Chapter 19
Differential Analysis of Fluid Flow
Euler's Equations of Motion
In a moving fluid, shear stresses develop due to viscosity. For water, which has low viscosity, these effects are negligible, simplifying fluid motion ...
Stream Function
In two-dimensional incompressible flow, there are horizontal and vertical velocity components.
The continuity equation ensures mass conservation by ...
Irrotational Flow
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 ...
Velocity 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 ...
Plane Potential Flows
Plane potential flows simplify fluid motion by assuming irrotational and incompressible flow, governed by a velocity potential function and a stream ...
Navier–Stokes Equations
In fluid motion under viscous conditions, shear stress is directly proportional to fluid deformation. In incompressible Newtonian fluids, this stress ...
Steady, Laminar Flow Between Parallel Plates
Steady, laminar flow between two parallel plates describes fluid movement in a narrow, confined channel, often used to model simple fluid systems.
For ...
Couette Flow
Couette flow describes fluid motion between two parallel plates where one is stationary, and the other moves with constant speed, creating a steady, ...
Steady, Laminar Flow in Circular Tubes
Consider steady, incompressible flow through a straight cylindrical tube of constant radius R, known as Hagen–Poiseuille flow.
The cylindrical ...
Design Example: Flow of Oil Through Circular Pipes
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 ...
Copyright © 2025 MyJoVE Corporation. All rights reserved