Fluid Mechanics Sessional_EXpt

CE 4013: Harbour and Coastal Engineering Denis O’Sullivan, 108348006

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Name: Eoghan O’Driscoll Collins

Student Number: 109326049

April 2013

Dr. Jimmy Murphy

CE 4013: Harbour

and Coastal Engineering

University College CorkColáiste na hOllscoile CorcaighDepartment of Civil and Environmental Engineering.


Table of ContentsExperiment 1: Wave Celerity.................................................................................................................3

1.1 Introduction...........................................................................................................................3

1.2 Apparatus..............................................................................................................................3

1.3 Method..................................................................................................................................4

1.4 Formulae................................................................................................................................4

1.5 Results and Calculations........................................................................................................5

1.6 Discussion and Conclusion.....................................................................................................7

Experiment2: Observation of Different Wave Types, Wave Run-up and Interaction with Obstacles....8

2.1 Observation of Different Wave Types....................................................................................8

2.1.1 Regular Waves...............................................................................................................8

2.1.2 Irregular Waves..............................................................................................................8

2.1.3 Bulls Eye Wave...............................................................................................................8

2.1.4 Freak Wave....................................................................................................................8

2.1.5 Observation of Wave Period and Wavelength...............................................................9

2.2 Observation of Reaction with Obstructions...........................................................................9

2.2.1 Interaction with Rubble Mound Breakwater (Beach)....................................................9

2.2.2 Interaction with Vertical Wall......................................................................................10

2.2.3 Interaction with Partial Depth Fixed Wave Barrier......................................................10

Experiment 3: Stability of a Floating Body...........................................................................................11

3.1 Introduction.........................................................................................................................11

3.2 Apparatus............................................................................................................................11

3.3 Method................................................................................................................................12

3.4 Formulae..............................................................................................................................13

3.4.1 Theoretical Metacentric Height...................................................................................13

3.4.2 Experimental Metacentric Height................................................................................14

3.5 Results and Calculations......................................................................................................14

3.6 Graph for Determination of Experimental Metacentric Height...........................................16

3.7 Discussion of Results and Conclusion..................................................................................17

Experiment 4: Sediment Transfer........................................................................................................18

4.1 What is happening?.............................................................................................................18

4.2 How is it happening?...........................................................................................................18

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4.3 Why are we studying it?......................................................................................................19

Experiment 1: Wave Celerity1.1 IntroductionThis experiment investigateslinear water wave theory with respect to real waves. Linear

wave theory models wave behavious. It is only an approximate method of analysis but

results can be suprisingly accurate and consistent.

The experiments to compare real waves and linear wave theory were carried out in the UCC

Hydraulics and Maritime Research Centre (HMRC) in Pouladuff, Cork City in the specialised

18 x 25 x 1 metre wave tank in which the waves are generated by 40 centrally controlled

flap type wedge shaped aluminium paddles. The wave tank in this facility is capable

generating waves up to a significant wave height of 0.18 metres at a period of 2.5 seconds.

In this experiment, it was decided to investigate the agreement with theoretical values for

wave periods varying from 0.8 to 2 seconds. The wave height in this case was selected as

50mm. This was however varied in order to enable the easy observation of the waves.

1.2 ApparatusThe only apparatus required in this experiment were a stopwatch and the aforementioned

HMRC wave tank: a picture and a schematic of which is shown in Figure 1.1 and Figure 1.2.

Figure 1.1: HMRC Wave Tank

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Figure 1.2: Schematic of HMRC Wave Tank

1.3 Method1. For a particular wave period, measure the time taken for ten waves to pass a point

and divide it by ten to determine the experimental wave period. Repeat this and

take the average figure.

2. Measure the time it takes for a wave to pass between the two marks on the side of

the tank (8 metres apart). Divide 8 by this value to determine the experimental

celerity of the wave.

3. Repeat steps 1 and two for wave periods of 0.8, 1, 1.1, 1.14, 1.33, 1.6 and 2 seconds.

4. Use the data collected to calculate C0, CTheory, λ0, λ Theory and λ Measured. Plot these values

against Period, T.

1.4 FormulaeThe waves are classified as either deep water waves or transitional waves. The relevant

formulae are as follows:

Parameter Deep Water Transitional Water

Wave Velocity (c) c0=¿2π λ= ¿

2πtanh( 2π hλ )

Wave Length (λ)λ0=

gT 2

2πλ=gT

2

2πtanh( 2π hλ )

Limits of Application dL>0.5 0.02≤

dL≤0.5

Table 1.1: Formulae of Linear Wave Theory

The shallow water equations are omitted as none of the waves were shallow water waves.

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1.5 Results and Calculations

The data collected and the calculated C0, C Theory, λ0, λ Theory and λ Measured are shown in Table

1.2 below.

Period

(T)TMeasured C0 λ0 CTheory λTheory CMeasured λMeasured Classification

0.8 0.8 1.25 1.00 1.25 1.00 1.27 0.99 Deep1 1 1.56 1.56 1.56 1.56 1.54 1.60 Deep

1.14 1.144 1.78 2.03 1.77 2.02 1.75 2.01 Transitional1.33 1.32 2.08 2.76 2.04 2.71 1.91 2.58 Transitional1.6 1.62 2.50 4.00 2.33 3.73 2.24 3.63 Transitional2 1.99 3.12 6.25 2.61 5.22 2.38 4.78 Transitional

Table 1.2: Results and Calculations

The variation of C0, C Theory and C Measured with Period (T) is shown in Figure 1.3 while the

variation of λ0, λ Theory and λ Measured with Period (T) is shown in Figure 1.4.

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0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.20.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

Plot of C0, CMeasured & CTheory Against Period (T)

C Measured C Theory C0

Period, T / (sec)

Cele

rity,

c /

(m/s

)

Figure 1.3: Variation of Wave Celerity with Period (T).

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.20.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

Plot of λ0, λMeasured & λTheory Against Period (T)

λ Measured λ Theory λ0

Period, T / (sec)

Wav

elen

gth,

λ /

(m)

Figure 1.4: Variation of Wavelength with Period (T).

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1.6 Discussion and ConclusionBased on this experiment, it is possible to deduce that, for a given wave height, both the

wave celerity (c) and the wavelength (λ) increase with increasing Period (T), as is illustrated

by Figures 1.3 and 1.4 respectively.

It is apparent that the TMeasured is nearly always greater than the actual Period (T). This can be

attributed to human error, resulting in a delay in turning off the stopwatch after the wave

passes the mark.

It can be seen that the linear water wave theory agrees reasonably well with real waves.

The agreement is very good for low periods. However, as the period increases, the

wavelengths and wave celerities recorded (I love cock) from the real waves deviate from

the values predicted by the linear water wave theory.

For each measurement of wavelength and wave celerity, the measured figure is lower than

that predicted by the linear wave theory. It is possible that this could be attributed to

experimental error. This is unlikely however as the any experimental error would have been

minimised by choosing a large number of waves (ten) over which to record the times. It is

more likely that the discrepancy occurs as a result of the fact that the linear water wave

theory is less accurate for periods over approximately 1.4 seconds.

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Experiment2: Observation of Different Wave Types, Wave Run-up and Interaction with Obstacles2.1 Observation of Different Wave Types

2.1.1 Regular WavesBoth long and short crested regular waves were observed in the wave tank. Regular waves

are waves which travel from one end of the tank to the other without changing or meeting

other waves.These waves are ultimately absorbed by the artificial Enkamat absorption

beach at the other end of the wave tank and hence, are not reflected back along the tank.

2.1.2 Irregular WavesIrregular waves were then observed in the wave tank. These types of wave simulate the

conditions likely to be found offshore. They are the types of wave which commonly occur in

the ocean. Waves come randomly from different directions, meet and break at different

locations and spread and diffract in different directions. The result is a choppy surface,

similar to that found when wind blows across an open stretch of water.

2.1.3 Bulls Eye WaveBulls Eye waves were then observed in the tank. These occur when a series of similar waves

travel towards each other at an angle and intersect at a central point. At this point, the

wave height increases. A bulls eye formation then occurspropagating from this point.This

type of wave is rarely occurs in reality.

2.1.4 Freak WaveFinally, freak waves were created in the tank. These occur when a series of waves with

varying height and period are created. Firstly, waves with a low celerity are created. These

are then followed by waves with a higher celerity. The waves with the higher celerity move

faster than those with the low celerity and therefore catch the slow moving waves. At the

point when the fast moving waves catch the slow moving waves, a breaking wave with a

large amplitude known as a “freak wave” is formed.

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2.1.5 Observation of Wave Period and WavelengthSeveral different types of waves were observed in the 26 metre wave flume. Firstly, waves

with a height of 50 mm, a Period (T) of 0.7 seconds and a wavelength (λ) of 0.76 metres

were observed. Following this, waves with a similar height a Period (T) of 1.75 seconds and

a wavelength (λ) of 4.78 metres were observed. It was noticed that the second group of

waves (with the greater Period and Wavelength) seemed much smaller owing to the fact

that they were less steep and more spread out as a result of their longer wavelength.

2.2 Observation of Reaction with ObstructionsThe elevation and plan view of the obstructions to which the waves were subjected in the

wave flume are shown below in Figure 2.1.

Figure 2.1: Layout of Obstructions in Wave Flume

2.2.1 Interaction with Rubble Mound Breakwater (Beach)At one end of the wave flume, a sloped rubble mound breakwater had been constructed

from loose granular material. The interaction of the waves with this obstruction was

observed. As the waves approached the beach, they changed from deep water waves (d >

0.5 L) to transitional waves (0.05 L ≤ d ≤ 0.5 L) and ultimately to shallow water waves (d <

0.05 L). As the waves hit the sloped rock beach (and propagated from deep to shallow

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water), the wave speed slowed at the leading edge and the wave length reduced. The

kinetic energy of the wave was converted to potential energy. As a result of this, the wave

height increased and the waves ultimately broke on the beach.This process is known as

shoaling. Breaking occurred when the ratio of the height to the wavelength (the steepness

ratio)exceeded approximately 1:7.The majority of the wave energy was dissipated by the

structure as the water percolated through the beach. However, approximately 20-30% of

the energy of the waves was reflected.

2.2.2 Interaction with Vertical WallAt one end of the wave flume, a vertical sea wall had been constructed from concrete

blocks. The interaction of the waves with this vertical wall was then observed.

Approximately 80-90% of the energy of the waves was reflected from this wall. It was

noticed that, just outside this wall, a non-breaking standing wave was formed as a result of

the reflected wavesapproximately 0.5metres from the vertical wall. This wave was a

combination of the approaching waves and the reflected waves, and as a result, its height

was approximately twice that of the approaching waves.In a real life situation, this standing

wave would have resulted in severe scouring of the sea bed and possible undermining of the

vertical wall, possibly resulting in loss of stability and subsequent rotational failure. The

height of the waves was then increased, ultimately resulting in the collapse of the blocks

forming the vertical wall.

It was therefore apparent that the waves had a much softer interaction with the rubble

mound breakwater than with the vertical wall. The energy of the waves was absorbed by

the rubble mound breakwater, but simply reflected by the vertical wall resulting in a

standing wave.

2.2.3 Interaction with Partial Depth Fixed Wave BarrierAt one end of the wave flume, a partial depth fixed wave barrier was constructed. The

depth of this barrier was varied and the extent to which the waves were transmitted beyond

the barrier was observed. It was noticed that the barrier had little effect when it did not

extend the whole way to the floor of the tank. In this case, the waves simply propagated

under the breakwater and continued almost at the same height. It is therefore evident that

a partial depth wave barrier has little use in the control of waves.

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Experiment 3: Stability of a Floating Body3.1 IntroductionA floating body is said to be stable if it returns to its original position following a small

disturbance. The metacentric height of a body is a measurement of the stability of a floating

body. It is the distance between the centre of gravity of the body and its metacentre. The

greater the metacentric height of the body, the greater its stability. The metacentric height

of vessels following loading is frequently calculated in order to gain an insight into the

stability of the vessel.

The purpose of this experiment is to determine the stability of a small floating pontoon by

calculating its metacentre in two different ways. Firstly, its metacentre will be predicted

theoretically, based on the dimensions of the barge and its forces. The metacentre will then

be determined experimentally by taking a series of readings obtained by varying the

position of weights on the pontoon. The experimental procedure is carried out on a

specially manufactured apparatus, similar to the one shown in the diagram below. It

consists of a barge with two weights attached. The first is free to slide up and down the

vertical mast in the centre of the barge. The second one (the jockey weight) is free to slide

along a shaft which is located at the middle of the longitudinal centreline. Also attached to

the barge is a plumbline, which enables the measurement of the angle to which the barge

lists following the adjustment of the jockey weight.

3.2 ApparatusBasin of water

Metacentric Height Apparatus (See Figure 3.1)

Steel Ruler

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Figure 3.1: Metacentric Height Apparatus


3.3 Method1. Measure the dimensions of the pontoon (height, width and length) as shown in

Figure 3.2. Also record the mass of the entire apparatus, and of the jockey weight.

2. Set the weight on the mast of the apparatus at a point, and measure its height. Set

the jockey weight at the centre of the pontoon.

3. Measure the centre of gravity of the barge using the balance test.

4. Float the barge in the basin of water and measure the depth of the barge below the

water level (z).

5. Move the jockey weight to different points along the horizontal shaft at the centre of

the boat, measuring the angle dθ (read from the plumbline) and the distance dx (the

distance from the centre of the jockey weight to the centre of the barge) as shown in

Figure 3.3.

6. Plot the graph of dx against dθ and find the slope of the graph. Calculate the

experimental metacentric height from this slope.

7. Calculate the theoretical metacentric height from the dimensions and weights of the

apparatus.

8. Compare the two values and calculate the experimental error.

9. Repeat steps 2 to 8 as many times as required.

of 20Figure 3.2: Dimensions of Apparatus


3.4 Formulae

3.4.1 Theoretical Metacentric Height

GM=I yyV

+zb−zg

Where: GM = Metacentric Height

I yy=yx3

12= First Moment of Water Plane Area

V=m / ρ=xyz = Displaced Volume

zb = Centre of Buoyancy

zg = Centre of Gravity (Balance Test)

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Figure 3.3: Determination of Stability


3.4.2 Experimental Metacentric Height

GM=w j

Wdxdθ

Where: GM = Metacentric Height

w j = Weight of Jockey Weight

W = Weight of Barge

dx = Distance of Jockey Weight from Centreline

dθ = Angle of Tilt of Barge

dx/dθ = Slope of Graph

3.5 Results and Calculations

Weight of Barge (W) = 2500 g

Weight of Jockey Weight (wj) = 200 g

Width of Barge (x) = 204 mm

Length of Barge (y) = 360 mm

Depth of Barge below water (z) = 35 mm

Height of Centre of Buoyancy (zb) = 17.5 mm

The calculations of the theoretical and experimental height are shown overleaf.

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Height of Mast Weight = 365 mmHeight of C.O.G = 91 mm

dx(metres

)

dθ(degrees)

dθ(radians)

0.074 10 0.1750.051 7.5 0.1310.036 5 0.0870.029 2.5 0.0440.014 0.5 0.009-0.001 -2.5 -0.044-0.016 -5 -0.087-0.031 -7.5 -0.131


dx(metres

)

dθ(degrees)

dθ(radians)

0.0075 0.5 0.0090.015 1.5 0.026

0.0225 2.5 0.0440.03 3.25 0.057

0.0375 4.1 0.072-0.0215 -2 -0.035

-0.039 -4.5 -0.079


dx(metres

)

dθ(degrees)

dθ(radians)

0.0075 0.25 0.0043630.015 1 0.017453

0.0225 1.75 0.0305430.03 2.25 0.03927

0.045 3.5 0.061087-0.026 -2 -0.03491

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Theoretical GMIyy = 0.000255 m4

V = 0.00257 m3

GM = 25.58 mm

Experimental GMSlope of Graph = 0.327

GM = 26.16

ERROR = 2.24 %


V = 0.00257 m3

GM = 39.58 mm


GM = 41.74

ERROR = 5.43 %


V = 0.00257 m3

GM = 51.58 mm


GM = 57.78

ERROR = 12.01 %


-0.042 -3.5 -0.06109

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3.6 Graph for Determination of Experimental Metacentric Height

-0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

f(x) = 0.722334057415177 x + 0.00157527147087857

f(x) = 0.521724110796499 x + 0.000469135880807647

f(x) = 0.326997497706311 x + 0.0120093223377555

Variation of dx with dθ

h = 365 mm Linear (h = 365 mm) h = 77 mm Linear (h = 77 mm)

h = 65 mm Linear (h = 65 mm)

dθ

dx (m

)

Figure 3.4: Variation of dx with dθ

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3.7 Discussion of Results and ConclusionBased on the data collected, the theoretical and experimental values for the metacentric

height of the barge were calculated for three different stabilities. The error between the

theoretical and experimental values was also calculated, relative to the theoretical value.

Errors of 2, 5 and 12 percent were calculated. An error of 5% is quiet acceptable in this case

as there are a number of places where experimental error could occur. However, an error

of 12% can be considered slightly high. Firstly, the calculation of the centre of gravity of the

barge (using the balance test) was prone to human error, as were the measurement of the

distances and height and the determination of the angle dθ due to the oscillation of the

barge in the basin of water. Overall, the experiment is considered fairly accurate however,

with a difference of only 6mm between the theoretical and experimental metacentric

heights in the worst case. It is possible to conclude that this experiment is a satisfactory

method of calculating the metacentric height of the barge.

It was noticed that the metacentric height of the barge increased as the weight on the mast

was lowered (corresponding with a lowering of the centre of gravity and hence increasing

stability of the barge). Figure 3.5 shows the increase in metacentric height as the centre of

gravity is lowered. It can therefore be concluded that a greater metacentric height implies

greater stability.

60 65 70 75 80 85 90 950

10

20

30

40

50

60

Variation of Metacentric Height with Height of Centre of Gravity

Height of Centre of Gravity (mm)

Met

acen

tric

Heig

ht (m

m)

Figure 3.5: Variation of Metacentric Height with Centre of Gravity Height

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Experiment 4: Sediment Transfer4.1 What is happening?In this location, it is apparent that there have been significant changes over the past 10

years. This location appears to be a place where a river and a stream meet the ocean.

There is considerable movement of sediment in this location. At the mouth of the larger

river, there is a build-up of sediment in 2001 which is being washed out to sea by the flow

from the larger river. By 2007, this seems to be nearly completely gone. However, by 2011,

this has built up again. It is likely that storm events around 2005/2006 are the cause for the

break down of these banks of sediment.

The sediment appears to have come from two locations. Firstly, it appears that it has been

washed downstream by both rivers. The sand spit located in the centre of the pictures is

being broken down and this is another source of sediment. This spit is being broken down

by the flow of the rivers and its sediment is being distributed around the area.

4.2 How is it happening?The sediment is being distributed by the flow of the two rivers in the picture. The flow from

the smaller river is wearing away at the sand spit, making it narrower. Between 2007 and

2010, a breach in the spit has begun to occur. This breach has further developed by 2011.

In addition, the build up of sediment noticeable inside the spit in 2001 has been disturbed

by 2011 and the tidal streams in this area have become deeper, eating away at the sand.

The sediment is being washed out into the path of the larger river by the smaller river. This

is in turn washed out to sea by the flow from the large river forming large banks outside the

estuary which build up and break down as storm events occur.

Indeed, it is likely that storm events were to blame for the breach of the spit. The breach

occurred after approximately 2007, when the sediment bank outside the spit had been

eliminated. It is possible that the waves from the ocean, which were allowed an easy path

to the spit following the elimination of the sand bank, eroded the sand spit during a series of

storm events and, in conjunction with the erosion from the small stream resulted in the

breach in the spit.

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4.3 Why are we studying it?It is important to study and monitor the transfer of sediment, and in particular, the effect

which waves have on the sediment. It is possible that changes in the transfer patterns of

sediment can be caused by the activities of people who tamper with the coastline. For

example, the construction of coastal structures can disrupt the movement of sediment. It is

important that we should have a picture of the movement patterns of sediment in order to

notice the effects which the tampering with the coastline has on it.

In addition to this, it is important to be aware of coastal processes which may be occurring

in case remedial action needs to be taken in order to remedy this before too much damage

has been done to the coastline.

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