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NAME-KOUSTOV ADHIKARY
CLASS-ME (3rd YEAR)
ROLL NO-14800712105
SUPERPOSITION OF BASIC
POTENTIAL FLOWS
The basic potential/elementary flows
are as follows-
I. Uniform flow
II. Source/Sink flow
III. Vortex flow
BASIC POTENTIAL FLOWS
UNIFORM FLOW
The simplest type of elementary flow for which the
streamlines are straight, parallel with constant velocity,
is known as uniform flow.
This flow can be represented as,
&
0;   vVu yVxV    ;
SOURCE/SINK FLOW
In a source(sink) flow, the streamlines are coming out
from(going towards) the origin radially and uniformly.
This flow can be represented as,
 )2/(;ln)2/( mrm 
VORTEX FLOW
Plane circular vortex flows are defined as flows where
streamlines are concentric circles.
This flow can be represented as,
&rcvvr /;0   rln)2/(;)2/(  
DOUBLET FLOW-I
This flow is the combination of source-sink pair of
equal strength in a special fashion. It leads to singularity
called as doublet.
The stream function of the combination can be
represented as,
)/2(tan)2/( 2221
ayxaym  

DOUBLET FLOW-II
If 2b0 within constraining equation the flow field
arrived is a doublet.
The stream function and potential function can be
represented as,
where
rcrc /cos;/sin   /amc 
COMBINATION OF SINK AND A
VORTEX AT ORIGIN
This is a fairly realistic simulation of a tornado or a
rapidly draining bathtub vortex.
The stream an potential function of the combination can
be represented as,
 crmrcm  ln;ln
RANKINE HALF BODY
A source of strength , located at origin is superimposed
with a uniform stream.
The resulting stream function can be written as,
 )2/(sin mrV  
THE RANKINE OVAL
This is the Combination of a Uniform Flow with a
Source-Sink Pair of equal strength.
The resulting stream function can be written as
)/2(tan)2/( 2221
byxbymyV  
 
NON LIFTING FLOW OVER A
CIRCULAR CYLINDER
A circular cylinder is one of the basic geometrical
shapes and the flow passing over it can be simulated by
combination of a uniform flow and doublet.
The stream function for the combined flow is,
Where)1(sin 2
2
r
R
rV    )2/(  VmR 
LIFTING FLOW OVER A
CIRCULAR CYLINDER-I
This flow is synthesized by addition of the non-lifting
flow over a cylinder of radius R and a vortex of strength
.
The stream function for the combined flow is,

)/ln()2/()1(sin 2
2
Rr
r
R
rV   
LIFTING FLOW OVER A
CIRCULAR CYLINDER-II
•F.M. White,Fluid
Mechanics,7ed,Macgraw-Hill,New
York,2011
•S.K. Som,G. Biswas ,Introduction to Fluid
Mechanics,2ed, Macgraw-Hill,New
York,2008
•http://nptel.ac.in/courses/101103004/13
BIBLIOGRAPHY
UNIFORM FLOW CONTD..
BACK
SOURCE/SINK FLOW CONTD…
SOURCE/SINK FLOW CONTD…
BACK
VORTEX FLOW CONTD…
VORTEX FLOW CONTD…
BACK

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Koustov adhikary

  • 1. NAME-KOUSTOV ADHIKARY CLASS-ME (3rd YEAR) ROLL NO-14800712105 SUPERPOSITION OF BASIC POTENTIAL FLOWS
  • 2. The basic potential/elementary flows are as follows- I. Uniform flow II. Source/Sink flow III. Vortex flow BASIC POTENTIAL FLOWS
  • 3. UNIFORM FLOW The simplest type of elementary flow for which the streamlines are straight, parallel with constant velocity, is known as uniform flow. This flow can be represented as, & 0;   vVu yVxV    ;
  • 4. SOURCE/SINK FLOW In a source(sink) flow, the streamlines are coming out from(going towards) the origin radially and uniformly. This flow can be represented as,  )2/(;ln)2/( mrm 
  • 5. VORTEX FLOW Plane circular vortex flows are defined as flows where streamlines are concentric circles. This flow can be represented as, &rcvvr /;0   rln)2/(;)2/(  
  • 6. DOUBLET FLOW-I This flow is the combination of source-sink pair of equal strength in a special fashion. It leads to singularity called as doublet. The stream function of the combination can be represented as, )/2(tan)2/( 2221 ayxaym   
  • 7. DOUBLET FLOW-II If 2b0 within constraining equation the flow field arrived is a doublet. The stream function and potential function can be represented as, where rcrc /cos;/sin   /amc 
  • 8. COMBINATION OF SINK AND A VORTEX AT ORIGIN This is a fairly realistic simulation of a tornado or a rapidly draining bathtub vortex. The stream an potential function of the combination can be represented as,  crmrcm  ln;ln
  • 9. RANKINE HALF BODY A source of strength , located at origin is superimposed with a uniform stream. The resulting stream function can be written as,  )2/(sin mrV  
  • 10. THE RANKINE OVAL This is the Combination of a Uniform Flow with a Source-Sink Pair of equal strength. The resulting stream function can be written as )/2(tan)2/( 2221 byxbymyV    
  • 11. NON LIFTING FLOW OVER A CIRCULAR CYLINDER A circular cylinder is one of the basic geometrical shapes and the flow passing over it can be simulated by combination of a uniform flow and doublet. The stream function for the combined flow is, Where)1(sin 2 2 r R rV    )2/(  VmR 
  • 12. LIFTING FLOW OVER A CIRCULAR CYLINDER-I This flow is synthesized by addition of the non-lifting flow over a cylinder of radius R and a vortex of strength . The stream function for the combined flow is,  )/ln()2/()1(sin 2 2 Rr r R rV   
  • 13. LIFTING FLOW OVER A CIRCULAR CYLINDER-II
  • 14. •F.M. White,Fluid Mechanics,7ed,Macgraw-Hill,New York,2011 •S.K. Som,G. Biswas ,Introduction to Fluid Mechanics,2ed, Macgraw-Hill,New York,2008 •http://nptel.ac.in/courses/101103004/13 BIBLIOGRAPHY
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