impact of a jet experiment

Le Vu Anh Phuong (U1320848B)

1

CHEMICAL AND BIOMEDICAL

ENGINEERING

(Division of Chemical & Biomolecular Engineering)

Nanyang Technological

University

Yr 2 / SEMESTER 2

N1.2-B4-16

CH2702

Experiment C3

Impact of a Jet

Name: Le Vu Anh Phuong Student ID: U1320848B Group: 14 Date: 17/2/15


2

I. Log Sheet

Table 1. Results for flat plane

y (mm) C (L) t (s) M (kg/s) V0 V1 MV1 Kx

10 25 106 0.236 3.004 2.888 0.681 0.392

20 25 84 0.298 3.791 3.700 1.101 0.784

30 25 75 0.333 4.246 4.165 1.388 1.176

40 25 66 0.379 4.825 4.754 1.801 1.568

50 25 59 0.424 5.398 5.334 2.260 1.960

60 25 55 0.455 5.790 5.731 2.605 2.352

70 25 51 0.490 6.245 6.189 3.034 2.744

y = 1.0014x - 0.2732R = 0.9979

0.000

0.500

1.000

1.500

2.000

2.500

3.000

0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500

Kx

MV1

Kx vs MV1 (flat plane)


3

Table 2. Results for hemispherical cup

y (mm) C (L) t (s) M (kg/s) V0 V1 MV1 Kx

20 25 132 0.189 2.413 2.266 0.429 0.784

40 25 92 0.272 3.462 3.361 0.913 1.568

60 25 76 0.329 4.190 4.108 1.351 2.352

80 25 67 0.373 4.753 4.681 1.746 3.136

100 25 59 0.424 5.398 5.334 2.260 3.920

120 25 54 0.463 5.898 5.839 2.703 4.704

130 25 52 0.481 6.124 6.068 2.917 5.096

y = 1.7368x + 0.023R = 0.9994

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

4.000

4.500

5.000

5.500

0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500

Kx

MV1

Kx vs MV1 (hemispherical cup)


4

II. Questions

1.

a). By the least-square method:

For the flat plane:

X (MV1) Y (Kx)

0.6811 0.392 1.001388 -0.27315 #N/A #N/A #N/A

1.1011 0.784 0.020396 0.040751 #N/A #N/A #N/A

1.3882 1.176 0.99793 0.042204 #N/A #N/A #N/A

1.8006 1.568 2410.631 5 #N/A #N/A #N/A

2.2601 1.960 4.293686 0.008906 #N/A #N/A #N/A

2.6049 2.352

3.0340 2.744

Hence the trend line equation and the coefficient of determination are

Kx = 1.0014MV1 - 0.2732

R = 0.9979

For the hemispherical cup:

X (MV1) Y(Kx)

0.4292 0.784 1.736779 0.023002 #N/A #N/A #N/A

0.9133 1.568 0.019398 0.037971 #N/A #N/A #N/A

1.3512 2.352 0.999377 0.043955 #N/A #N/A #N/A

1.7465 3.136 8016.442 5 #N/A #N/A #N/A

2.2601 3.920 15.48845 0.00966 #N/A #N/A #N/A

2.7033 4.704

2.9174 5.096

Hence the trend line equation and the coefficient of determination are

Kx = 1.7368MV1 + 0.023 R = 0.9994

Comments:

Both the experiment data sets show the positive relationship between Kx and MV1 as expected from the theory and equation (10) and (12) because higher rate of momentum transfer from the liquid jet (MV1) leads to the stronger the reaction force (Kx) needed to keep the vane at the balance position. However the measured reaction force Kx is consistently less than the expected rate of momentum transfer MV1 (for the flat plane) and 2MV1 (for the hemispherical plane). This shows that not all the momentum transferred was delivered to the vane. Hence the model equation (10) and (12) are not accurate due to the inability to account for this momentum loss. This loss could be due to the momentum loss to friction in the nozzle and to the rough surfaces of the plane and the cup.

b). Some sources of experimental errors apart from the loss to friction include human parallax errors in reading the water level at 0L and 25L. However this error is likely to be insignificant since the water level was rising rather slowly, giving sufficient time for human reaction in measuring the time interval. The more significant error could have arisen from the parallax error in reading the balance position of the tally. Firstly the tally was high, leading to difficulty in levelling the eye level with the tally balance mark. Secondly, though we tried to keep the weigh


5

beam from oscillating up and down due to the jet force, it was not possible to achieve zero oscillation, and hence the flow rate could be unbalanced by the jockey weigh. Furthermore the distance between the 2 balance marks on the tally were wider than the thickness of the top plate, leading to difficulty in determine when the plate fell right in between these 2 marks. Thus the balance position could have been inaccurate.

2. To reduce the experimental errors the following could be considered: the nozzle, the vane and

the hemispherical cup walls can be made smoother to reduce momentum loss to friction.

Additionally the distance of the two marks on the tally can be reduce to be closer to the

thickness of the top plate to reduce the uncertainty in reading the balance position. The height

of the tank can be made lower to make it easier to read the tally position.

3. The flat plane design should be used because in theory, at a given jet momentum transfer of MV1, a force of Kx=MV1 will be harnessed. If the hemispherical cup is used, the force obtained for the same MV1 will only be Kx=0.5MV1.

4. The force on the vane Kx is calculated by:

= 1 = 02 2 =

2

202 2 =

2 2202

20

If the flow rate is doubled, the time t required to collect the same amount of water will be halved, hence from the above equation, Kx will be increased by 4 times (if we neglect the correction on V1 due to the distance s, the 2nd term inside the square root will be canceled and Kx will be proportional to 1/t2).

Lets take the position y=70mm as an example

y (mm) C (L) t (s) M (kg/s) V0 V1 MV1

70 25 51 0.490 6.245 6.189 3.034

70 25 25.5 0.980 12.489 12.462 12.217

Here the theoretical Kx (=MV1) is about 4 times bigger when the time t is halved.

impact of a jet experiment

Documents