Name: pressure and velocity in inviscid flow
Uploaded: 2025-02-13T15:43:25.000Z
Duration: 1 min 28 s
Channel: JoVE

في السائل المتحرك ، تتطور ضغوط القص بسبب اللزوجة. بالنسبة للماء ، الذي يحتوي على لزوجة منخفضة ، فإن هذه التأثيرات لا تكاد تذكر ، مما يبسط تحليل حركة السوائل.
عندما تكون ضغوط القص ضئيلة ، يعتبر السائل غير لزج أو عديم الاحتكاك. في السوائل غير اللزجة ، يكون الإجهاد الطبيعي هو نفسه في جميع الاتجاهات ، مما يعني أن الضغط مستقل عن اتجاه الإجهاد.
الضغط هو سلبي الإجهاد الطبيعي ، مما يضمن أن الضغوط الانضغاطية تؤدي إلى قيمة ضغط إيجابية.
تصف المعادلات العامة للحركة للتدفق غير اللزج ، والمعروفة باسم معادلات أويلر ، الحفاظ على الزخم. تمثل هذه المعادلات قانون نيوتن الثاني المطبق على عنصر سائل، ويربط تغيرات السرعة بالقوى المؤثرة على السائل.
تفسر معادلات أويلر تدرجات الضغط ، وقوى الجسم مثل الجاذبية ، والتسارع - المحلي والحمل الحراري - التي تدفع التغيرات في سرعة السائل.
إنهم يهملون القوى اللزجة ، ويبسطون التحليل ، لكنهم لا يزالون يصعب حلها بسبب مصطلحات السرعة غير الخطية في المعادلات التفاضلية الجزئية.
يستمد دمج معادلات أويلر على طول خط الانسيابية معادلة برنولي ، مما يوفر نظرة ثاقبة على تغيرات الضغط والسرعة والارتفاع في التدفقات غير اللزجة ، مما يجعلها أداة رئيسية في ميكانيكا الموائع.

معادلات أويلر للحركة.

Euler&#39;s Equations of Motion

<div style="direction:rtl">في ميكانيكا الموائع، تتسبب اللزوجة في نشوء إجهادات القص ، والتي تمثل مقاومة المائع الداخلية للتشوه. بالنسبة للموائع ذات اللزوجة المنخفضة، مثل الماء، تكون يكون مقدار هذه الإجهادات ضئيلا، مما يسهل من عملية تحليل التدفق بمعاملة المائع على أنه غير لزج أو منعدم الاحتكاك. في حالة المائع الغير لزج، تنعدم إجهادات القص، و تستمر الاجهادات عادية بالتواجد، والتي تؤثر بشكل عمودي على اجزاء المائع. ومن الجدير بالذكر أن الضغط - والذي يُعرَّف بأنه سالب للإجهاد العادي - يظل موحدًا عبر اتجاهات مختلفة ولا يتأثر باتجاه الإجهاد. تخضع حركة الموائع الغير لزجة لمعادلات أويلر المستمدة من قانون نيوتن الثاني المطبق في ديناميكا الموائع. تعبر هذه المعادلات عن بقاء كمية الحركة من خلال ربط معدل التغير في السرعة بالقوى المؤثرة على اجزاء المائع. بالنسبة للمائع الغير لزج، تشمل القوى المؤثرة كل من تدرجات الضغط وقوى الجسم، مثل الجاذبية. تعبر معادلات أويلر عن توازن هذه القوى، باستثناء تأثير اللزوجة، على النحو التالي: <img alt="Equation 1" src="/files/ftp_upload/18057/18057_Equation_1.svg" style="text-align: center; height: 30px;"> حيث ρ هي كثافة السوائل، وv هو متجه السرعة، وp هو الضغط، وg​ يمثل تسارع الجاذبية. بينما تتجاهل معادلات أويلر اللزوجة، إلا أنها تظل معقدة بسبب علاقاتها الغير خطية، حيث تضع في الاعتبار تسارع لجزيئات السوائل. وعند تكاملها على طول خطوط الجريان، تنتج هذه المعادلات معادلة برنولي، التي تعبر عن علاقة أساسية في ميكانيكا الموائع ، والتي تربط بين الضغط والسرعة والارتفاع للتدفقات الغير لزجة. تُعد معادلة برنولي أداة فعالة في تحليل توزيع الطاقة في تدفقات الموائع، وتدعم تطبيقات انتقال الموائع، وديناميكيات الهواء، وديناميكيات المياه.</div>

في السائل المتحرك ، تتطور ضغوط القص بسبب اللزوجة. بالنسبة للمياه ، ذات اللزوجة المنخفضة ، فإن هذه التأثيرات لا تكاد تذكر ، مما يبسط حركة السوائل ...

Education

JoVE Core

Civil Engineering

الهندسة المدنية

Unit 1

الوحدة الأولى

Differential Analysis of Fluid Flow

التحليل التفاضلي لتدفق السوائل

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

pressure and velocity in inviscid flow

Pressure and velocity in inviscid flow are linked by Euler's equations of motion. In fluid mechanics, viscosity creates shear stress, which is a force that acts along a surface. For low-viscosity fluids like water, these shear stresses are very small. That lets the fluid be treated as inviscid, or frictionless.

In an inviscid fluid, shear stresses are absent. Only normal stresses remain, and these act perpendicular to a fluid element. Pressure is the negative of the normal stress. It stays the same in different directions and does not depend on how the stress is oriented.

Euler's equations come from Newton's second law applied to fluid motion. They describe momentum conservation by linking the change in velocity to the forces on a fluid element. For inviscid flow, those forces are pressure gradients and body forces such as gravity. The equations include density, velocity, pressure, and gravitational acceleration, but they leave out viscous terms.

Even without viscosity, Euler's equations are still nonlinear. That means they are complex because they include convective acceleration, which follows the motion of fluid particles. When the equations are integrated along a streamline, they lead to Bernoulli's equation. Bernoulli's equation connects pressure, velocity, and elevation in inviscid flows and is useful for fluid transport, aerodynamics, and hydrodynamics.

Pressure and Velocity in Inviscid Flow

euler&#39;s equations of motion

Pressure and velocity in inviscid flow are linked by Euler's equations of motion. In fluid mechanics, viscosity creates shear stress, which is a force that acts along a surface. For low-viscosity fluids like water, these shear stresses are very small. That lets the fluid be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent. Only normal stresses remain, and these act perpendicular to a fluid element. Pressure is the negative of the normal stress. It stays the...

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Plane Potential Flow Patterns and Models

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navier&#8211;stokes equations

Fluid Stress and Flow Equations

Fluid stress and flow equations describe how incompressible Newtonian fluids move under pressure, shear, and gravity. In these fluids, density stays constant, and stress changes linearly with the rate of deformation. The main stress types are normal stress and shear stress. Normal stress depends on pressure acting on the fluid and on deformation rate in specific directions. Shear stress acts along the surface of a fluid layer. It shows how neighboring layers slide past one another, so velocity...

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Laminar Flow Profile Between Parallel Plates

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Linear Shear Between Moving Plates

Linear shear between moving plates describes fluid motion in a simple channel with two parallel plates. One plate stays fixed, and the other moves at a constant speed. This setup helps show how viscosity and incompressible flow shape fluid motion under the Navier-Stokes equations. The model uses a steady, laminar, incompressible flow with no pressure gradient in the flow direction. The x-axis points along the moving direction of the upper plate, and the y-axis is perpendicular to both plates.

steady, laminar flow in circular tubes

Parabolic Flow in Circular Tubes

Parabolic flow in circular tubes describes the steady, incompressible motion of a viscous fluid through a tube with a constant radius. This Hagen-Poiseuille flow is a classic example of laminar flow. It is often used to study fluid transport in narrow channels, including capillaries. Cylindrical coordinates are used to describe the tube. The radial direction is r, the angular direction is θ, and the axial direction is z. In this flow, the velocity is purely axial. That means the fluid moves...

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Pressure drop in oil pipe design depends on pipe size, oil properties, and the flow rate needed through a circular pipe. For steady, incompressible, laminar flow, Hagen-Poiseuille's law gives an exact solution from the Navier-Stokes equations. It is used to find the pressure difference needed to keep oil moving through a pipeline section. The pressure drop equation uses the oil's dynamic viscosity, the pipeline length, the desired volumetric flow rate, and the pipe's inner radius. This...

key terms and concepts

Learn how pressure, velocity, and gravity shape inviscid fluid motion through Euler's equations, and how they lead to Bernoulli's equation along a streamline.

Pressure and Velocity in Inviscid Flow | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Pressure and Velocity in Inviscid Flow

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