Irrotationality leads to the condition which demands , where φ is known as a potential function. For a potential flow .
The stream function also obeys the Laplace’s equation for
the potential flows. Laplace’s equation is linear, hence any number of
particular solutions of Laplace’ s equation added together will yield another
solution. So a complicated flow for an in viscid, incompressible,
irrotational condition can be synthesized by adding together a number
of elementary flows which are also inviscid, incompressible and irrotational.
This is called the method of superposition.
Some inviscid flow configurations of practical importance are solved
by using the method of superposition. The circulation in a flow field is
defined as . Subsequently , the velocity may be defined as
circulation per unit area . The circulation for a closed path in an irrotational
flow field is zero. However , the circulation for a given closed
path is an irrotational flow containinga finite number of singular points
is a non -zero constant.
The lift around an immersed body is generated when the flow field processes
circulation. The lift around a body of any shape is given by , where ρ is the density and U0 is the velocity in the streamwise
direction.
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which demands 
, where φ is known as a potential function. For a potential flow 
.
for
the potential flows. Laplace’s equation is linear, hence any number of
particular solutions of Laplace’ s equation added together will yield another
solution. So a complicated flow for an in viscid, incompressible,
irrotational condition can be synthesized by adding together a number
of elementary flows which are also inviscid, incompressible and irrotational.
This is called the method of superposition.
. Subsequently , the velocity may be defined as
circulation per unit area . The circulation for a closed path in an irrotational
flow field is zero. However , the circulation for a given closed
path is an irrotational flow containinga finite number of singular points
is a non -zero constant.
, where ρ is the density and U0 is the velocity in the streamwise
direction.
