Fluids
AP Physics 1 Topic 8 8:06 English narration · English + 中文 subtitles burned in
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Transcript
A steel nail dropped into water goes straight to the bottom.
一枚钢钉丢进水里，会直接沉到底。
Now look at this ship.
现在看这艘船。
It is built from the same steel, tens of thousands of tonnes of it, and it floats.
它用的是同样的钢材， 好几万吨重，可是它浮着。
Same metal, opposite result.
同样的金属，结果完全相反。
So the material by itself decides nothing.
所以，光看材料是决定不了的。
The fluid decides.
真正起作用的是流体。
That is what this unit is about.
这就是本单元要讲的内容。
Here is the plan.
这是今天的安排。
First density: how tightly matter is packed.
首先是密度：物质堆得有多紧。
Then pressure, and how it grows with depth.
然后是压强，以及它如何随深度增大。
Then buoyancy, the upward push a fluid gives, and Archimedes' principle.
接着是浮力，也就是流体给出的向上的推力，还有阿基米德原理。
And finally flow, with the two conservation laws that govern it.
最后是流动，以及支配它的两条守恒定律。
Four ideas, and the exam asks about all four.
四个概念，考试四个都会考。
So what is a fluid?
那么，什么是流体？
Watch the particles.
看这些粒子。
In a solid they are locked in place and only vibrate, so the shape is fixed.
在固体里，它们被锁在原位，只能振动，所以形状是固定的。
Heat it, and they start sliding past each other. That is a liquid.
加热之后，它们开始互相滑动，这就是液体。
Heat it more, and they fly apart and fill the whole container. That is a gas.
再加热，它们四散开来，填满整个容器， 这就是气体。
Liquids and gases both flow, so both are fluids.
液体和气体都能流动，所以两者都是流体。
A fluid has no fixed shape.
流体没有固定的形状。
A fluid is described first by its density.
描述流体，首先看它的密度。
Look at the two boxes: same size, but the right one has more particles packed inside, so its density is higher.
看这两个盒子：大小一样，但右边装进了更多粒子， 所以密度更大。
Density is mass divided by volume, and it belongs to the substance, not the amount.
密度等于质量除以体积，它属于这种物质，而不取决于数量多少。
Throughout, we assume an ideal fluid: incompressible — it cannot be squashed, whatever the pressure — and with no viscosity, no internal friction.
整个单元我们都假设是理想流体：不可压缩——无论压强多大都压不缩——而且没有黏度，也就是没有内部摩擦。
Now pressure.
现在讲压强。
Pressure is the perpendicular force on a surface, divided by the area it is spread over, in pascals.
压强是垂直作用在表面上的力，除以它分布的面积，单位是帕斯卡。
The same force on a smaller area gives a bigger pressure, which is why a sharp knife cuts.
同样大的力压在更小的面积上，压强就更大，这就是刀要磨快的原因。
Two exam points.
两个考点。
Pressure is a scalar, with no direction of its own.
压强是标量，没有自己的方向。
And in a fluid that push is the sum of countless particle collisions.
而在流体里，这个推力是无数粒子碰撞的总和。
Why does pressure grow as you go deeper?
为什么越深压强越大？
Because of the weight of the fluid above you.
因为上方流体的重量压着你。
Picture a column of liquid standing on a small area.
想象一根液柱立在一小块面积上。
The deeper the point, the taller that column and the heavier it is.
位置越深，这根柱子越高，也就越重。
So the extra pressure is the density, times the strength of gravity, times the depth.
所以多出来的压强，等于密度， 乘以重力强度，再乘以深度。
The total is the surface pressure plus that extra amount.
总压强就是液面压强加上多出来的这一部分。
Two facts the exam loves.
两个考试爱考的事实。
First, at a point in a fluid the pressure pushes equally in every direction, always at right angles to the surface it meets.
第一，在流体中的某一点，压强朝各个方向都一样大， 而且总是垂直作用在它遇到的表面上。
Second, it depends only on depth and density.
第二，它只取决于深度和密度。
Not on the shape of the container, not on its width, not on how much liquid there is.
与容器的形状无关，与它有多宽无关，也与液体有多少无关。
A thin tube and a huge tank filled to the same depth have the same pressure at the bottom.
一根细管和一个大水箱，只要装到同样的深度，底部的压强就相同。
Now a distinction AP asks about directly.
现在讲一个AP会直接考的区分。
Gauge pressure is only the extra amount the fluid column adds.
表压只是流体柱额外加上去的那一部分。
Absolute pressure is the total, including the atmosphere on the surface.
绝对压强是总量，包括液面上的大气。
Think about a car tyre.
想想汽车轮胎。
The gauge reads two hundred kilopascals, but the air inside is really at about three hundred, because the atmosphere already supplies a hundred.
压力表读数是二百千帕，但轮胎里的空气其实大约是三百千帕， 因为大气本身已经贡献了一百千帕。
Unless the question says gauge, add the atmosphere.
除非题目说的是表压，否则要把大气加上。
That hundred kilopascals is not a guess.
那一百千帕不是猜的。
This is a barometer.
这是一只气压计。
A sealed metal box inside flexes as the air outside pushes harder or softer, and the needle turns.
里面的密封金属盒， 会随着外面空气压得更重或更轻而形变，指针随之转动。
At sea level it reads about one atmosphere.
在海平面，它的读数大约是一个大气压。
A diver is ten metres below the surface of water.
一位潜水员在水面下十米处。
The density of water is one thousand kilograms per cubic metre, and the surface pressure is one times ten to the fifth pascals.
水的密度是每立方米一千千克， 水面压强是一乘以十的五次方帕。
Find the total pressure.
求总压强。
Start from the depth equation.
先用深度公式。
The extra pressure from the water is one thousand, times nine point eight, times ten: ninety-eight thousand pascals.
水带来的额外压强是一千，乘以九点八，再乘以十：九万八千帕。
Now add the surface pressure.
现在加上水面压强。
The total is one point nine eight times ten to the fifth pascals.
总压强是一点九八乘以十的五次方帕。
Every ten metres of water adds about one atmosphere.
每十米深的水，大约多加一个大气压。
So where does the upward push come from?
那么，向上的推力从哪里来？
From the pressure difference we just found.
来自我们刚刚求出的压强差。
The bottom of the object is deeper than the top, so the fluid pushes up on the bottom harder than it pushes down on the top.
物体的底面比顶面更深，所以流体向上顶底面的力，比向下压顶面的力更大。
The sideways pushes cancel.
两侧的推力互相抵消。
What is left is a net upward force: the buoyant force.
剩下的就是一个向上的合力：浮力。
It is not a new force. It is pressure, doing what pressure does with depth.
它不是新的力， 它就是压强，只是压强随深度在变化。
Archimedes found how big that force is, and the answer is beautifully simple.
阿基米德算出了这个力有多大，答案漂亮得出奇。
The buoyant force equals the weight of the fluid the object pushes out of the way.
浮力等于物体排开的那部分流体的重量。
Shove aside two kilograms of water, and the water pushes back with the weight of two kilograms.
排开两千克的水， 水就以两千克的重量顶回来。
On screen: the fluid's density, times the volume displaced, times gravity.
屏幕上写的是：流体的密度，乘以排开的体积， 再乘以重力强度。
That density is the fluid's, never the object's.
这个密度是流体的，绝不是物体的。
Compare the two forces.
比较这两个力。
Cork is very light for its size, so only a quarter goes under before the push balances its weight.
软木相对体积很轻，所以只有四分之一沉下去， 浮力就和重量平衡了。
Wood is denser, so it settles lower.
木头密度更大，沉得更低。
Steel is denser than water, so buoyancy can never win: it sinks.
钢比水密度大， 浮力永远赢不了：它沉底。
The rule: for anything floating, the fraction below the surface equals its density divided by the fluid's.
规律是：对任何漂浮的物体， 水面以下的比例，等于它的密度除以流体的密度。
So how does a steel ship float?
那钢船为什么能浮？
A ship is mostly air inside. The nail is not.
因为船里主要是空气，而钢钉里没有。
Let's prove it.
我们来证明它。
A block of density six hundred floats in water, density one thousand.
一个密度六百的方块浮在水里，水的密度是一千。
What fraction sits below the surface?
水面以下的部分占多大比例？
Pause and try it.
先暂停，自己试一试。
Ready?
好了吗？
Floating means the forces balance, so buoyancy equals weight.
漂浮意味着受力平衡， 所以浮力等于重力。
Write both sides out: the water's density, times the submerged volume, times gravity, equals the block's density, times the whole volume, times gravity.
把两边都写出来：水的密度，乘以浸入的体积，乘以重力强度， 等于方块的密度，乘以它的总体积，乘以重力强度。
Gravity cancels, so the fraction is six hundred over one thousand.
重力强度约掉， 所以这个比例是六百比一千。
Sixty percent is under.
百分之六十在水面以下。
An iceberg, at nine hundred, hides nine tenths.
冰山密度九百，藏起了十分之九。
A floating object displaces its own weight.
漂浮的物体排开的流体重量等于它自己的重量。
Last part: fluids that move.
最后一部分：会流动的流体。
Squeeze a hose and the water shoots out faster.
捏一下水管，水就会喷得更快。
Why?
为什么？
Because the same amount of water must get through every second.
因为每一秒钟必须有同样多的水通过。
That is continuity, and it is conservation of mass.
这就是连续性，本质是质量守恒。
Area times speed is the same everywhere along the pipe, so if the area shrinks, the speed must grow by the same factor.
沿着管道，面积乘以速度处处相同，所以面积变小，速度就必须以同样的倍数变大。
The second law is Bernoulli's equation, conservation of energy per unit volume.
第二条定律是伯努利方程，也就是单位体积的能量守恒。
Along a streamline, the pressure, plus the speed term, plus the height term, stays constant.
沿着一条流线， 压强加上速度项，再加上高度项，保持不变。
Look at the narrow part of this pipe.
看这根管子的窄处。
The fluid there moves fastest, so its speed term is biggest, which forces its pressure to be smallest.
那里的流体速度最快，速度项最大，这就迫使压强最小。
Faster flow, lower pressure.
流得越快，压强越低。
That is what lifts a wing.
飞机机翼的升力就是这么来的。
Water flows at two point zero metres per second through a pipe of cross-section zero point zero one zero square metres.
水以每秒二点零米的速度，流过横截面积零点零一零平方米的管子。
The pipe narrows to zero point zero zero four zero square metres.
管子随后收窄到零点零零四零平方米。
How fast is the flow?
水流多快？
The width changed, so start with continuity.
宽度变了，所以先用连续性方程。
Rearrange for the second speed: the first area times the first speed, divided by the second area.
把第二个速度解出来：第一个面积乘以第一个速度，再除以第二个面积。
That gives five point zero metres per second.
结果是每秒五点零米。
And here is the exam skill.
这里有一个考试技巧。
Width changes: continuity first.
宽度变了：先用连续性方程。
Bernoulli only when a pressure is asked for.
问压强时，才用伯努利方程。
Three marks students lose.
三个学生常丢的分。
One: fluid pressure depends on depth only, never on the shape or width of the container.
第一，流体压强只取决于深度， 与容器的形状或宽度无关。
Two: the buoyant force uses the fluid's density and the volume displaced, not the object's density and not its whole volume.
第二，浮力用的是流体的密度和排开的体积， 不是物体的密度，也不是它的总体积。
Three: a narrower pipe means faster flow, and faster flow means lower pressure.
第三，管子越窄，流体流得越快， 而流得越快，压强就越低。
Students reverse that constantly.
这一点学生总是记反。
Get these right, and this unit is yours.
把这些做对，这个单元就是你的了。