One dimensional flow

One dimensional flow is the type of flow in which the flow characteristics such as velocity, pressure, density, temperature etc. are the function of time and one space co-ordinate only.

Mathematically,

u=f(x) ; v=0 ; w=0… for steady flow
u=f(x) ; v=0 ; w=0… for unsteady flow

where u, v and w are velocity components in x, y and z directions respectively.

Examples:
Two dimensional flow
Two dimensional flow

Flow in a pipe where the average flow parameters are considered for analysis.

Two dimensional flow is the type of flow in which the flow characteristics are the function of time and two rectangular space co-ordinates.

Mathematically,

u=f1(x,y)
v=f2(x,y)
w=0…for steady flow
u=f1(x,y,t)
v=f2(x,y,t)
w=0…for unsteady flow

Examples:
  • Flow between parallel plates of infinite extent.
  • Flow in main stream of a wide river.

Three dimensional flow is a type of flow in which the flow characteristics are the function of time and three mutually perpendicular directions.

Three dimensional flow
Three dimensional flow

Mathematically,

u=f1(x,y,z); v=f2(x,y,z); w=f3(x,y,z) for steady flow
u=f1(x,y,z,t); v=f2(x,y,z,t); w=f3(x,y,z,t) for unsteady flow

Examples:
  • Flow in a converging or diverging pipe or channel.
  • Flow in an open channel in which the width and the water depth are of the same order of magnitude.
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