Compressible Flow In Convergence Nozzle

Fluid Mechanics Lab Report

Compressible flow in Convergence Nozzle

Nurzarith Izzat Bt Othman

8755

Muhamad Hafiz bin Bohari

8187

Luis Periera

7255

Mohammad Amer Qais Abro

10522

Annaorazov Rejep

8864

Mered Chariyev

7214

OBJECTIVE To demonstrate the effect of compressibility on the flow equations for a convergent flow. THEORY For air flow higher than 0.3 Mach, the flow is considered compressible. It means that there is a noticeable change in density.

Where T is the local temperature in Kelvin, K. From conservation of energy principle, we get:

Where Po= (V2/2g) +P at state 1 or 2, or (in or out)

From continuity equation p1V1A1=p2V2A2

From 1.a and 2, getting; In theoretical form (Po-P2)=(A1/A2)2(P0-P1)

APPARATUS

Armfield Compressible Flow Bench, convergent-divergent duct, two inclined tube manometers, mercury manometer.

Figure 1 : The compressible Flow Bench PROCEDURE 1. An inclined tube manometer to read P0-P1 using the 12.7mm range is connected. 2. Another inclined tube manometer to read P0-P2 using the 25.4mm range is connected. 3. The flow to give approximately equal increments of (P0-P1) is adjusted. 4. The readings of both manometers are read for each flow rate. 5. Using the 50.8mm range of an inclined tube manometer and with mercury manometer to measure P0-P1, the steps were repeated.

RESULTS and CALCULATIONS First Experiment At 1000rpm,

(P0-P1)

kPa

12.7mm

(P0-P2) 25.4mm

mmH2O

kPa

Theoretical value

Vin

Vout

(m/s)

(P0-P2)

(m/s)

kPa

20

0.196

0.000

7.984

0.0623

0.0000

40

0.392

0.010

15.967

0.0879

0.0140

60

0.588

0.020

23.951

0.1077

0.0199

80

0.784

0.025

31.935

0.1244

0.0222

100

0.980

0.040

39.919

0.1391

0.0281

120

1.176

0.045

47.902

0.1524

0.0298

140

1.372

0.050

55.886

0.1646

0.0314

160

1.568

0.060

63.869

0.1759

0.0344

180

1.764

0.070

71.854

0.1866

0.0372

200

1.960

0.080

79.837

0.1967

0.0397

Conversion of unit : mmH2O to kPa 1 mmH2O x 0.0098 kPa = 0.0098kPa Theoretical value

P0-P2 =

Vin

(A1/A2) 2(P0-P1)

=

(40.733) (0.196kPa)

=

7.984 kPa

=

√ (2(P0-P1)/ P0)

=

√ (2(0.196)/ 101.325)

;

P0 = 101.325kPa

Vout

=

0.0622

m/s

=

√ (2(P0-P2)/ P0)

=

√ (2(0)/ 101.325)

=

0 m/s

P0-P2 vs P0-P1 0.09 0.08 0.07 P0-P2

0.06 0.05 0.04 0.03 0.02 0.01 0 0

0.5

1

1.5 P0-P1

Graph 1

Second Experiment At 3000 rpm,

2

2.5

(P0-P1)

Mercury manometer

50.8mm mmH2O

(P0-P2) mmHg

kPa

mmHg

kPa

Theoretica l value

Vin

Vout

(m/s)

(m/s)

(P0-P2) kPa

0.05

0.0004 9

256

252

4

0.5328

0.0199

0.003 1

0.1026

0.10

0.0009 8

258

250

8

1.0656

0.0399

0.004 4

0.1450

0.15

0.0014 7

260

248

12

1.5984

0.0599

0.005 4

0.1776

0.20

0.0019 6

262

247

15

1.9980

0.0798

0.006 2

0.1986

0.25

0.0024 5

263

245

18

2.3976

0.0998

0.007 0

0.2175

0.30

0.0029 4

264

244

20

2.6640

0.1158

0.007 6

0.2293

0.35

0.0034 3

266

242

24

3.1968

0.1397

0.008 2

0.2512

0.40

0.0039 2

268

240

28

3.7296

0.1597

0.008 8

0.2713

0.45

0.0044 1

270

239

31

4.1292

0.1796

0.009 3

0.2855

0.50

0.0049 0

272

236

36

4.7952

0.1996

0.009 8

0.3077

Conversion unit of mmH2O to kPa 1mmH2O x 0.0098 kPa = 0.0098kPa

Conversion unit of mmHg to kPa 1mmHg x 0.1332kPa =0.1332 kPa

Theoretical value

P0-P2 =

Vout

=

(40.733) (0.00049)

=

0.01996 kPa

=

√ (2(P0-P1)/ P0)

=

√ (2(0.00049)/ 101.325)

=

0.0031 m/s

=

√ (2(P0-P2)/ P0)

=

√ (2(0.5328)/ 101.325)

=

0.1026 m/s

;

P0= 101.325kPa

Po-P2 vs. Po-P1 5 4.5 4 3.5 Po-P2

Vin

(A1/A2) 2(P0-P1)

3 2.5 2 1.5 1 0.5 0 0

0.001

0.002

0.003 Po-P1

0.004

0.005

Graph 2

DISCUSSION First experiment used inclined manometer test set to measure pressure. From the graph 1, we can see as the different in pressure at convergent duct increase, the pressure of air flow also increase. This is due to the increasing of velocity after passing through the throat although the flow area increases rapidly in the region. When the fluid density decrease, the velocity passing the throat also increase. The second experiment used 3000rpm motor rotating. Then we measure the pressure by using manometer. Based on the graph 2, Po-P2 increases when Po-P1 increase but velocity inlet is smaller than velocity outlet. This is because area of nozzle larger than area of compressor. A plot of pressure distribution along the nozzle provides a good way of summarizing its behavior. To understand how the pressure behaves there are a few basic rules to remember : -When the flow accelerates (sub or supersonically) the pressure drops -The pressure rises instantaneously across a shock -The pressure throughout the jet is always the same as the ambient (i.e. the back pressure) unless the jet is supersonic and there are shocks or expansion waves in the jet to produce pressure differences. -The pressure falls across an expansion wave. Often viscous effects are not important in compressible flows, since the boundary layers are very thin. Flows in the nozzle are easily controlled by varying the backpressure. From the graph we can see that it is different from the theoretical value that were calculated. This might be due to some misconduct or the condition of the instrument. Apart from that it can also be due to the readings that we have done (parallax) or even the connections between the pipes are not well connected. CONCLUSION From this experiment, we were able to demonstrate the effect of compressibility on the flow equations for a convergent flow and how it varied at different points for example from the plot of pressure difference, we could understand how the pressure behaves in a nozzle.