AD 2marks 2nd Units

8/18/2019 AD 2marks 2nd Units

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UNIT 2TWO DIMENSIONAL INVISCID , INCOMPRESSIBLE FLOW

2 Marks Questio a! As"ers

Aero!#a$i%s &

1. 'o" are t(e strea$ )ies i a sour%e sik *air+

The stream lines are circles with centre on y- axis for a source sink pair. Stream lines

are circles with common chord.

2 W(at is $ea -# Dou-)et .)o" a! /i0e !ia/ra$$ati% re*resetatio +

There is a special, degenerate case of a source-sink pair that leads to a singularity called

a doublet. The doublet is frequently used in the theory of incompressible flow.

Doublet flow with strength k.

. W(at is t(i%kess ratio 1 .ieess ratio o. a Rakie o0a)+

!t is the ratio of maximum thickness to chord of "ankine o#al.

Superposition of a uniform flow and a source-sink pair flow

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Aero!#a$i%s &

3 Dra" a! e4*)ai o )i.ti/ .)o" o0er a %#)i!er

Superposition of a uniform flow and a doublet$ nonlifting flow o#er a circular cylinder.

5 Write t(e e6uatio o. C* .)o" o0er a %#)i!er

The surface pressure coefficient o#er a circular cylinder is

2pC 1 4sin= − θ

7 W(at is $eat -# 0orte4 .)o" +

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Aero!#a$i%s &

%onsider a flow howe#er all the streamlines are concentric circles about a gi#en

poin.&oreo#er, let the #elocity along any gi#en circular streamline be constant, but let it

#ary from one streamline to another in#ersely with distance from the common center.Such a flow is called a #ortex flow. !t is easily shown 'try it yourself( that '1( #ortex flow

is a physically possible incompressible flow, that is,.V 0∇ =

at e#ery point, and ')(

#ortex flow is irrotational, that is,

V 0,∇× = at e#ery point except the origin.

8 W(# 0orte4 .)o" is irrotatioa) e4%e*t at t(e ori/i W(at (a**es at r 9 :+

2C VdSπ = ∇ ×

2CVdSπ∇ × =

*owe#er, as r → +, dS → +. Therefore, in the limit as r → +, from quation, we ha#e

V∇ × → ∞

%oncluation ortex flow is irrotational e#erywhere except at the point r / +,

where the #orticity is infinite.

0. W(at is 0orte4 *air+

Two #ortices of equal strength but of opposite sign or with opposite directions of

rotation constitute a #ortex pair.

. De.ie )i.t a! !ra/

Since the fluid is in motion, we can define a flow direction along the motion. The

component of the net force perpendicular ' or normal( to the flow direction in called the

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Aero!#a$i%s &

lift, the component of the net force along the flow direction is called the drag.

1+. 'o" t(e !o" "as( o. a "i/ is re)ate! !o" "as( o. tai) *)ae+

The down wash on the tail resulting from the wing wake is almost twice as great as

the down wash on the wing resulting from wing wake.

11. Brie. out (o" "i/ ti* 0orti%es are .or$e!+

2n account of larger pressure below the wing surface than on the top, some flow is there

from bottom to top round the wing tips incase of a finite using. This produces #elocity

side ways o#er most of the wing surface. This causes a surface discontinuity in the air

lea#ing the wing which rolls up to distinct #ortices.

1). Su//est $et(o!s to reso)0e i!u%e! !ra/ o. a "i/;

a. &ake life distribution on wing elliptical

b. !ncrease the aspect ratio.

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Aero!#a$i%s &

&3 E4*)ai )i.ti/ .)o" o0er a %#)i!er

The synthesis of lifting flow o#er a circular cylinder

&5 Sta/atio *oits )o%atio i 0arious %ases .or t(e )i.ti/ .)o" o0er a %ir%u)ar

%#)i!er

&7 De.ie =utta>?ouko"ski t(eore$

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Aero!#a$i%s &Figure .he creation o% the starting vorte and the resulting generation o% circulation

around the air%oil#

AD 2marks 2nd Units

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