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🌊 伯努利方程计算器Bernoulli Equation Calculator
按伯努利方程 P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂，由其余量求截面 2 的压力、流速、高度，或截面 1 的压力，并给出总水头。Solve Bernoulli's equation P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ for the pressure, velocity or height at point 2, or the pressure at point 1, from the other values — with the total head.
使用说明与常见问题How-to & FAQ
「伯努利方程计算器」是什么？What is the Bernoulli Equation Calculator tool?
按伯努利方程 P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂，由其余量求截面 2 的压力、流速、高度，或截面 1 的压力，并给出总水头。Solve Bernoulli's equation P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ for the pressure, velocity or height at point 2, or the pressure at point 1, from the other values — with the total head.
如何使用「伯努利方程计算器」？How do I use the Bernoulli Equation Calculator tool?
在「伯努利方程计算器」中，填写「求」、「压力 P₁（Pa）」、「流速 v₁（m/s）」、「高度 h₁（m）」、「压力 P₂（Pa）」等参数，结果会随输入实时计算并显示在下方。In the Bernoulli Equation Calculator: Fill in "Solve for", "Pressure P₁ (Pa)", "Velocity v₁ (m/s)", "Height h₁ (m)", "Pressure P₂ (Pa)"; results are recalculated instantly as you type.
伯努利方程是什么？What is Bernoulli's equation?
对理想流体（不可压缩、无黏性、定常流动）沿同一流线：P + ½ρv² + ρgh = 常数。静压、动压和位压之和保持不变，所以流速变大处压力降低，位置升高处压力也降低。For an ideal fluid (incompressible, inviscid, steady flow) along a streamline, P + ½ρv² + ρgh is constant. Static, dynamic and elevation pressure add up to the same total, so pressure drops where the flow speeds up or rises.
总水头是什么？What is total head?
把各项除以 ρg 得到以长度表示的能量：H = P/(ρg) + v²/(2g) + h，分别叫压力水头、速度水头和位置水头。理想情况下两个截面的总水头相等。Dividing each term by ρg expresses the energy as a height: H = P/(ρg) + v²/(2g) + h — the pressure, velocity and elevation heads. In the ideal case both points have the same total head.
压力用绝对压力还是表压？Absolute or gauge pressure?
都可以，只要两个截面用同一种。结果与所用基准一致；表压可以为负（真空）。实际管道有摩擦损失，需要在截面 2 一侧加上水头损失项，本工具未计入。Either, as long as both points use the same one; the answer comes out on the same basis, and gauge pressure can be negative (vacuum). Real pipes lose head to friction, which would add a loss term on the point-2 side; that is not included here.
计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?
「伯努利方程计算器」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Bernoulli Equation Calculator uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.
「伯努利方程计算器」免费吗？需要注册吗？Is the Bernoulli Equation Calculator free? Do I need an account?
「伯努利方程计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Bernoulli Equation Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.