Impact-of-water-jet.docx

Experiment Title

:

Impact of Water Jet

Course

:

UEME2123 Fluid Mechanics I

Program

:

Civil Engineering

Name of Student

:

Muhammad Iqbal Budiawan

Student ID No

:

16.6480

Year and Trimester :

Y1T3

Date of Experiment :

9 August 2018

Name of Lecturer

Dr. Ng Chai Yan

:

Title: Impact of Water Jet Objective: To demonstrate the application of the momentum equation as applied to the impact of a jet of water on to 3 defectors of different angles of deflection. Introduction: The impact of water jet experiment is carried out to demonstrate and verify the integral momentum equation by calculating and comparing the force produced by a jet of water as it strikes to 60°, 90° 𝑎𝑛𝑑 130° deflector. The study of this equation is necessary to apply it to hydraulic machinery tools which use liquid power to do simple works such as Pelton wheel and impulse turbine. The total kinetic energy and momentum should be conserved if there is no energy loss in the system.

Newton’s second law state that The applied forces are equal to the rate change of momentum ∑𝐹 =

𝑑 𝑀𝑜𝑚𝑠𝑦𝑠 = ∑ṁ0 𝑣0 − ∑ṁ𝑖 𝑣𝑖 𝑑𝑡

∑𝐹 = −𝐹𝑥 𝑖 − 𝐹𝑦 𝑗 ṁ0 𝑣0 = ṁ𝑣0 𝑠𝑖𝑛Ɵ𝑖 + ṁ𝑣0 𝑐𝑜𝑠Ɵ𝑗 ṁ𝑖 𝑣𝑖 = ṁ𝑣0 𝑗

−𝐹𝑥 = ṁ𝑣0 𝑠𝑖𝑛Ɵ −𝐹𝑦 = ṁ𝑣0 𝑐𝑜𝑠Ɵ − ṁ𝑣1 Newton's Second Law of Motion states that The Applied Force is equal to the Rate of Change of Momentum 𝐹𝑦 = 𝜌𝑄𝑉𝑦2 − 𝜌𝑄𝑉𝑦1 = −𝜌𝑄𝑉𝑦1 (1 − cos Ɵ) if we assume V2 =V1 =Vy1 Where ρ is the density of water Vy1 is the inlet jet velocity in the y direction Vy2 is the outlet jet velocity in the y direction Q is the volumetric flow rate Ɵ is the angle of deflection of jet flow measured from the vertical The negative sign means the Applied Force is opposite to the direction of the inlet jet stream

Nozzle diameter

= 8 mm

Nozzle-impact distance = 15 mm

Water turbines are widely used throughout the world to generate power. By allowing fluid under pressure to strike the vanes of a turbine wheel, mechanical work can be produced. Rotational motion is then produced by the force generated as the jet strikes the vanes. One of the common types of water turbines is Pelton wheel. In this type of water turbine, one or more water jets are directed tangentially on to a vanes or buckets that are fastened on the rim of the turbine disc. The impact of the water on the vanes generates a torque on the wheel causing it to rotate and to develop power. To predict the output of a Pelton wheel and to determine its optimum rotational speed, understanding on how the deflection of the jet generates a force on the buckets and how the force is related to the rate of momentum flow in the jet are needed. This experiment aims at assessing the different forces exerted by the same water jet on a variety of geometrical different plates. Under this experiment, the force generated by a jet of water striking a deflector is measured.

Equipment and Materials:

Item Description

*Item category

Impact of Jet Apparatus Jockey Weight (4×20 g, 3×50 g, and 2× 100g) Target plates 36 mm diameter flat, 120° cone, 180° hemisphere nylon Hydraulic Bench LS-1801

E

*Item category SP

Sample or specimen

C

Consumable

CH Chemical

E

Labware, glassware, components Equipment

S

Software

W

tool,

and

Quantity estimation (e.g. per set/group of student) 1

W

1

W

1

E

1

Procedures: 1.

The top cover of the impact jet assembly was opened.

2.

The flat deflector plate (angle = 90 degrees) was installed.

3.

The top cover was replaced and the wing nuts was tighten to secure the cover tightly on to the impact jet chamber.

4.

The pointer on top of the cover was adjusted so that it is pointing to the central groove on the side of the base plate that is used to hold the weights.

5.

The 0.5 N weight was applied on top of the base plate. The base plate is now lower than the pointer.

6.

The main input water flow valve was fully opened; the bypass water valve was adjusted to control the volume flow rate until the pointer points to the central grove at the edge of the base plate.

7.

The volume flow rate reading was taken and entered into the spreadsheet in the computer provided for the purpose.

8.

The procedures were repeated with applied loads of 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 N.

9.

The steps 1-8 for deflector cup were repeated with angles = 130 degrees.

10. The steps 1-8 for deflector cup were repeated with angles = 60 degrees.

Data and Results: As shown in spreadsheet Table 1: Ɵ = 60° Cone q = 60o d

0.008 m

p

3.142

r q

1000 60 1.047 5.03E-05 0.0000631 9.81 0.015

Area Gal/min -> m3/s g Nozzle -Impact Dist

kg/m3 o

radians m2 m/s 2 m V1 equal to V 2

Q

Q

V1y

V1impact

Fy =-r*Q*V1y *(1-cos(q))

N 0.00 0.50 1.00 1.50

gal/min

m3/s

m/s

m/s

3.500 5.000 6.000

2.21E-04 3.15E-04 3.79E-04

4.39E+00 6.28E+00 7.53E+00

4.36 6.25 7.51

N 0.00 0.48 0.99 1.43

V1 not equal to V 2 Load/Fy

Fy =-r*Q*(V1y -V1impact* cos(q)) Load/Fy

1.03 1.01 1.05

N 0.00 0.49 0.99 1.43

1.02 1.01 1.05

1.03

Average

1.03

1.60

Theoretical applied force (N)

1 2 3

Load

1.40 1.20

y = 0.956x + 0.0079 R² = 0.9991

1.00 0.80 0.60 0.40 0.20 0.00 0.00

0.50 1.00 1.50 Actual applied force (N)

2.00

Table 2: Ɵ = 90° Flat Plate q = 90o d

0.008 m

p

3.142

r q

1000 90 1.571 Area 5.03E-05 Gal/min -> m3/s 0.0000631 g 9.81 Nozzle -Impact Dist 0.015

kg/m3 o

radians m2 m/s 2 m V1 equal to V 2

Q

Q

V1y

V1impact

Fy =-r*Q*V1y *(1-cos(q))

N 0.00 0.50 1.00 1.50 2.00 2.50 3.00

gal/min

m3/s

m/s

m/s

2.000 3.000 4.250 5.000 5.750 6.250

1.26E-04 1.89E-04 2.68E-04 3.15E-04 3.63E-04 3.94E-04

2.51E+00 3.77E+00 5.33E+00 6.28E+00 7.22E+00 7.84E+00

2.45 3.73 5.31 6.25 7.20 7.82

N 0.00 0.32 0.71 1.43 1.98 2.62 3.09

Theoretical applied force (N)

1 2 3 4 5 6

Load

V1 not equal to V 2 Load/Fy

Fy =-r*Q*(V1y -V1impact* cos(q)) Load/Fy

1.58 1.40 1.05 1.01 0.96 0.97

N 0.00 0.32 0.71 1.43 1.98 2.62 3.09

1.58 1.40 1.05 1.01 0.96 0.97

1.16

Average

1.16

3.50 y = 1.0819x - 0.173 3.00 R² = 0.9904 2.50 2.00 1.50 1.00 0.50 0.00 0.00 -0.50

1.00

2.00

3.00

Actual applied force (N)

4.00

Table 3: Ɵ = 130° Hemispherical cup q = 130o d

0.008 m

p

3.142

r q

1000 130 2.269 Area 5.03E-05 Gal/min -> m3/s 0.0000631 g 9.81 Nozzle -Impact Dist 0.015

o

radians m2 m/s 2 m V1 equal to V2

V1 not equal to V2

Load

Q

Q

V1y

V1impact

Fy =-r*Q*V1y *(1-cos(q))

Load/Fy Fy =-r*Q*(V1y -V1impact* cos(q)) Load/Fy

N 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

gal/min

m3/s

m/s

m/s

2.000 2.750 3.250 3.750 4.250 4.500 5.000 5.500

1.26E-04 1.73E-04 2.05E-04 2.37E-04 2.68E-04 2.84E-04 3.15E-04 3.47E-04

2.51E+00 3.45E+00 4.08E+00 4.71E+00 5.33E+00 5.65E+00 6.28E+00 6.90E+00

2.45 3.41 4.04 4.67 5.31 5.62 6.25 6.88

N 0.00 0.52 0.98 1.37 1.83 2.35 2.63 3.25 3.93

0.96 1.02 1.09 1.09 1.06 1.14 1.08 1.02

N 0.00 0.52 0.98 1.37 1.82 2.34 2.63 3.25 3.93

0.97 1.02 1.10 1.10 1.07 1.14 1.08 1.02

1.06

Average

1.06

4.50 4.00 y = 0.9402x - 0.0054 3.50 R² = 0.9944 3.00 2.50 2.00 1.50 1.00 0.50 0.00 2.00 -0.500.00

Theoretical applied force (N)

1 2 3 4 5 6 7 8

kg/m3

4.00

Actual applied force (N)

6.00

Calculation: (cone Ɵ = 60°) For 0.50N load 𝑁𝑜𝑧𝑧𝑙𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 0.008𝑚 𝑁𝑜𝑧𝑧𝑙𝑒 − 𝑖𝑚𝑝𝑎𝑐𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 0.015𝑚 𝜌 = 1000𝑘𝑔/𝑚3 𝜃 = 60° ×

𝐴𝑟𝑒𝑎 =

3.142𝑟𝑎𝑑 = 1.047𝑟𝑎𝑑 180°

𝜋𝑑 2 = 5.03 × 10−5 𝑚2 4

1𝐺𝑎𝑙/𝑚𝑖𝑛 = 6.31 × 10−5 𝑚3 /𝑠 𝑔 = 9.81𝑚/𝑠 2 1) Calculate volume flow rate 𝑄 = 3.5 𝐺𝑎𝑙/min(6.31 × 10−5 𝑚3 /𝑠) = 2.209 × 10−4 𝑚3 /𝑠

2) Calculate 𝑉1𝑦 𝑄 = 𝐴𝑉 𝑉1𝑦 =

(2.209 × 10−4 𝑚3 /𝑠) (5.03 × 10−5 𝑚2 )

= 4.392 𝑚/𝑠

3) Calculate 𝑉1𝑖𝑚𝑝𝑎𝑐𝑡 𝑣 2 = 𝑢2 + 2𝑎𝑠 𝑣1𝑖𝑚𝑝𝑎𝑐𝑡 2 = 𝑉1𝑦 2 + 2𝑔ℎ

𝑣1𝑖𝑚𝑝𝑎𝑐𝑡 = √4.3922 + 2(9.81)(0.015) 𝑉1𝑖𝑚𝑝𝑎𝑐𝑡 = 4.43 𝑚/𝑠

4) 𝑉1 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑉2 𝐹𝑦 = −𝜌𝑄𝑉1𝑦 (1 − 𝑐𝑜𝑠𝜃) = −(1000)(2.209 × 10−4 )(4.392)(1 − 𝑐𝑜𝑠60°) = −0.49𝑁 = 0.57𝑁 (𝑑𝑜𝑤𝑛𝑤𝑎𝑟𝑑)

5) 𝑉1 𝑛𝑜𝑡 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑉2 𝐹𝑦 = −𝜌𝑄(𝑉1𝑦 − 𝑉1𝑖𝑚𝑝𝑎𝑐𝑡 𝑐𝑜𝑠𝜃) = −(1000)(2.209 × 10−4 )(4.392 − 4.43𝑐𝑜𝑠60°) = −0.48𝑁 = 0.48𝑁 (downward)

6) Percentage error % 𝑒𝑟𝑟𝑜𝑟 =

=

|𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 − 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙| × 100% 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙

|0.49 − 0.50| × 100% 0.50

=2%

Discussion: In this experiment, 3 different deflector plates have been used to study the impact of water jet. The deflector cup of 60° has a lower calculated force compared to the actual. As for the 90° flat plate, the calculated force for the first 4 results showing a lower value than the actual. But, the last 2 shows higher value than the actual force. Finally, for the 130° deflector cup, all of the results except for the first one showed a lower calculated force compared to the actual force. These errors may be caused by several factors. One of them is human errors. Human tend to make mistakes, for example when reading the gauge, we have to make assumptions out of the scale. The pointer may also not right in the middle when the readings were taken. All three of the graphs of load/ 𝐹𝑦 have a positive gradient. Among these three graphs, 60° 𝑎𝑛𝑑 90° deflector have shown a clear deviation if compare to 130° deflector. By making an assumption, 𝑣1 equals to 𝑣2 have neglected the friction force across the solid surface. Therefore, the deviation happens in the graph. The collision between water to the deflector is not perfectly elastic. Besides that, the upflow stream created by 60° 𝑎𝑛𝑑 90° deflector towards the top cover could be another factor lead to deviation. Energy Equation: 2

Pi

2

v P v  i  zi  o  o  zo (Po & Pi = 0, atmospheric pressure)  2g  2g 2

2

vo v  i  s (Let zi  zo  s ) 2g 2g

vo  vi  2 gs (Proved) 2

When vo ≠ vi : Fy  rQ(v2 cos q  v1 ) , (vi  v1 , vo  v2 ) v1  v2 Fy   rQ(v1  v2 cos q )

When vo = vi : Fy  rQ(v2 cos q  v1 ) Assume v1  v2 Fy   rQv1 (1  cos q )

Based on the findings of the experiment, less flow rate required for the larger angle of deflector under same applied force. The result show that the higher the angle of deflector, the higher the impact produced under same flow rate. The experiment efficiency (Load/Fy) increases when the angle of deflector is also increased. Therefore, the deflector of 130° is the most suitable for impulse hydraulic machinery compared with the other two due to the efficiency and the impact produced. A few precaution steps were taken while conduction the experiment. Firstly, to avoid errors, the readings were taken several times. Besides, the reading was done by one of the members in order to keep the readings consistent.

Conclusion: As conclusion, the impact of a jet on 3 types of deflectors can be calculated by the application of the momentum equation. The calculated applied forces are just a fraction out of the actual applied force. They are acceptable as the error percentage is no more than 10%.

Reference: IMPACT

OF

A

JET.

(n.d.).

Retrieved

August

16,

2018,

from

https://www.tecquipment.com/impact-of-a-jet H. C., L. C., T. T., & N. A. (2013, July 16). A numerical study on high-speed water jet impact. Retrieved

August

16,

2018,

https://www.sciencedirect.com/science/article/pii/S0029801813002588

from