INTRODUCTION:
This particular flow is a ideal flow which is not a real flow.This particular flow may not be there in physically possible flows due to viscosity.we consider potential flow as the non-viscous flow i.e neglecting viscosity.This potential flow will help us to understand the lift force on an object.But doesn't talk about the drag force.
continuity equation:
velocity vector⇒ v=uî+vĴ
then,
ටu/ ටx + ටv/ ටy = 0
This is the continuity equation.
*The velocity vectors which satisfies the above equation such flow fields are physically possible flow fields.That particular flow field will have a stream function (ψ) or else no streamm function.
Irrotationality:
Rotational means rotating itself on its own axis.not rotating about a common axis.
ටv/ ටx - ටu/ ටy = 0
This is irrotationality condition.
DERIVATION FOR POTENTIAL FLOW EQUATIONS:
>>stream line is a mathematical line which flow velocity is tangential.
eq of stream line:
udy -vdx =0
u= ටψ/ටy v= - ටψ/ටx
tanθ=dy/dx =v/u.
eq of stream line:
>> udy -vdx =0
>>(ටψ/ටy)dy - (- ටψ/ටx)dx =0
>> (ටψ/ටx)dx + (ටψ/ටy)dy =0
This is the total derivative of ψ.
>>d ψ=0
integrating on both sides
>> ψ=const.
*This says that along any stram line, stream function is constant.
*Another point is no two stream lines have the same stream function ψ.
From irrotationality condition:
>> ටv/ ටx - ටu/ ටy = 0
>>ට(ටФ/ටy)/ ටx - ට(ටФ/ටx)/ ටy = 0
*If a flow field is possible and irrotational it can have only ψ.
*If the flow field is not possible and irrotational it can have Ф.
*suppose the flow field is possible,irrotational such flow field can be represented by ψ and Ф.
*If a flow field is possible and irrotational it can have only ψ.
*If the flow field is not possible and irrotational it can have Ф.
*suppose the flow field is possible,irrotational such flow field can be represented by ψ and Ф.
equations of potential flow:
If any flow have ψ and Ф.Then,it is called potential flow and it satisfies the below equations
and
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