Pressure | 压强

📚 Pressure | 压强

Pressure is a core idea in CIE A-Level Physics because it links mechanics, fluids and thermal physics. Understanding pressure as force per unit area allows you to explain everything from sharp knives to deep-sea diving and from mercury barometers to the behaviour of trapped gases.

压强是 CIE A-Level 物理的核心概念之一，因为它把力学、流体和热物理联系起来。将压强理解为作用在单位面积上的力，可以帮助你解释从锋利的刀、深海潜水到水银气压计以及密闭气体行为等各种现象。

---

1. Defining Pressure | 压强的定义

Pressure is defined as the normal force acting per unit area on a surface. If a force F acts perpendicularly to a surface of area A, the average pressure p is given by:

压强定义为垂直作用在单位面积上的力。如果力 F 垂直作用在面积为 A 的表面上，平均压强 p 为：

p = F / A

In this equation, F is measured in newtons (N) and A in square metres (m²). The SI unit of pressure is thus the pascal (Pa), where 1 Pa = 1 N m⁻².

在此公式中，F 的单位是牛顿 (N)，A 的单位是平方米 (m²)。因此压强的国际单位是帕斯卡 (Pa)，1 Pa = 1 N m⁻²。

A key point is that pressure depends on the area over which a force is spread. The same force can produce a large pressure if the area is small, or a small pressure if the area is large.

关键点是压强取决于力所分布的面积。相同的力，如果面积很小，会产生很大的压强；如果面积很大，则压强很小。

---

2. Pressure Units and Scalar Nature | 压强单位与标量性质

The pascal is a derived SI unit. In base units, 1 Pa = 1 kg m⁻¹ s⁻² because 1 N = 1 kg m s⁻² and pressure is force divided by area.

帕斯卡是国际单位制中的导出单位。用基本单位表示，1 Pa = 1 kg m⁻¹ s⁻²，因为 1 N = 1 kg m s⁻²，而压强是力除以面积。

Although force is a vector, pressure itself is treated as a scalar quantity in most A-Level calculations. This is because the direction of the force is always normal to the surface, so pressure describes the magnitude of that normal force per unit area.

虽然力是矢量，但在大多数 A-Level 计算中，压强本身被视为标量。这是因为力的方向总是垂直于表面，所以压强描述的是单位面积上法向力的大小。

Common multiples such as kPa and MPa are often used: 1 kPa = 10³ Pa and 1 MPa = 10⁶ Pa.

常用倍数单位如 kPa 和 MPa：1 kPa = 10³ Pa，1 MPa = 10⁶ Pa。

---

3. Pressure in a Fluid at Rest | 静止流体中的压强

In a stationary fluid, pressure acts equally in all directions at a given point. It increases with depth because the weight of the fluid above exerts a downward force on the layers below.

在静止流体中，某一点的压强向各个方向作用相等。压强随深度增加，因为上方流体的重量对下方流体层施加向下的力。

For a liquid of density ρ in a uniform gravitational field g, the pressure difference between two points separated by vertical height h is:

对于密度为 ρ、处在均匀重力场 g 中的液体，垂直高度差为 h 的两点之间的压强差为：

Δp = ρgh

This equation gives the additional pressure due to the liquid alone, sometimes called the hydrostatic pressure. It does not include the atmospheric pressure acting on the free surface.

该方程给出的是仅由液体本身产生的附加压强，有时称为流体静压强。它不包括作用在自由表面上的大气压。

---

4. Deriving p = ρgh | 推导 p = ρgh

Consider a vertical column of liquid with cross-sectional area A and height h. The volume of the column is V = Ah, and its mass is m = ρV = ρAh.

考虑一个截面积为 A、高度为 h 的竖直液柱。液柱的体积为 V = Ah，质量为 m = ρV = ρAh。

The weight of this column is W = mg = ρAhg. This weight is supported by the base of the column, so the pressure at the bottom due to the liquid is:

该液柱的重量为 W = mg = ρAhg。这个重量由液柱底部支承，因此底部由液体产生的压强为：

p = W / A = ρAhg / A = ρgh

This derivation shows that hydrostatic pressure depends only on density, gravitational field strength and vertical depth, not on the cross-sectional area or total volume of the liquid.

这个推导表明，流体静压强只取决于密度、重力场强度和垂直深度，而与液体的截面积或总体积无关。

A practical consequence is that at the same depth, pressure is the same regardless of the shape of the container, which is often called the hydrostatic paradox.

一个实际结论是，在相同深度处，无论容器形状如何，压强都相同，这常被称为流体静力学佯谬。

---

5. Density and Pressure Calculations | 密度与压强计算

Density ρ is defined as mass per unit volume: ρ = m / V. Its SI unit is kg m⁻³. For water, ρ ≈ 1000 kg m⁻³, and for mercury, ρ ≈ 13 600 kg m⁻³.

密度 ρ 定义为单位体积的质量：ρ = m / V。其国际单位是 kg m⁻³。水的密度约为 1000 kg m⁻³，水银的密度约为 13 600 kg m⁻³。

When calculating total pressure at a point in a liquid open to the atmosphere, you must add atmospheric pressure pₐ to the liquid pressure:

计算暴露在大气中的液体内某一点的总压强时，必须将大气压 pₐ 与液体压强相加：

p_total = pₐ + ρgh

Worked example: find the total pressure 5.0 m below the surface of fresh water. Use ρ = 1000 kg m⁻³, g = 9.81 m s⁻² and pₐ = 1.01 × 10⁵ Pa.

例题：求淡水表面下 5.0 m 处的总压强。取 ρ = 1000 kg m⁻³，g = 9.81 m s⁻²，pₐ = 1.01 × 10⁵ Pa。

ρgh = 1000 × 9.81 × 5.0 = 49 050 Pa, so p_total ≈ 1.01 × 10⁵ + 4.91 × 10⁴ = 1.50 × 10⁵ Pa.

ρgh = 1000 × 9.81 × 5.0 = 49 050 Pa，所以 p_total ≈ 1.01 × 10⁵ + 4.91 × 10⁴ = 1.50 × 10⁵ Pa。

---

6. Atmospheric Pressure | 大气压强

The atmosphere exerts pressure on every surface at the Earth’s surface due to the weight of the air above. Standard atmospheric pressure at sea level is about 1.01 × 10⁵ Pa, also written as 101 kPa.

大气由于上方空气的重量，对地球表面的每个表面都施加压强。海平面处的标准大气压约为 1.01 × 10⁵ Pa，也写作 101 kPa。

Atmospheric pressure decreases with altitude because the column of air above becomes shorter and less dense. This variation is important for weather, aviation and barometric measurements.

大气压随高度增加而减小，因为上方的空气柱变短且密度变小。这种变化对天气、航空和气压测量都很重要。

In many liquid pressure problems, atmospheric pressure is treated as constant over small depth changes, but for large altitude changes it cannot be ignored.

在许多液体压强问题中，当深度变化较小时，大气压可视为恒定；但在高度变化很大时，就不能忽略其变化。

---

7. Mercury Barometer | 水银气压计

A mercury barometer measures atmospheric pressure using a vertical glass tube closed at one end and filled with mercury, then inverted into a mercury reservoir. The space above the mercury column is a vacuum, so the column height h is directly related to atmospheric pressure.

水银气压计利用一根一端封闭、充满水银后倒置于水银槽中的竖直玻璃管来测量大气压。水银柱上方为真空，因此水银柱高度 h 与大气压直接相关。

At equilibrium, atmospheric pressure pₐ equals the hydrostatic pressure of the mercury column:

平衡时，大气压 pₐ 等于水银柱产生的流体静压强：

pₐ = ρ_Hg g h

At standard atmospheric pressure, h ≈ 0.760 m = 760 mm. Using ρ_Hg = 13 600 kg m⁻³ and g = 9.81 m s⁻² gives pₐ ≈ 1.01 × 10⁵ Pa.

在标准大气压下，h ≈ 0.760 m = 760 mm。代入 ρ_Hg = 13 600 kg m⁻³ 和 g = 9.81 m s⁻²，得到 pₐ ≈ 1.01 × 10⁵ Pa。

Because mercury is very dense, the barometer tube can be conveniently short. A water barometer would need to be about 10.3 m tall, which is impractical.

由于水银密度很大，气压计的管子可以较短。如果用水做气压计，则需要约 10.3 m 高，这不切实际。

---

8. Manometer and Pressure Difference | U形管压力计与压强差

A manometer is a U-shaped tube containing a liquid such as mercury or water. One side is connected to the gas whose pressure is to be measured, and the other side is open to the atmosphere.

U 形管压力计是一根含有水银或水等液体的 U 形管。一端连接待测压强的气体，另一端与大气相通。

If the gas pressure is greater than atmospheric pressure, the liquid level on the open side rises. The pressure difference is given by the height difference h between the two liquid levels:

如果气体压强大于大气压，开口侧的液面会升高。压强差由两侧液面的高度差 h 给出：

Δp = ρ g h

The absolute gas pressure is then p_gas = pₐ + ρgh if the gas side is lower. If the gas pressure is below atmospheric pressure, the difference is subtracted: p_gas = pₐ − ρgh.

如果气体侧液面较低，则气体的绝对压强为 p_gas = pₐ + ρgh。如果气体压强低于大气压，则要减去差值：p_gas = pₐ − ρgh。

Manometers measure gauge pressure, which is the difference between an absolute pressure and atmospheric pressure. Many industrial gauges are calibrated in this way.

U 形管压力计测量的是表压，即绝对压强与大气压之差。许多工业压力表就是这样标定的。

---

9. Boyle’s Law and Gas Pressure | 玻意耳定律与气体压强

For a fixed mass of an ideal gas at constant temperature, the pressure p and volume V are inversely proportional. This is Boyle’s law:

对于一定质量、温度不变的理想气体，压强 p 与体积 V 成反比。这就是玻意耳定律：

pV = constant or p₁V₁ = p₂V₂

This law can be understood using the kinetic theory of gases: if the volume is reduced while temperature stays constant, gas molecules hit the container walls more frequently, so the pressure rises.

这一规律可以用气体分子动理论来理解：如果温度不变、体积减小，气体分子会更频繁地撞击容器壁，因此压强升高。

Boyle’s law is often tested in pressure-related experiments, such as trapping air in a syringe or using a gas column with an oil or mercury trap. A graph of p against 1/V gives a straight line through the origin.

玻意耳定律常在与压强相关的实验中考查，例如用注射器封住空气，或用油或水银封住一段气柱。p 对 1/V 作图会得到一条过原点的直线。

---

10. Pressure and Kinetic Theory | 压强与分子动理论

In the kinetic theory model, a gas consists of many small particles in random motion. The pressure exerted by a gas on the walls of its container arises from the rate of change of momentum of particles colliding with the

Published by TutorHao | A-Level Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）