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EXPERIMENT No. 8

STUDY OF THE MEAN FLOW OF A FREE

AIR (SUBMERGED) JET

Objective:

To study the mass flow characteristics of a free air jet and to study the application of theintegral forms of the continuity, momentum and energy equations.

Theory :The term Submerged jet refers to liquid jet flowing in another miscible liquid or to a gaseous jet flowing in air. As the jet interacts with the surrounding air, velocity at the periphery beginsto decrease due to mixing with the surrounding still air. The development of jet flow is dividedinto 3 zones:

1. Potential core zone2. Zone of establishment

3. Fully developed zone

For an axisymmetric jet, if u(r) denotes the downstream velocity as a function of r, thevolumetric flux, Q, the momentum flux, M and the energy flux are given by:

Q = u. 2rdr,M = u 2. 2rdr, and

E = u 3. 2rdr.The velocity of the jet is measured with a pitot tube connected to an inclined manometer

making angle to the horizontal.u(r) = *2(m/ 1)gh(r)sin+

Since m >> , equation (i) can be written as,u(r) = *2(m/)gh(r)sin+

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Procedure:

Look into the values of density of air to be used in the calculation of velocities. Note down the nozzle diameter, d and horizontal scale factor. Lower the pitot tube, such that its tip is at an axial distance, x/d=0.5; using the

transverse mechanism. Use plumb-bob provided to align the Pitot tube with the center of nozzle; and reset zero

on the horizontal scale.

Now take the manometer readings as you take Pitot tube away from the center; till thefinal reading is zero.

Repeat these steps for different (x/d) ratios (0.5, 4, 8, 12, and 16).

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Observations:

Traverse mechanism 10 counts = 3.0625 mmManometer angle = 21.6Nozzle diameter, d = 2.486 cm m = 0.889 g/cc; = 0.0011 g/cc

Note that for the graphs of u*r, u*r^2 and u*r^3 vs. r; with help of computer the curvewas approximated by a straight line such that area under the curve remained same asoriginal.

1)x/d = 0.5

Sr no Scale units Radius (mm) Manometer Reading (cm) u r*u r*u^2 r*u^3

1 0 0 35.8 46.52118 0 0

2 44 13.475 27.3 40.62474 0.547418 22.23873 903.4424

3 45 13.78125 23.8 37.9313 0.522741 19.82824 752.1107

4 46 14.0875 18.3 33.26096 0.468564 15.58488 518.3681

5 47 14.39375 12.6 27.59907 0.397254 10.96385 302.592

6 48 14.7 6 19.04517 0.279964 5.331962 101.5481

7 49 15.00625 3.1 13.68958 0.205429 2.81224 38.49838

8 50 15.3125 0.8 6.954313 0.106488 0.74055 5.150019

9 51 15.61875 0.3 4.25863 0.066514 0.283261 1.206302

10 52 15.925 0.1 2.458721 0.039155 0.096272 0.236705

11 53 16.23125 0 0 0 0

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x/d=0.5 ( u vs r)

x/d=0.5 ( u vs r)

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Axis Title

x/d=0.5(r*u^2 vs r)

Linear (x/d=0.5(r*u^2 vs r))

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2) x/d = 4

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Linear (x/d=0.5( r*u vs r))

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x/d=0.5(r*u^3 vs r)

Linear (x/d=0.5(r*u^3 vs r))

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x/d=4 ( u vs r)

x/d=4 ( u vs r)

Sr no Scale unitsRadius(mm) Manometer Reading (cm) u r*u r*u^2 r*u^3

1 0 0 31 43.29025 0 0 0

2 10 3.0625 29.8 42.4441 0.129985 5.5171 234.1684

3 20 6.125 24.4 38.40645 0.23524 9.034714 346.9913

4 30 9.1875 16.9 31.96337 0.293663 9.386475 300.0234

5 40 12.25 10.3 24.95329 0.305678 7.627668 190.3354

6 50 15.3125 5.5 18.23436 0.279214 5.091284 92.83631

7 60 18.375 2.3 11.79161 0.216671 2.554899 30.12637

8 70 21.4375 1 7.775158 0.16668 1.295963 10.07632

9 80 24.5 0.3 4.25863 0.104336 0.44433 1.892238

10 90 27.5625 0.1 2.458721 0.067768 0.166624 0.409681

11 93 28.48125 0 0 0 0 0

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x/d=4 (r*u vs r)

Linear (x/d=4 (r*u vs r))

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x/d=4 ( r*u^3 vs r)

Linear (x/d=4 ( r*u^3 vs r))

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3) x/d = 8

Sr no Scale unitsRadius(mm) Manometer Reading (cm) u r*u r*u^2 r*u^3

1 0 0 19.1 33.9802 0 0 0

2 20 6.125 17.1 32.15195 0.196931 6.331705 203.5767

3 40 12.25 11.3 26.13656 0.320173 8.368219 218.7165

4 50 15.3125 9.4 23.83818 0.365022 8.701466 207.4272

5 60 18.375 6 19.04517 0.349955 6.664953 126.9352

6 70 21.4375 4.2 15.93433 0.341592 5.443045 86.73129

7 80 24.5 2.7 12.77589 0.313009 3.998972 51.090428 90 27.5625 1.7 10.13757 0.279417 2.832605 28.71572

9 100 30.625 0.9 7.376163 0.225895 1.666238 12.29044

10 110 33.6875 0.5 5.497867 0.185209 1.018257 5.59824

11 120 36.75 0.2 3.477157 0.127786 0.44433 1.545006

12 136 41.65 0 0 0 0 0

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x/d=8(u vs r)

x/d=8(u vs r)

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4) x/d = 12

Sr no Scale unitsRadius(mm) Manometer Reading (cm) u r*u r*u^2 r*u^3

1 0 0 11.3 26.13656 0 0 0

2 20 6.125 9.2 23.58322 0.144447 3.406532 80.33699

3 30 9.1875 8.3 22.40001 0.2058 4.609926 103.2624

4 40 12.25 6.6 19.97474 0.244691 4.887632 97.6292

5 50 15.3125 5.7 18.56294 0.284245 5.276421 97.94587

6 60 18.375 4.4 16.30931 0.299684 4.887632 79.71391

7 70 21.4375 3.7 14.95582 0.320615 4.795063 71.71408

8 80 24.5 2.4 12.04522 0.295108 3.554642 42.81645

9 100 30.625 1.4 9.199691 0.281741 2.591926 23.84492

10 120 36.75 0.4 4.917442 0.180716 0.88866 4.369936

11 140 42.875 0.2 3.477157 0.149083 0.518385 1.802507

12 164 50.225 0 0 0 0 0

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x/d=12 ( u vs r)

x/d=12 ( u vs r)

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5) x/d = 16

Sr no Scale unitsRadius(mm) Manometer Reading (cm) u r*u r*u^2 r*u^3

1 0 0 5.7 18.56294 0 0 0

2 30 9.1875 5.1 17.55878 0.161321 2.832605 49.73709

3 40 12.25 4.6 16.67586 0.204279 3.406532 56.80683

4 50 15.3125 3.9 15.35471 0.235119 3.610183 55.4333

5 60 18.375 3.4 14.33668 0.263437 3.776807 54.14688

6 70 21.4375 2.8 13.01033 0.278909 3.628697 47.21053

7 80 24.5 2.5 12.2936 0.301193 3.702752 45.52017

8 100 30.625 1.8 10.43147 0.319464 3.332476 34.76263

9 120 36.75 1.1 8.154655 0.299684 2.443816 19.92848

10 140 42.875 0.6 6.022612 0.258219 1.555156 9.366099

11 160 49 0.3 4.25863 0.208673 0.88866 3.784476

12 180 55.125 0.1 2.458721 0.135537 0.333248 0.819363

13 190 58.1875 0 0 0 0 0

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x/d=16 (u vs r)

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x/d=16 (r*u^2 vs r)

Linear (x/d=16 (r*u^2 vs r))

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Now assuming velocity calculated at the center for (x/d) ratio of 0.5 as Uo, we can calculate thevalues of Qo, Mo and Eo.

Q o = UoA =0.022584 m 3/s Mo = AUo2 = 1.155693 m 4/s 2 Eo = AUo3 = 53.764227 m 5/s 3

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x/d=16(r*u^3 vs r)

Linear (x/d=16(r*u^3 vs r))

Serialno.

(x/d)ratio

Q M E (Q/Qo) (M/Mo) (E/Eo)

1 0.5 0.01943 0.6872 23.56134743 0.86034 0.594622 0.4382352 4 0.029799 0.76977 23.13267062 1.319473 0.666068 0.4302613 8 0.059412 1.13577 24.4716241 2.630712 0.982761 0.4551664 12 0.062807 0.923486 15.97006334 2.781039 0.799076 0.2970395 16 0.0745926 0.9049843 11.46313534 3.3028958 0.783066 0.213211

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CONCLUSION

As the jet progresses through the potential core zone to the zone of establis hment and finallyenters fully developed zone, the central velocity (at r = 0) is observed to decrease. This isbecause there is more and more mixing with stagnant air around.

The shape of the velocity profile:- Location 1 => u more or less constant and then very steep fall => POTENTIAL CORE- Locations 2 & 3 => the profile spreads and the central velocity decreases with x =>ESTABLISHMENT ZONE- Locations 4 & 5 => the shape is same though the central velocities are diffe rent => FULLYDEVELOPED ZONE

No external force on the system => the momentum flux should remain constant. The graphverifies this: M/M0 curve is more or less constant.

0

0.5

1

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2.5

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3.5

0 2 4 6 8 10 12 14 16 18

Q/Qo vs (x/d)

M/Mo vs (x/d)

E/Eo vs (x/d)

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SOURCES OF ERROR

1. The equation used for calculating the velocity is derived from Bernoullis equation which isvalid for inviscid and incompressible flow but our system is not ideally so.

2. The graph representing the fluxes may deviate form actuality due to the end effects of thenozzle.

3. The centering of the pitot tube may not be right.

POSSIBLE CORRECTIONS1. The traverse mechanism can be made to be more sensitive;2. More efficient and accurate instrument other than pitot tube can be used as pitot tube

may give deviant results in presence of a velocity gradient;3. Manual errors in reading the manometer and positioning the pitot tube may be

minimized.

- AMAN AGAWAL- 2009CH10058- GROUP 2