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SEMESTERTOETS 3 / SEMESTER TEST 3 23 MEI 2012 / 23 MAY 2012

KURSUS / COURSE: MEGANIESE INGENIEURSWETENSKAPPE / MECHANICAL

ENGINEERING SCIENCE TYD / TIME: 120 MIN BLADSYE / PAGES: 4 VRAESTEL / PAPER: STROMINGSLEER / FLUID DYNAMICS 3A PUNTE / MARKS: 65

BEANTWOORD AL DIE VRAE / ANSWER ALL THE QUESTIONS SAKREKENAARS WORD TOEGELAAT / CALCULATORS ARE ALLOWED

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QUESTION 1 [20] By using the Navier-Stokes equation, determine the velocity distribution for fully developed, laminar flow in a tube with radius R1 (See Figure 1). In the middle of the tube is a solid rod with radius R2. The viscosity of the fluid flowing in the annulus is and the pressure drop over a distance L is P. [15] Determine also the position of the maximum velocity. [5]

Figure 1

NOTE: Show all algebraic calculations.

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QUESTION 2 [15]

Find expressions for the velocities Vr and V for a cylinder without circulation

0cosV xr

Make use of Bernoullis equation to find an expression for the boundary pressure around a cylinder without circulation. Refer to figure above (Figure 2). Calculate the drag and discuss the result briefly.

Figure 2

QUESTION 3 [10]

The velocity potential for a certain inviscid flow field is given by:

323 yyx

Where has the units of m/s when x en y are in meters. Determine the pressure difference (in pa) between point 1 (1, 2) and point 2 (4, 4) where the coordinates are in meter, if the fluid is water and elevation changes are neglible. The temperature of the water is 20C.

QUESTION 4 [5] Water approaches a device for diverting a portion of the flow. The water is moving at a speed of 3m/s and is at a temperature of 5C. At what distance from A along the horizontal part of the diverter will the laminar boundary layer be a thickness of 1.2mm? Use Blasius solution and 610519.1 v

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QUESTION 5 [15] In the autogyro, the lift is developed by freely rotating vanes. The rotation is caused by the aerodynamic forces on the vanes themselves. Using flat-plate theory, what is the aerodynamic torque needed to overcome skin friction for an angular speed of the vanes of 50 r/min? Take each vane to be a flat plate of dimension 4.5m by 0.3m. The autogyro has 3 vanes. The air is at a temperature of 10C. Transition takes place

at 5102.3Re cr .

Consider as an approximation, the equation for smooth plates, low Reynolds number

flow to be valid for the turbulent boundary layer. Take 51055.1 and p=101.404

Pa

FORMULA SHEET

2

2 2

2 2 2 2 2

2

2 2 2

1 1 2

1 1 1 2

r r r rr z

r r r rr

rr z

v vv v v vv vt r r r z

vv v v vpB rr r r r r r r z

v v v v v v vv vt r r r z

v v vpB rr r r r r r

2

2 2

2 2

2 2 2

1 1

r

z z z zr z

z z zz

vvr z

vv v v vv vt r r z

v v vp rz r r r r z

0

zV

yV

xV zyx 1

r r

1r r

0

zV

yV

xV zyx const

gVzp 2

2

g

xV y

yV x

x

Vx

yVy

1rV r

rVr

r

V 1r r

1r r

V

r

4

yx

xy

kx

Vy

VVcurl yx

21

0

zV

yV

xV zyx

212

wfc U

4.96Rexx

0.664

Ref xc

2

2

yUyUu

212

fDCU A

1.328Ref L

C

RDT

A

wdAD 15

0.074ReRe

fLL

AC 2.5

1.89 1.62logflCe

1.328Ref L

C

212

fDCU A

w

w dydu

4.64

Rexx

crRe 300 000 500 000 610 6103 A 1050 1700 3300 8700