Week 4 Notes, Math 8610, Tanveer 1. More Exact Solutions with nonzero Vorticity 1.1. Flow in a pipe: Steady axisymmetric Poiseuille Flow. Consider the steady unidirectional flow in an infinitely long pipe of radius
ثبت نشده
چکیده
1.1. Flow in a pipe: Steady axisymmetric Poiseuille Flow. Consider the steady unidirectional flow in an infinitely long pipe of radius a. To solve this problem, it is convenient to consider the NavierStokes equation in the cylindrical coordinates (r, θ, z) in the absence of any external force (b = 0). In this coordinate system u = (ur, uθ, uz). The scalar components of the Navier-Stokes equation are given by:
منابع مشابه
Vortexons in axisymmetric Poiseuille pipe flows
We present a study on the nonlinear dynamics of small long-wave disturbances to the laminar state in non-rotating axisymmetric Poiseuille pipe flows. At high Reynolds numbers, the associated Navier-Stokes equations can be reduced to a set of coupled Korteweg–de Vries-type (KdV) equations that support inviscid and smooth travelling waves numerically computed using the Petviashvili method. In phy...
متن کاملAixsymmetric Stagnation Point Flow of a Viscous Fluid on a Moving Cylinder with Time Dependent Axial Velocity
The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite moving cylinder with time-dependent axial velocity is investigated. The impinging free stream is steady with a strain rate k. An exact solution of the Navier-Stokes equations is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations. The general self-si...
متن کاملNumerical and Empirical Investigation of Flow Separation Phenomenon around Semi-buried Pipelines due to Steady Currents
In this paper, in order to understand the flow-pipe interaction more clearly, the variations on flow pattern around semi-buried pipelines due to steady current have physically and numerically been investigated. In physical modeling section, the experiments have been carried out in a flume with 10 meter length, 0.3 meter width and 0.5 meter depth using a P.V.C pipe with 6.35 cm in diameter (for ...
متن کاملNumerical Simulation in Steady flow of Non-Newtonian Fluids in Pipes with Circular Cross-Section
In the chemical and process industries, it is often required to pump fluids over long distances from storage to various processing units and/or from one plant site to another. There may be a substantial frictional pressure loss in both the pipe line and in the individual units themselves. It is thus often necessary to consider the problems of calculating the power requirements for pumping throu...
متن کاملWaterhammer Caused by Intermittent Pump Failure in Pipe Systems Including Parallel Pump Groups
The use of pumps linked in parallel or series in large scale pipe systems is usually inevitable, to meet the required head and discharge. Transient flow occurs following a pump failure in a pump group as a result of variations in the flow rate. This research is an investigation about waterhammer caused by one or more pump-switch off in a pump group when they are connected in parallel. The opera...
متن کامل