Name: how depth changes fluid pressure
Uploaded: 2023-09-22T11:49:33.000Z
Duration: 1 min 14 s
Channel: JoVE

Давление определяется как величина силы на единицу площади. Рассматривая несжимаемую жидкость, сила может быть выражена в терминах удельного веса или плотности жидкости.
Рассмотрим четыре точки в воде. Давление одинаково для всех точек на одной и той же глубине от поверхности, но меньше на небольших глубинах. Давление линейно увеличивается с глубиной от поверхности.
Согласно закону Паскаля, интенсивность давления в любой заданной точке несжимаемой статической жидкости одинакова во всех направлениях.
Предположим, что клиновидный бесконечно малый элемент жидкости имеет единичную ширину. Сила с каждой стороны выражается как произведение давления на площадь.
Поскольку жидкость находится в состоянии покоя, сумма горизонтальной и вертикальной составляющих сил должна быть равна нулю.
Беря горизонтальные компоненты и используя тригонометрические соотношения, уравнения упрощаются до получения px равного ps.
Аналогично, рассматривая вертикальные компоненты, уравнения упрощаются для получения py, равного ps. 
Таким образом, давление в любой точке одинаково во всех направлениях.

<ol>
	<li>Хиббелер, Р.К. (2016). Инженерная механика: Статика. Четырнадцатое издание, Нью-Джерси: Пирсон. С. 512.</li>
</ol>

Давление жидкостей

В механической инженерии давление жидкости играет критическую роль в проектировании систем, использующих поток жидкости, таких как гидравлические системы, насосы и клапаны. При проектировании этих систем инженеры должны обеспечить их способность выдерживать силы, создаваемые давлением жидкости, чтобы избежать повреждений или отказов.

Согласно закону Паскаля, неподвижная жидкость создает одинаковое давление во всех направлениях. Это давление измеряется как сила на единицу площади, и его величина зависит от плотности или массовой плотности жидкости и глубины точки измерения от поверхности жидкости. Мы можем выразить это математическим образом, как p = ρgz, где ρ - плотность жидкости, g - это ускорение свободного падения и z - это глубина.

Следует отметить, что это уравнение верно для несжимаемых жидкостей, таких как большинство жидкостей, но не для газов, плотность которых значительно меняется в зависимости от температуры и давления. Чтобы понять, как это уравнение применяется к жидкостям, рассмотрим три точки, расположенные внутри воды. На одинаковой глубине от поверхности давление одинаково для всех трех точек. Однако давление уменьшается на мелкой глубине. Давление линейно увеличивается с глубиной по мере удаления от поверхности.

В машиностроении давление жидкости играет решающую роль при проектировании систем, использующих поток жидкости, таких как гидравлические системы, насосы и ...

Education

JoVE Core

Mechanical Engineering

Машиностроение

Unit 1

Раздел 1

Center of Gravity and Centroid

Центр тяжести и центр масс (центроид)

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

Fluid Pressure

how depth changes fluid pressure

Fluid pressure changes with depth in liquids used in engineering systems. It matters in hydraulic systems, pumps, and valves, where the forces from moving and resting fluid must be considered to prevent damage or failure.

For a fluid at rest, Pascal’s law says the pressure is equal in all directions. Pressure is force per unit area. Its size depends on the fluid’s specific weight, or mass density, and on how deep the measurement point is below the fluid surface.

This relationship can be written as p = ρgz. In this equation, ρ is fluid density, g is the acceleration due to gravity, and z is depth. The equation applies to incompressible fluids, such as most liquids, but not to gases, because gas density can change greatly with temperature and pressure.

The pattern is easy to see in water. If three points are at the same depth, their pressure is the same. A point closer to the surface has lower pressure. As depth increases, pressure rises in a linear way.

How Depth Changes Fluid Pressure

center of gravity

Center of Gravity in Balance and Design

The center of gravity is the point where an object’s weight appears to act. It is the spot used to balance the object most evenly. In mechanics, this point helps explain stability and moments of inertia. The center of gravity does not always sit inside the object’s shape. In some cases, it can lie outside the body. That is why the idea is useful for both simple and more complex shapes. Its location can be found with the principle of moments. The object is divided into very small parts, and...

center of mass

Center of Mass in Motion

The center of mass helps explain how an object moves through space. It is the point where the total mass of an object can be treated as concentrated. This idea applies to objects of different shapes and sizes. The center of mass is related to the center of gravity, but they are not the same. The center of gravity is the point where an object’s weight seems to be concentrated. It can be used to balance an object perfectly. Knowing the center of mass also helps predict motion. When a ball is...

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Finding the Center of a Body

The centroid is the geometric center of a body. It is an important idea in engineering, physics, and mechanics. For many objects, it lies inside the body. A body with holes or cavities can be an exception. For a homogeneous body, the centroid matches the center of mass or the center of gravity. Homogeneous means the material has a uniform density. In that case, the centroid can often be found by balancing the moments of the body’s volume. Symmetry can also help locate the centroid. If a...

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Centroid of a Quarter Circle Wire

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Centroid and Uses of a Paraboloid Shape

The centroid of a paraboloid of revolution is the point where its mass is balanced. A paraboloid of revolution is an axially symmetric surface made by rotating a parabola around its axis. In engineering, this location matters because it helps show how forces spread across the shape. Knowing the centroid can help when building parts that must handle stress and pressure reliably. The paraboloid shape has useful structural properties, including rotational symmetry and strength against stress...

composite bodies

Center of Gravity in Composite Bodies

Composite bodies are made of multiple connected parts that act as one larger object. Each part still has its own weight and center of gravity. To find the center of gravity of the whole body, engineers must account for every part. When the density or specific weight is constant, the center of gravity matches the centroid. The centroid is the geometric center of a shape. This idea is useful when analyzing parts that behave as a single unit. Composite bodies are common in mechanical engineering.

theorems of pappus and guldinus

Surface Area and Volume by Centroid Paths

Pappus and Guldinus theorems help find the surface area and volume of bodies of revolution. A body of revolution is formed when a plane curve or plane area is turned around an axis that does not intersect it. For surface area, a curve is revolved around a non-intersecting axis. A small line element on the curve creates a thin ring as it moves. Adding these ring areas gives the total surface area of the solid. The first theorem says that this surface area equals the length of the generating...

theorems of pappus and guldinus: problem solving

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Pappus and Guldinus Theorems for Surface Area

Pappus and Guldinus's theorems help find the surface area and volume of composite shapes. These rules are useful when a solid is made from simple parts that are hard to measure directly. A cylindrical storage tank with a conical top is one example. The tank can be split into two simple shapes: a cylinder and a cone. To find surface area, the first theorem is used for the solid formed by revolving each generating curve around a non-intersecting axis. The calculation uses the length of the...

resultant of a general distributed loading

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Finding the Resultant of Distributed Loads

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load. This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel...

fluid pressure

Fluid pressure changes with depth in liquids used in engineering systems. It matters in hydraulic systems, pumps, and valves, where the forces from moving and resting fluid must be considered to prevent damage or failure. For a fluid at rest, Pascal’s law says the pressure is equal in all directions. Pressure is force per unit area. Its size depends on the fluid’s specific weight, or mass density, and on how deep the measurement point is below the fluid surface. This relationship can be...

fluid pressure over flat plate of constant width

fluid-pressure-over-flat-plate-of-constant-width

Center of Pressure on a Submerged Plate

Fluid pressure on a submerged flat plate depends on depth and shape. A plate under water experiences pressure acting normal to its surface, and the force is spread across the whole area. For a rectangular plate of constant width, this pressure increases from the top edge to the bottom edge. Because the pressure rises with depth, the loading forms a trapezoidal distribution. The resultant force on the plate comes from the trapezoidal volume of water with a specific weight. The line of action of...

fluid pressure over curved plate of constant width

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Finding Force on a Curved Plate in Water

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fluid pressure over flat plate of variable width

fluid-pressure-over-flat-plate-of-variable-width

A submerged flat plate experiences fluid pressure that changes with depth. This pressure can create effects such as drag and buoyancy. To study a flat plate with variable width, the pressure distribution across the plate must be analyzed first. The force on a small strip of the plate is found by multiplying the pressure by the strip’s differential area. The pressure can also be written using the fluid’s specific weight and the depth of that strip below the surface. To find the total, or...

key terms and concepts

Explore how fluid pressure changes with depth, why Pascal’s law matters, and how the equation p = ρgz describes pressure in liquids like water.

How Depth Changes Fluid Pressure | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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How Depth Changes Fluid Pressure

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