Pressure · 压强
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| pressure/ˈpreʃə/ | 压强 | yā qiáng |
| pascal/ˈpæskl/ | 帕斯卡 | pà sī kǎ |
| fluids/ˈfluːɪdz/ | 流体 | liú tǐ |
Why a sharp knife cuts
- Press a blunt stick into your hand — nothing happens. A sharp pin at the same push hurts.
- The force is the same; what changed is the area it acts on.
- That idea is pressure 压强 — and it explains knives, snowshoes, and the deep sea.
为什么一把锋利的刀能切
- 把一根钝的棍子压进你的手——什么都不发生。一根锋利的针在同样的推力下会疼。
- 力是相同的;变化的是它作用的面积。
- 那个想法是压强(pressure)——它解释刀、雪鞋和深海。
What is pressure?
- Pressure is the force pressing on each unit of area:
- The unit is the pascal 帕斯卡 (Pa); $1\ \text{Pa} = 1\ \text{N/m}^2$.
- Same force, smaller area → bigger pressure.
什么是压强?
- 压强是压在每单位面积上的力:
- 单位是帕斯卡(pascal,Pa);$1\ \text{Pa} = 1\ \text{N/m}^2$。
- 相同的力,更小的面积 → 更大的压强。
Pressure · 压强
p = ρg·h
Pressure in a liquid is proportional to depth. · 一种液体中的压强与深度成正比。
A box pushes down with a force of $200\ \text{N}$ over an area of $0.50\ \text{m}^2$. What is the pressure, in Pa? · 一个盒子以 $200\ \text{N}$ 的力在 $0.50\ \text{m}^2$ 的面积上向下压。压强是多少,以 Pa 计?
$p = \dfrac{F}{A} = \dfrac{200}{0.50} = 400\ \text{Pa}$. · $p = \dfrac{F}{A} = \dfrac{200}{0.50} = 400\ \text{Pa}$。
Why area matters
- A sharp knife or a drawing pin has a tiny area, so it makes a huge pressure and cuts or pierces easily.
- Snowshoes and tractor tyres have a large area, so they make a small pressure and do not sink in.
- Camels' wide feet work the same way on soft sand.
Same force, different area → different pressure. The narrow base sinks; the wide base stays on top.
Worked example. A 600 N person stands on one foot (area $0.02\ \text{m}^2$). Pressure $= \dfrac{600}{0.02} = 30\,000\ \text{Pa}$. On both feet (area $0.04\ \text{m}^2$): pressure $= 15\,000\ \text{Pa}$ — half as much.
Pressure acts in all directions in fluids 流体. When you dive deep, water pushes on your ears from every side — not just from above. The formula $\Delta p = \rho g\,\Delta h$ gives the pressure at that depth in all directions.
为什么面积重要
- 一把锋利的刀或一个图钉有一个微小的面积,所以它产生一个巨大的压强并容易切或刺穿。
- 雪鞋和拖拉机轮胎有一个大面积,所以它们产生一个小压强且不会陷进去。
- 骆驼的宽脚在软沙上以相同的方式起作用。
相同的力,不同的面积 → 不同的压强。窄底座陷下去;宽底座留在顶上。
例题。 一个 600 N 的人单脚站立(面积 $0.02\ \text{m}^2$)。压强 $= \dfrac{600}{0.02} = 30\,000\ \text{Pa}$。双脚(面积 $0.04\ \text{m}^2$):压强 $= 15\,000\ \text{Pa}$——一半那么多。
压强在流体中向所有方向作用。 当你潜入深处时,水从每一边压你的耳朵——不只是从上面。公式 $\Delta p = \rho g\,\Delta h$ 给出在那个深度所有方向上的压强。
Why does a sharp knife cut better than a blunt one (with the same push)? · 为什么一把锋利的刀比一把钝的切得更好(用相同的推力)?
Same force on a tiny area means a very large pressure ($p = F/A$), so it cuts easily. · 相同的力在一个微小的面积上意味着一个非常大的压强($p = F/A$),所以它容易切。
Snowshoes stop you sinking into snow because they: · 雪鞋阻止你陷进雪里,因为它们:
A larger area means a smaller pressure for the same weight, so you do not sink in. · 一个更大的面积意味着相同重量下一个更小的压强,所以你不陷进去。
Pressure in a liquid
- In a liquid, pressure increases with depth and with the liquid's density:
- It acts in all directions, not just downward.
- This is why a dam is built thicker at the bottom, where the water pressure is greatest, and why your ears hurt deep underwater.
The deeper the liquid, the greater the pressure, so the outward push on the wall grows with depth
液体中的压强
- 在一种液体中,压强随深度增加并随液体的密度增加:
- 它向所有方向作用,不只是向下。
- 这就是为什么一座坝建得底部更厚,那里水压最大,以及为什么你的耳朵在水下深处疼。
液体越深,压强越大,所以对墙壁向外的推力随深度增大
Pressure in a liquid acts in all directions, not just downward. · 一种液体中的压强向所有方向作用,不只是向下。
A liquid pushes equally in all directions at a given depth — that is why it presses on the sides of a container too. · 一种液体在一个给定的深度向所有方向相等地推——这就是为什么它也压在一个容器的侧面上。
Find the extra pressure $2.0\ \text{m}$ deep in water ($\rho = 1000\ \text{kg/m}^3$, $g = 9.8\ \text{N/kg}$), in Pa. · 求水中 $2.0\ \text{m}$ 深处的额外压强($\rho = 1000\ \text{kg/m}^3$,$g = 9.8\ \text{N/kg}$),以 Pa 计。
$\Delta p = \rho g\,\Delta h = 1000 \times 9.8 \times 2.0 = 19\,600\ \text{Pa}$. · $\Delta p = \rho g\,\Delta h = 1000 \times 9.8 \times 2.0 = 19\,600\ \text{Pa}$。
You've got it
- pressure $p = \dfrac{F}{A}$, unit the pascal ($1\ \text{Pa} = 1\ \text{N/m}^2$)
- small area → big pressure (knife); large area → small pressure (snowshoes)
- in a liquid, pressure rises with depth and density: $\Delta p = \rho g\,\Delta h$, acting in all directions
你掌握了
- 压强 $p = \dfrac{F}{A}$,单位帕斯卡($1\ \text{Pa} = 1\ \text{N/m}^2$)
- 小面积 → 大压强(刀);大面积 → 小压强(雪鞋)
- 在一种液体中,压强随深度和密度上升:$\Delta p = \rho g\,\Delta h$,向所有方向作用