PIRI REIS UNIVERSITY

ENGINEERING FACULTY

NAVAL ARCHITECTURE and MARINE ENGINEERING DEPARTMENT

LABORATORY REPORT
COVER SHEET

Name of the experiment: H8 Impact of a Jet

Group leader : OĞUZ KAĞAN BOZKURT

Data recorder : 5a-5b

Date report is due : 10.05.2023

PRU student numbers, names, and signatures of group members.

1) 20200201011 OĞUZ KAĞAN

BOZKURT

2) 20200202001 EMİRHAN SERT

3) 20210201070 BERKE TUTGUN

4)

5)

1
 ABSTRACT

The purpose of this experiment is to examine the force produced by the impact of a water
jet on various target vanes and to calculate and compare the experimental and theoretical
forces exerted by the water jet separately with the obtained data. The procedure followed
for this experiment is by changing the flow rate, balancing the weight with the required t,y
and m such as data acquisition. The same procedure can be repeated at 4 different speeds
for different target vanes. During each repetition, the weight must first be brought to the
zero point and then moved to the relevant y point for balance. The vanes used for this
experiment are of four types. Straight, curved, spherical and conical vanes were used for
this experiment. Comparison of the theoretical and experimental results obtained as a result
of the calculations made after the completion of the procedures can be revealed with the
error percentage. The result of the experimental forces is impact velocity, m, and depends
on the angle the vane has. Theoretical forces, on the other hand, depend on the
gravitational acceleration and the y values.

2
CONTENTS

CHAPTERS PAGE

1. OBJECTIVES OF THE EXPERIMENT 4

2. THEORY AND ANALYSIS 4-6

3. BRIEF DESCRIPTION OF THE EQUIPMENT 6-7

4. METHODS AND TEST PROCEDURE 8

5. SUMMARY OF RESULTS 9-12

6. DISCUSSION 13-14

7. CONCLUSIONS 14

8. APPENDICES 15-32

3
1. OBJECTIVES OF THE EXPERIMENT

Our objective in this experiment is to see how we could produce mechanical work from a
fluid that is accelerated by pressure and hitting 4 different kinds of vane plates, these being
the Flat Plate at 90o, the Hemispherical Cup at 120 o, the Conical Plate at 180 o and the
Angled Plate (H8b) at 30o. We investigate the forces caused by the change in the
momentum of the fluid when the jet of water strikes these surfaces and compare the results
we got from this experiment by applying our data in the momentum equation.

2. THEORY AND ANALYSIS

A symmetrical vane on the x-axis is assumed as shown in the figure. A jet of water flowing
along the x-axis with velocity 𝑢0 strikes the vane on the x-axis and deflects the vane water
along the angle 𝛽. Changes in elevation and pressure in the jet are ignored from the time
the water hits the propeller to leaving the vane. Momentum enters the system in the
xdirection at the rate:

4
 𝑚𝑢̇ 0 [𝑘𝑔. 𝑚. 𝑠-2] (1)

After the water deviates by an angle 𝛽, the momentum leaves the system in the same
direction. Momentum leaves the system at the following rate:

𝑚 ̇ 𝑢1 cos(𝛽) [𝑘𝑔. 𝑚. 𝑠-2] (2)

The force in the x-direction on the vane is equal to the rate of change of momentum. In this
case, the equation is:

𝐹 = 𝑚 ̇ (𝑢0 – 𝑢1 cos(𝛽)) [𝑁] (3)

Ideally, the jets are at a constant velocity so 𝑢0 = 𝑢1. In this case:

𝐹 = 𝑚𝑢̇ 0(1 − cos(𝛽)) [𝑁] (4)

For example;
a. For a 30° angled plate (𝛽 = 30°) and cos(𝛽) = 0.87, equation 4 becomes:

𝐹 = 0.87𝑚𝑢̇ 0[𝑁] (5)

b. In the case of a flat plate (𝛽 = 90°) and cos(𝛽) = 0, equation 4 becomes:

𝐹 = 𝑚𝑢̇ 0[𝑁] (6)

c. For a conical plate (𝛽 = 120°) and cos(𝛽) = -0.5, equation 4 becomes:

𝐹 = 1.5𝑚𝑢̇ 0[𝑁] (7)

d. For a hemispherical container (𝛽 = 180°) and cos(𝛽) = -1, equation 4 becomes:

5
 𝐹 = 2𝑚𝑢̇ 0[𝑁] (8)

Table 2.1

The mass flow of the fluid is equal to the product of its density, the flow area, and the
velocity:

𝑚 ̇ = 𝜌𝐴𝑢 [𝑘𝑔/𝑠] (9)

3. BRIEF DESCRIPTION OF THE EQUIPMENT

3.1 The Experimental Placement of Equipment.

Figure 3.1
The effect of the jet device consists of a pipe with a vertical tapered end and a supply hose.
6
The hose sprays water to hit the plate in the middle. Vane; it can be Hemispherical Cup,
Flat Plate, 30° Angled Plate, or Conical Plate. The hose and plate are in a plastic
cylindrical tank. There is a hole in the bottom of this tank. Water enters the weighing tank
through this hole. The vane is mounted on a vertical axis and supported by a pivot beam
that carries the weight of a jockey and is limited by a spring. The force exerted by the
water jet on the vane can be equalized by placing the weight against the gauge on the beam
until it returns to its normal position.

3.2 Technical Specifications

Density of water ρ = 103 kg/m3

Diameter of nozzle = 10 mm
Cross-sectional area of nozzle, A = 78.5 mm2
Mass of jockey weight = 0.6 kg
Distance from center of the vane to the pivot of lever = 0.15 m

3.3 Test Description of the Apparatus.

The experimental unit used is on a hydraulic bench. This bench provides water and can
measure flow. The unit is a transparent cylindrical tank. The entire unit stands on three
adjustable feet. The water enters the tank vertically through a conical mouth pipe in the
tank. This; produces a jet of water to strike plates in the shape of a Hemispherical Cup, Flat
Plate, 30° Angle Plate, or Conical Plate. This jet of water exerts a force on the plate on the
vane. The vane is supported by a beam bounded by a slight spring. A jockey weight W is
placed on the beam to counteract the force F due to momentum transfer in the plate. The
plate returns to its original position. The force F exerted by the jet on the flat plate is equal
to the weight W. The water is separated from the tank by a drain pipe. The water
discharged into the weighing tank after hitting the flat plate is used to measure the
discharge by the volumetric method.

7
4. METHODS AND TEST PROCEDURE

The experiment is about how much the weight above is displaced by changing the flow of
water in different vanes. First, we placed the weight on the weight carrier, then balanced it
so that the weight marker was in the middle position. At the same time, we recorded the
information on the weight indicator. We started the pump by pressing the green button,
then we moved the flow regulating valve and changed the water supply. We performed 4
experiments by changing the flow rate of the water for each vane. As the pressure of the
water changed, the position of the vane and weight marker changed, we changed the
location of the weight so that the weight marker was in the middle position again. (These
data have been recorded.) By closing the water drain, we measured with a stopwatch until
the water accumulates 5 litres and we recorded the stopwatch values here. Finally, we
closed the valve and the pump and let the water of the device drain. We were in the
laboratory for about 1 hour when the experiment would take.

8
5. SUMMARY of RESULTS
5.1 Data and Result Tables

5.1.1 Flat Plate 90o

Quantit t (s) y (m) ṁ (kg/s) u (m/s) u0^2 (m/s) u0 (N) ṁu0 (N) F (N)
5 14 0,045 0,3571428 4,5495905 20,011774 4,4734521 1,5976614 1,7658
5 11,5 0,069 0,4347826 5,5386319 29,989443 5,4762618 2,3809834 2,7075
5 11 0,076 0,4545454 5,7903879 32,841592 5,7307584 2,6048902 2,9822
5 10 0,08 0,5 6,3694267 39,882597 6,3152669 3,1576334 3,1392
5 9 0,083 0,5555555 7,0771408 49,39892 7,0284366 3,9046870 3,2569
Table 5.1

5.1.2 Conical Cup 120o

Quantit t (s) y (m) ṁ (kg/s) u (m/s) u0^2 (m/s) u0 (N) 1,5ṁu0 (N) F (N)
5 19,25 0,035 0,2597402 3,3087931 10,261111 3,2032970 1,2480252 1,3734
5 12,1 0,096 0,4132231 5,2639890 27,022580 5,1983248 3,2222223 3,7670
5 10,8 0,11 0,4629629 5,8976173 34,094890 5,8390830 4,0549186 4,3164
5 10,6 0,12 0,4716981 6,0088931 35,419797 5,9514533 4,2109283 4,7088
5 10,15 0,125 0,4926108 6,2752972 38,692356 6,2203180 4,5962960 4,905
Table 5.2

5.1.3 Hemispherical Cup 180o

Quantit t (s) y (m) ṁ (kg/s) u (m/s) u0^2 (m/s) u0 (N) 2ṁu0 (N) F (N)
5 17,05 0,065 0,2932551 3,7390029 13,293142 3,6459762 2,138412 2,5506
5 12,25 0,121 0,4081632 5,2040816 26,395465 5,1376517 4,1940007 4,7480
5 11,2 0,14 0,4464285 5,6919642 31,711457 5,6312926 5,0266999 5,4936
5 10,6 0,15 0,4716981 6,0141509 35,483011 5,9567618 5,6187933 5,886
5 10,35 0,155 0,4830917 6,1594202 37,251458 6,1033972 5,8965010 6,0822
Table 5.3

9
5.1.4 Angled Plate 30o

ṁu0
Quantit t (s) y (m) ṁ (kg/s) u (m/s) u0^2 (m/s) u0 (N) (N)0,87 F (N)
5 22 0,019 0,2272727 2,8951939 7,695148 2,7740130 0,5484915 0,7455
5 16 0,028 0,3125 3,9808917 15,160498 3,8936485 1,0585856 1,0987
5 13 0,04 0,3846153 4,8995590 23,318678 4,8289417 1,6158382 1,5696
5 12 0,048 0,4166666 5,3078556 27,486331 5,2427408 1,9000493 1,8835
5 11 0,056 0,4545454 5,7903879 32,841592 5,7307584 2,2662544 2,1974
Table 5.4

5.2 Graphics

Impact of a Jet. Impact of a jet Apparatus.

Figure 5.1 Typical test results.

10
Impact of a Jet. Impact of a jet Apparatus.

Figure 5.2 Typical test results.

Impact of a Jet. Impact of a jet Apparatus.

Figure 5.3 Typical test results.

11
Impact of a Jet. Impact of a jet Apparatus.

Figure 5.4 Typical test results.

IDEAL RESULTS

Figure 5.5 Force developed on vanes of various shapes.

12
6. DISCUSSION

The main objective of this experiment is to examine the effect of a water jet on different
vane types through an experimental analysis. The water jet apparatus is used to
demonstrate how fluid force is used to create a force. Some of the fluid energy is converted
into kinetic energy. This conversion is done in a nozzle emitting a jet of fluid at high
velocity. The jet works with the principle of directing the force generated by the change of
momentum of the fluid to the vane, according to Newton's second law of motion.

Although the collected data differed slightly from the theoretical values, the experiment
was carried out successfully. Differences in these values are due to several errors affecting
the data collected during the experiment. Some error percentages are very large due to
several errors made during the experiment.

Error calculations and other reviews can be viewed in Table 5.1, 5.2, 5.3 and 5.4, as well as
in chapter 8.1 calculations. The calculations made are shown in detail in the 8th chapter of
the report. Calculations are given in the 8th section in detail so that the process steps can be
followed easily. It has been put forward in theory that the u and u0 velocities will be equal
to each other. When the data obtained during the experiment is also examined, the data
confirm the theory. These results can be obtained from Tables 5.1, 5.2, 5.3 and 5.4. In
Chapter 5.2, there are scatter graphs prepared with the data obtained as a result of the
experiment. As can be seen from the graphs, there is a linear relationship between Force on
vane and Rate of delivery of momentum.

The reasons for the errors to occur during the experiment;

a. Use of stopwatch: Error when recording time.

b. Position of the observer's eye: Error when the pointer is not exactly at zero. To avoid this
error, the observer's eye must be 90° perpendicular to the object.
c. Pump Error: The pump needs a continuous water supply. An error may occur if the
pump cuts off the supply. Also, the condition of the pump, which creates a vibration

13
 across the bench, causes the water to have an inconsistent flow throughout the
experiment.

d. Vane position: An error may occur when the jet is inclined to the wing. The jet should
hit the center of the vane.

to. Reservoir: The presence of impurities in the reservoir disrupts the water flow. In this
case, there is a high probability of error in the received data.

To prevent these errors, the text of the experiment should be read carefully and the
important parts should be understood before the experiment. In addition, help should be
sought from the laboratory manager at the point of difficulty during the experiment, so that
the error can be minimized.

7. CONCLUSIONS

According to the information observed during the experiment, it can be observed that the
velocity of the water during the experiment depends on the pressure below the amount of
water supplied at that moment. That said, it should also be mentioned that the deflection
angle varied depending on the intensity and the numerical value of the force applied to the
mass of water in the hydraulic bench. During the experiment, the measurements were
recorded by making changes in the velocity of the water and the vane geometries, and the
calculations in the 5th and 8th sections were made with these data, and the tables were
filled.

14
8. APPENDICES
8.1 Calculations
8.1.1 Flat Plate 90o

Data and calculations in the first row of Table 5.1.

5 𝐿 = 0.005 𝑚3

𝑡 = 14 𝑠

𝜌𝑉 𝑘𝑔/𝑚3)
𝑚̇ = =
𝑡 14s

𝑚̇ = 0. 35714𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢 𝑚̇

𝑢 𝑚/𝑘𝑔) (0,35714𝑘𝑔/𝑠)

𝑢 =4,5495 𝑚/𝑠

𝑢
𝑢°=4,47345 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠90°)

Experimental Force :

𝐹 = 𝑚̇ 𝑢0

𝐹 = (0.357142 𝑘𝑔/𝑠)(4,47345 𝑚/𝑠)

𝐹 = 1,597656𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.045 𝑚)

𝐹 = 1,7658 𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = |(1,76-1,59)/1,76 | 𝑥100

15
𝐸𝑟𝑟𝑜𝑟 (%) = 96,5%

16
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡=
(1000 𝑘𝑔/𝑚3)
(0.005 𝑚̇ =
second row of Table 5.1.

11,5 𝑠

𝜌𝑉 𝑚3)
=
𝑡 (11,5 𝑠)

𝑚̇ = 0.43478 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔)(0,43478 𝑘𝑔/𝑠)

𝑢=5,5386𝑚/𝑠

𝑢
𝑢⁰=5,4762 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠90°)

Experimental Force :

𝐹 = 𝑚̇ 𝑢0

𝐹 = (0.43478 𝑘𝑔/𝑠)(5,54762𝑚/𝑠)

𝐹 = 2,41 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.069 𝑚)

17
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡=
(1000 𝑘𝑔/𝑚3)
(0.005 𝑚̇ =
𝐹 = 2,71 𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = |(2,71-2,41)/2,71|𝑥100

𝐸𝑟𝑟𝑜𝑟 (%) = %11%

third row of Table 5.1.

11𝑠

𝜌𝑉 𝑚3)
=
𝑡 (11 𝑠)

𝑚̇ = 0,454 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔) (0,454𝑘𝑔/𝑠)

𝑢=5,79038𝑚/𝑠

𝑢
𝑢⁰=5,73075𝑚/𝑠
Experimental Force :

18
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡=
(1000 𝑘𝑔/𝑚3)
(0.005 𝑚̇ =
𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠90°)

𝐹 = 𝑚̇ 𝑢0

𝐹 = (0.454 𝑘𝑔/𝑠)(5,7307 𝑚/𝑠)

𝐹 = 2,60 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.076 𝑚)

𝐹 = 2,98 𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = |(2,98-2,6)/2,98| 𝑥100

𝐸𝑟𝑟𝑜𝑟 (%) = 12 %

fourth row of Table 5.1.

10 𝑠

𝜌𝑉 𝑚3)
=
𝑡 (10 𝑠)

𝑚̇ = 0.5 𝑘𝑔/𝑠

19
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡=
(1000 𝑘𝑔/𝑚3)
(0.005 𝑚̇ =
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔)(0,5𝑘𝑔/𝑠)

𝑢=6,3694 𝑚/𝑠

𝑢
𝑢⁰=6,3152 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠90°)

Experimental Force :

𝐹 = 𝑚̇ 𝑢0

𝐹 = (0.5 𝑘𝑔/𝑠)(6,3152 𝑚/𝑠)

𝐹 = 3,15𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.08 𝑚)

𝐹 = 3,13𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = |3,13-3,15)/3,13|𝑥100

𝐸𝑟𝑟𝑜𝑟 (%) = 0,6%

20
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡=
(1000 𝑘𝑔/𝑚3)
(0.005 𝑚̇ =

21
8.1.2 Conical Cup 120o

Data and calculations in the first row of Table 5.2.

5 𝐿 = 0.005 𝑚3

𝑡 = 19,25 𝑠

𝜌𝑉 𝑘𝑔/𝑚3)
𝑚̇ = =
𝑡 19,25s

𝑚̇ = 0.259 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔) 0,259𝑘𝑔/𝑠)

𝑢=3,30 𝑚/𝑠

𝑢
𝑢⁰=3,20 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠120°)

Experimental Force :

𝐹 = 1.5𝑚̇ 𝑢0

𝐹 = (1.5)(0.259 𝑘𝑔/𝑠)(3,20 𝑚/𝑠)

𝐹 = 1,24 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0,035 𝑚)

𝐹 = 1,37𝑁
Error (%) :

22
Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100
𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 9,4%

Data and calculations in the second row of Table 5.2.

5 𝐿 = 0.005 𝑚3

𝑡 = 12,1 𝑠

𝜌𝑉 𝑘𝑔/𝑚3)
𝑚̇ = =
𝑡 12,1s

𝑚̇ = 0.0,4132 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔) 𝑘𝑔/𝑠)

𝑢=5,263 𝑚/𝑠

𝑢
𝑢⁰=5,198 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠120°)

Experimental Force :

𝐹 = 1.5𝑚̇ 𝑢0

𝐹 = (1.5)(0.4132 𝑘𝑔/𝑠)(5,198 𝑚/𝑠)

𝐹 = 3,22 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.096𝑚)

𝐹 = 3,77𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

23
 𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 14%

Data and calculations in the third row of Table 5.2.

5 𝐿 = 0.005 𝑚3

𝑡 = 10,8 𝑠

𝜌𝑉 𝑘𝑔/𝑚3)
𝑚̇ = =
𝑡 10,8

𝑚̇ = 0,462 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔)(0,462𝑘𝑔/𝑠)

𝑢=5,897 𝑚/𝑠

𝑢
𝑢⁰=5,839𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠120°)

Experimental Force :

𝐹 = 1.5𝑚̇ 𝑢0

𝐹 = (1.5)(0.462 𝑘𝑔/𝑠)(5,839 𝑚/𝑠)

𝐹 = 4,04𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.11 𝑚)

𝐹 = 4,31 𝑁

24
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 6%

25
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡= 𝑠

(1000 𝑘𝑔/𝑚3)(0.005
𝑚̇ = =
fourth row of Table 5.2.

10.6

𝜌𝑉 𝑚3)

𝑡 (10,6 𝑠)

𝑚̇ = 0.472 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔) 𝑘𝑔/𝑠)

𝑢 𝑚/𝑠

𝑢
𝑢 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠120°)

Experimental Force :

𝐹 = 1.5𝑚̇ 𝑢0

𝐹 = (1.5)(0.472 𝑘𝑔/𝑠)(5.96 𝑚/𝑠)

𝐹 = 4.22 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.12 𝑚)

𝐹 = 4,7 𝑁
Error (%) :

26
Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100
𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 10,2%

8.1.3 Hemispherical Cup 180o

Data and calculations in the first row of Table 5.3.

5 𝐿 = 0.005 𝑚3

𝑡 = 17,05 𝑠

𝜌𝑉 𝑘𝑔/𝑚3)
𝑚̇ = =
𝑡 17,05 s

𝑚̇ = 0.293 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔)(0,293 𝑘𝑔/𝑠)

𝑢=3,739 𝑚/𝑠

𝑢
𝑢⁰=3,645 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠180°)

Experimental Force :

𝐹 = 2𝑚̇ 𝑢0

𝐹 = (2)(0.0,293 𝑘𝑔/𝑠)(3,645 𝑚/𝑠)

𝐹 = 2,138 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

27
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡= 𝑠

(1000 𝑘𝑔/𝑚3)(0.005
𝑚̇ = =
𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.021 𝑚)

𝐹 = 0.2,55 𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 16%

second row of Table 5.3.

12,25

𝜌𝑉 𝑚3)

𝑡 (12,25 𝑠)

𝑚̇ = 0,408 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔)(0,408 𝑘𝑔/𝑠)

𝑢=5,204 𝑚/𝑠

𝑢
𝑢⁰=5,137𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠180°)

Experimental Force :

𝐹 = 2𝑚̇ 𝑢0

𝐹 = (2)(0.0,408 𝑘𝑔/𝑠)(5,137 𝑚/𝑠)

28
 𝐹 = 4,194 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.121 𝑚)

𝐹 = 4,74 𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) =11,68%

Data and calculations in the third row of Table 5.3.

5 𝐿 = 0.005 𝑚3

𝑡 = 11,2 𝑠

𝜌𝑉 𝑘𝑔/𝑚3)
𝑚̇ = =
𝑡 11,2

𝑚̇ = 0.446 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔)(0.446 𝑘𝑔/𝑠)

𝑢=5,691 𝑚/𝑠

𝑢
𝑢⁰=5,631 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠180°)

Experimental Force :

29
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡= 𝑠

(1000 𝑘𝑔/𝑚3)(0.005
𝑚̇ = =
𝐹 = 2𝑚̇ 𝑢0

𝐹 = (2)(0.446 𝑘𝑔/𝑠)(5,631 𝑚/𝑠)

𝐹 = 5,02 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.14 𝑚)

𝐹 = 5,49 𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 8,2%

fourth row of Table 5.3.

10,6 𝜌𝑉 𝑚3)

𝑡 (10,6 𝑠)

𝑚̇ = 0.471 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔)(0,471 𝑘𝑔/𝑠)

𝑢=6,014 𝑚/𝑠

30
𝑢
𝑢⁰=5,956𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽) = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠180°)

Experimental Force :

𝐹 = 2𝑚̇ 𝑢0

𝐹 = (2)(0.471 𝑘𝑔/𝑠)(5.956 𝑚/𝑠)

𝐹 = 5,61 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.15 𝑚)

𝐹 = 5,88 𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 4,6%

8.1.4 Angled Plate 30o

Data and calculations in the first row of Table 5.4.

5 𝐿 = 0.005 𝑚3

𝑡 = 22.3 𝑠

𝜌𝑉 𝑘𝑔/𝑚3)
𝑚̇ = =
𝑡

𝑚̇ = 0.224 𝑘𝑔/𝑠
𝑚̇ 𝑚̇

31
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡= 𝑠

(1000 𝑘𝑔/𝑚3)(0.005
𝑚̇ = =
𝑢
𝑚̇

𝑢 𝑚/𝑘𝑔) 𝑘𝑔/𝑠)

𝑢 𝑚/𝑠

𝑢 𝑚/𝑠
Experimental Force :
𝐹 = 0.87𝑚̇ 𝑢0

𝐹 = (0.87)(0.224 𝑘𝑔/𝑠)(2.74 𝑚/𝑠)

𝐹 = 0.53 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.019 𝑚)

𝐹 = 0.74 𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 29,1%

32
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡=
(1000 𝑘𝑔/𝑚3)
(0.005 𝑚̇ =
second row of Table 5.4.

16𝑠

𝜌𝑉 𝑚3)
=
𝑡 (12 𝑠)

𝑚̇ = 0.3125 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢 𝑚̇

𝑢 𝑚/𝑘𝑔) (0,3125𝑘𝑔/𝑠)

𝑢=3,98 𝑚/𝑠

𝑢
𝑢⁰=3,893 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽)
Experimental Force :

𝐹 = 0.87𝑚̇ 𝑢0

𝐹 = (0.87)(0.3125 𝑘𝑔/𝑠)(3,893 𝑚/𝑠)

𝐹 = 1,05 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.028 𝑚)

33
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡=
(1000 𝑘𝑔/𝑚3)
(0.005 𝑚̇ =
𝐹 = 1,09 𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 2,8%

third row of Table 5.4.5 𝐿 = 0.005 𝑚3

𝑡 = 13 𝑠

𝜌𝑉 𝑘𝑔/𝑚3)
𝑚̇ = =
𝑡 13 s

𝑚̇ = 0.384 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢 𝑚̇

𝑢 𝑚/𝑘𝑔)(0,384 𝑘𝑔/𝑠)

𝑢=4,9 𝑚/𝑠

𝑢
𝑢⁰=4,828 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽)
Experimental Force :

34
Data and calculations in the

𝐹 = 0.87𝑢0

𝐹 = (0.87)(0.450 𝑘𝑔/𝑠)(5.68 𝑚/𝑠)

𝐹 = 1,90 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.04 𝑚)

𝐹 = 1,56 𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 17%

fourth row of Table 5.4.

12 𝑠

𝜌𝑉 𝑚3)
=
𝑡 (12 𝑠)

𝑚̇ = 0.416 𝑘𝑔/𝑠
𝑚̇ 𝑚̇
𝑢 𝑚̇

𝑢 𝑚/𝑘𝑔)(0,416𝑘𝑔/𝑠)

35
Data and calculations in the

5 𝐿 = 0.005 𝑚3

𝑡=
(1000 𝑘𝑔/𝑚3)
(0.005 𝑚̇ =
𝑢=5,307 𝑚/𝑠

𝑢
𝑢⁰=5,242 𝑚/𝑠

𝐹 = 𝑚̇ 𝑢0(1 − 𝑐𝑜𝑠𝛽)
Experimental Force :

𝐹 = 0.87𝑚̇ 𝑢0

𝐹 = (0.87)(0.416 𝑘𝑔/𝑠)(5,242 𝑚/𝑠)

𝐹 = 1,9 𝑁
Theoretical Force :

𝐹 = 4𝑔𝑦

𝐹 = (4 𝑘𝑔/𝑚)(9.81 𝑚/𝑠2)(0.048 𝑚)

𝐹 = 1,88𝑁
Error (%) :

Error (%)= |𝐹 𝑇ℎ𝑒𝑜−𝐹𝐸𝑥𝑝 | 𝑥100

𝐹𝑇ℎ𝑒𝑜

𝐸𝑟𝑟𝑜𝑟 (%) = 0,8%

36
8.2 References
[1] Çengel Y., Cimbala J. M., Fluid Mechanics Fundamentals and Applications, Mc
Graw Hill, New York, NY, USA, 2014.
[2] Giancoli D. C., Physics Principles with Applications, Pearson, England, 2016.
[3] Impact of Jet, TecQuipment Ltd., 2018.

37