压力随深度的变化
可以合理地假设，一个人进入液体或气体的深度越深，周围流体施加在他身上的压力就越高。压力增加的原因是，一个人进入液体越深，他身上的液体就越多，因此他的体重就越大。
压力：施加的力与施加力的表面积之比称为压力。液体施加的压力称为静水压力。压力的国际单位制单位是帕斯卡。
流体压力
施加压力时，固体不会改变形状，而流体显然不是这样。在密闭容器中，流体压力可由重力、加速度或力产生。由于流体没有固定的形式，因此流体在所有方向上的作用相同。当你给瓶子装满水时，水的重量会均匀地作用在瓶子的两侧。
力总是垂直于容器的表面施加。这可以在气球中看到。当你用空气填充气球时，你会注意到它均匀地增长，没有一侧比另一侧充气更多。容器中的液体也表现出这种行为。
静水压力
The hydrostatic pressure is the pressure exerted by a fluid in equilibrium owing to gravity at any given period. When a downward force is applied, hydrostatic pressure is proportional to the depth measured from the surface as the weight of the fluid increases.
流体在所有方向上施加相等的压力。由于这条规则，另一个有趣的事件发生了。当我们检查瓶子顶部的水层时，它施加的压力作用在容器的边缘、顶部的空气表面和底部的水层上。当我们从上到下向下移动瓶子时，顶层对底部施加的压力会增加。
由于该过程，容器底部的流体比其上方的流体承受更高的压力。
压力随深度的变化
请看下图以获取容器的示例。其内部流体的重量由其底部支撑。让我们看看液体的重量对底部施加了多大的压力。流体重量“mg”除以面积“A”等于压力。
Weight of the fluid, W = m g
Mass of the fluid is equal to product of volume and density of substance, i.e., m = ρ V
Volume of the fluid is equal to the dimension of the container, i.e., V = A h
Combine the last two equations for mass.
m = ρ A h
Therefore, weight of the fluid, W = ρ A h g
The pressure exerted on the bottom of the container is given as:
P = W ⁄ A
P = (ρ A h g) ⁄ A
P = ρ h g
where,
- ρ is the density of fluid
- A is the surface area of container
- h is the height upto the fluid is filled in container
- V is the volume of fluid
- m is the mass of fluid
- g is the acceleration due to gravity
- W is the weight of fluid
- P is the pressure exerted on the bottom of the container.
这是由流体重量产生的压力。除了此处推导它的特定条件之外，该等式具有一般有效性。即使容器不在那里，周围的流体也会施加这种压力，从而保持流体静止。对于实际上不可压缩的液体，这个方程仍然适用于深层。该方程可用于非常可压缩的气体，只要在所覆盖的深度上的密度变化最小。
示例问题
问题1：定义压力和液柱高度之间的关系。
回答：
The pressure exerted by a liquid depends on the height of the liquid column.
Pressure can be written as P = ρ g h where h is height and ρ is density. The formula shows the direct relation between the pressure and height of the column.
Therefore, as the height increases, pressure will also increase .
问题 2：计算水在一个面积为 3 m 2的水箱底部加满水至 2 m 高时所施加的力。 （水的密度为 1000 kg m -3和 g = 10 ms -2 ）。
解决方案：
Given:
Area of base of tank, A = 3 m2
Height of the tank filled with water, h = 2 m
Density of the fluid, ρ = 1000 kg m−3
The formula of the pressure is given as:
P = ρ g h
= (1000 × 10 × 2) N m−2
= 20000 N m−2
The force exerted by the water,
F = P A
= (20000 × 3) N
= 60000 N
Hence, the force exerted by the water is 60000 N.
问题3：为什么蓄水池的坝底很厚？
回答：
The dam of a water reservoir is thick at the bottom because the pressure of water is highest at the maximum depth, and the dam must be strong at the bottom to withstand this maximum pressure.
问题4：什么是静水压力？
回答：
The hydrostatic pressure is the pressure exerted by a fluid in equilibrium owing to gravity at any given period. When a downward force is applied, hydrostatic pressure is proportional to the depth measured from the surface as the weight of the fluid increases.
问题 5：在 4°C 时，作用在 2 m 深度的水上的压力是多少？
解决方案：
Given:
The depth of water column, h = 2 m
The density of water at 4°C, ρ = 1000 kg ⁄ m3
The formula of the pressure is given as:
P = ρgh
= (1000 × 9.81 × 1) Pa
= 9810 Pa.
Hence, the pressure acting on the water at a depth of 2 m is 9810 Pa.