic energy, uses Bernoulli only under its conditions, and separates viscous from turbulent flow with the Reynolds number.
本主题把连续性与压强、高度和动能结合起来，只在满足条件时使用伯努利方程，并用雷诺数区分黏性流动和湍流。
For steady flow, the mass passing successive cross-sections per unit time is equal: rho A v is constant.
对于稳定流动，单位时间内通过连续截面的质量相等：rho A v 为常数。
An incompressible liquid has nearly constant density, so Q equals A v is the volume flow rate.
不可压缩液体的密度几乎恒定，因此 Q 等于 A 乘以 v，即为体积流量。
Halving pipe radius quarters area and multiplies mean speed by four for the same Q.
若将管道半径减半，横截面积变为四分之一，而相同流量 Q 下的平均流速则增至四倍。
Pressure does not determine Q without a model of the rest of the system.
若无系统其余部分的模型，压力无法单独决定流量。
In a stationary liquid, d p by d z equals minus rho g, with z upward; therefore pressure increases by rho g h a distance h below a surface.
在静止液体中，dp 对 dz 的导数等于负 rho g，其中 z 轴向上；因此，距表面下方深度 h 处，压力增加 rho g h。
Use absolute or gauge pressure consistently on both sides.
两侧须统一使用绝对压力或表压。
For steady, incompressible, inviscid motion along a streamline with no pump or dissipative loss, Bernoulli gives p plus rho v squared over 2 plus rho g z equals a constant.
对于沿流线的定常、不可压缩、无粘流动，且没有泵或耗散损失，伯努利方程给出 p 加 ρ v 平方除以 2 加 ρ g z 等于常数。
These three terms are energy per volume and have pressure units.
这三项都是单位体积的能量，单位与压强相同。
At equal height, larger speed requires smaller static pressure under these assumptions.
在这些假设下，同一高度处流速越大，静压越小。
A higher outlet also uses pressure and kinetic energy to gain gravitational energy.
较高的出口也要消耗压强能和动能来获得重力势能。
Bernoulli along one streamline need not imply the same constant on different streamlines in rotational flow.
在有旋流动中，沿一条流线成立的伯努利方程不意味着不同流线上的常数相同。
A stagnation point has v equal to zero and converts local speed energy to a pressure rise in the ideal model.
驻点处 v 等于零，在理想模型中局部的速度能转化为压强升高。
Viscosity transports momentum between neighbouring fluid layers.
粘性在相邻流体层之间传递动量。
For steady, fully developed laminar flow of a Newtonian incompressible liquid in a circular tube, Q equals pi R to the fourth delta p, over 8 eta L.
对于牛顿不可压缩液体在圆管中的定常、充分发展的层流，Q 等于 π 乘以 R 的四次方乘以 Δp，再除以 8 η L。
Here delta p is the pressure drop along the tube, eta the dynamic viscosity and L the tube length.
其中 Δp 是沿管的压降，η 是动力粘度，L 是管长。
Doubling the radius at fixed delta p, eta and L multiplies Q by sixteen.
在 Δp、η 和 L 不变时，半径加倍使 Q 变为十六倍。
Doubling Q at fixed geometry needs twice the pressure drop.
几何形状不变时，Q 加倍需要两倍的压降。
This viscous pressure loss cannot be added to a loss-free Bernoulli equation as though nothing changes; include a dissipative pressure or head loss, or use the viscous model.
这种粘性压强损失不能当作没有变化一样加进无损耗的伯努利方程；应计入耗散的压强或水头损失，或使用粘性模型。
The Reynolds number Re=ρvD/η compares inertial and viscous effects using characteristic speed v and length D.
雷诺数 Re 等于 rho v D 除以 eta，利用特征速度 v 和特征长度 D 比较惯性效应与粘性效应。
For a pipe use mean speed and internal diameter, not radius.
对于管道，请使用平均速度和内径，而非半径。
Re is dimensionless: density times speed times length has the same units as dynamic viscosity.
Re 是无量纲量：密度乘以速度乘以长度的单位与动力粘度相同。
Small Re favours viscous dominance; transition to turbulence depends on geometry and disturbances, so a single threshold is not a universal law.
小 Re 有利于粘性主导；向湍流的转变取决于几何形状和扰动，因此单一阈值并非普适定律。
Poiseuille scaling is not safe after assuming a turbulent flow.
在假设湍流后使用泊肃叶标度是不安全的。
Check volume continuity, sign of pressure change and the regime before selecting a formula.
在选择公式前，请检查体积连续性、压力变化的符号以及流动状态。
A steady horizontal flow passes from 4 square centimetres to 1 square centimetre at 1 metre per second.
稳定的水平流动从 4 平方厘米的截面流到 1 平方厘米的截面，入口速度为 1 米每秒。
Continuity gives v 2 equals A 1 v 1 over A 2: 4 metres per second.
由连续性，v2 等于 A1 v1 除以 A2：4 米每秒。
Bernoulli at one height gives p 1 minus p 2 equals one half rho times v 2 squared minus v 1 squared: one half times 1000 times 15, or 7500 pascals.
同一高度上，伯努利方程给出 p1 减 p2 等于二分之一 ρ 乘 v2 平方减 v1 平方：二分之一乘 1000 乘 15，即 7500 帕。
This assumes no pump, no viscous loss and no change in height.
这假设没有泵、没有黏性损失、也没有高度变化。
Two fully developed laminar Newtonian tubes of equal length and viscosity connect in series.
两根长度和粘度均相同的充分发展层流牛顿管串联连接。
Their radii are R and 2R.
它们的半径分别为 R 和 2R。
Find their pressure drop ratio and equivalent hydraulic resistance.
求它们的压降比和等效液压阻力。
Compare with connecting the same tubes in parallel.
再与这两根管子并联连接的情况进行比较。
Define the narrow tube's resistance as pressure drop over flow: 8 eta L over pi R to the fourth.
把细管的阻力定义为压降除以流量：8 η L 除以 π R 的四次方。
The wide tube has one sixteenth of it.
粗管的阻力是它的十六分之一。
In series the flow is common, so the pressure drops are 16 to 1 and the total is 17 sixteenths of the narrow resistance.
串联时流量相同，所以压降之比为 16 比 1，总阻力是细管阻力的十六分之十七。
In parallel the pressure drop is common, the flows are 1 to 16, and the equivalent resistance is one seventeenth.
并联时压降相同，流量之比为 1 比 16，等效阻力是十七分之一。
Continuity keeps Q constant across one steady pipe; Poiseuille compares Q between different systems at a specified pressure drop.
连续性方程保持单根稳定管道中的流量Q恒定。 泊肃叶定律则是在指定压降下比较不同系统中的流量Q。
State what is held fixed before comparing radius powers.
在比较半径的幂次之前，请先明确哪些量保持不变。
volume flow rate: Volume crossing a section per unit time, Q=Av for mean speed v.
体积流量：单位时间内穿过截面的体积，Q等于A乘v，其中v为平均速率。
dynamic viscosity: The coefficient relating shear stress to velocity gradient in a Newtonian fluid.
动力黏度：在牛顿流体中，将剪切应力与速度梯度联系起来的系数。
Retrieve the meanings without reading the definitions, then change a parameter in the original transfer and test the limiting case.
在不阅读定义的情况下回忆含义，然后改变原始传递中的一个参数并检验极限情况。