Chapter 19
Differential Analysis of Fluid Flow
オイラーの運動方程式
In a moving fluid, shear stresses develop due to viscosity. For water, which has low viscosity, these effects are negligible, simplifying fluid motion ...
ストリーム関数
In two-dimensional incompressible flow, there are horizontal and vertical velocity components.
The continuity equation ensures mass conservation by ...
非回転流
Irrotational flow refers to the movement of fluid particles that do not rotate along the flow path, characterized by a velocity field with zero curl and ...
ポテンシャル速度
Consider water flowing steadily through a long, straight pipe with a uniform cross-section.
In central regions of the pipe, where flow is irrotational, a ...
平面ポテンシャル フロー
Plane potential flows simplify fluid motion by assuming irrotational and incompressible flow, governed by a velocity potential function and a stream ...
Navier–Stokes 方程式
In fluid motion under viscous conditions, shear stress is directly proportional to fluid deformation. In incompressible Newtonian fluids, this stress ...
平行プレート間の安定した層流
Steady, laminar flow between two parallel plates describes fluid movement in a narrow, confined channel, often used to model simple fluid systems.
For ...
クエットフロー
Couette flow describes fluid motion between two parallel plates where one is stationary, and the other moves with constant speed, creating a steady, ...
円形チューブ内の安定した層流
Consider steady, incompressible flow through a straight cylindrical tube of constant radius R, known as Hagen–Poiseuille flow.
The cylindrical ...
設計例:丸パイプを通るオイルの流れ
An engineer needs to design a pipeline to transport oil from a storage tank to a processing facility.
Given the oil's viscosity, density, and the ...
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