Chapter 19
Differential Analysis of Fluid Flow
Eulers Bewegungsgleichungen
In a moving fluid, shear stresses develop due to viscosity. For water, which has low viscosity, these effects are negligible, simplifying fluid motion ...
Stream-Funktion
In two-dimensional incompressible flow, there are horizontal and vertical velocity components.
The continuity equation ensures mass conservation by ...
Irrotierende Strömung
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 ...
Geschwindigkeits-Potential
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 ...
Potentialflüsse in der Ebene
Plane potential flows simplify fluid motion by assuming irrotational and incompressible flow, governed by a velocity potential function and a stream ...
Navier-Stokes-Gleichungen
In fluid motion under viscous conditions, shear stress is directly proportional to fluid deformation. In incompressible Newtonian fluids, this stress ...
Gleichmäßige, laminare Strömung zwischen parallelen Platten
Steady, laminar flow between two parallel plates describes fluid movement in a narrow, confined channel, often used to model simple fluid systems.
For ...
Couette-Fluss
Couette flow describes fluid motion between two parallel plates where one is stationary, and the other moves with constant speed, creating a steady, ...
Gleichmäßige, laminare Strömung in kreisförmigen Rohren
Consider steady, incompressible flow through a straight cylindrical tube of constant radius R, known as Hagen–Poiseuille flow.
The cylindrical ...
Konstruktionsbeispiel: Ölfluss durch kreisförmige Rohre
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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