engi 8751 - coastal engineering - solutions - 2010 - v2
TRANSCRIPT
Question A01
Given Value Units
Period (T) 8 s
Height (H) 2 m
gravity (g) 9.81 m/s^2
Part A
Value Units
Lo 99.92 m
Value Units
D 49.96 m
Part B
Value Units
A wave with a period of 8 seconds and a wave height of 2 meters is observed to be approaching the
shoreline.
a) Assuming that the period remains constant, at what water depth will the wave begin interacting
with the bottom?
b) At what water depth will the wave be considered a shallow water wave?
c) What will the wavelength be once it is becomes a shallow water wave?
d) Assuming that the change in wave height is negligible, at what water depth will the wave break?
Use the period to determine the deepwater wavelength:
Wave interact with the bottom (become intermediate) when D/Lo = 0.5
Waves become shallow when D/L = 0.05. Use Table A5 to determine ratio to deep
water wavelength (D/Lo)
oLD 5.0
o
o
LD
L
D
L
D
015.0
015.005.0
Value Units
D 1.50 m
Part C
Value Units
L 29.98 m
Part D
Value Units
Hmax/d 0.90
D break 2.22 m
Shallow wave will break when Hmax/d = 0.9
Once in shallow water, we must use the shallow water depth to wavelength ration
(D/L = 0.05) to determine the shallow water wavelength (L). Note shallow water
depth was calcuated in part B.
oLD 5.0
o
o
LD
L
D
L
D
015.0
015.005.0
Question A02
Given Value Units
Distance from berg 50 m
Water depth 40 m
Period 1 2 s
Period 2 4 s
Part A
Value Units
Lo 1 6.25 m
Lo 2 24.98 m
Value Units Class
D/Lo 1 6.40 Deep
D/Lo 2 1.60 Deep
Part B
Value Units
C1 3.12 m/s
C2 6.25 m/s
Value Units
Cg1 1.56 m/s
Cg2 3.12 m/s
Value Units
t1 32.02 s
t2 16.01 s
Part C
t1 (s) t2 (s) ∆t (s)
32.02 16.01 16.01
A tourist is kayaking 50 meters away from an iceberg that is grounded just outside St. John's harbor (40 meter water
depth). The iceberg calves creating waves with periods between 2 and 4 seconds.
a) What range of wavelengths are created?
b) How long will it take for the waves to reach the kayakers current position?
c) Assuming that the waves are created over a short duration, how long will it take for the waves to pass by the
kayaker?
Calculate the time required for the group to travel the required distance
First wave hits the boat at t2, last group hits boat at t1. Thedifference is the time required to pass by
the kayaker
Use the periods to determine the deepwater wavelengths
Check to ensure this is deepwater (table A5 D/Lo > 0.5)
Calculate the celerity of both waves
Calculate the group celerity of both waves
Question A03
Given Value Units
Period (T) 8 s
Height (H) 1.5 m
gravity (g) 9.81 m/s^2 NEED to fix this with an L in the formula for energy and power
Depth (D) 50 m
Power (P) 100000 W
Efficiency 0.5
Part A
Value Units
Ep,Ek 1414.02 J/m
Total energy is the sum of potential and kenetic
Value Units
El 2828.04 J/m
Value Units
L 99 92
It is desired to develop a wave energy system on the east coast of Newfoundland. According to the Wind and
Wave Atlas, the yearly average significant wave height is about 1.5 meters with a period of 8 seconds. The
system should therefore be optimized for this condition. The location for the system has a typical water depth
of 50 meters
a) If the system is to produce 100kW of power under this condition at an assumed efficiency of 50%, over
what area must the wave energy be extracted?
b) During fall and winter storms, the significant wave height can be as high as 7 meters. What is the expected
wave power generated in this condition?
First calculate the average wave energy per unit width
Use the periods to determine the deepwater wavelengths
16
2gHEE kp
16
2gHEE kp
Lo 99.92 m
Value Units Class
D/Lo 0.50 m Deep
Value Units
Cg 6.25 m/s
Using the wave power equation, determine the required width
Value Units
W 11.32 m
Part B
H max (m) Value Units
7 Ep,Ek 30794.20 J/m
Total energy is the sum of potential and kenetic
Value Units
El 61588.41 J/m
Value Units
P 2178 kW
Lo and Cg do not change since they are functions of period, not height
Check to ensure this is deepwater (table A5 D/Lo > 0.5)
Calculate the group celerity
Re do the same calculations with a new wave height (7m) to find max power
16
2gHEE kp
16
2gHEE kp
Question A04
Given Value Units
Depth (D) 5 m
Stucture Height (SH) 2 m
gravity (g) 9.81 m/s^2
Wave height (H) 2 m
Period (T) 9 s
SF dynamic pressure 3
Solution
Value Units Class
Lo 126.47 m
D/Lo 0.040 N/A
D/L 0.0833 N/A Intermediate
L 60.02 m
Value Units
Design Angle 0.00 deg
Design elevation (z) ‐5 m
Wave number (k) 0.105 /m
An underwater observatory is being built in 5 meters of water. The observatory is to sit on the bottom and has a height of 2 meters. The
design wave for the site is a 2 meter wave with a period of 9 seconds. If a safety factor of 3 is applied to the dynamic pressure only, what
is the maximum design pressure on the structure?
First determine the deepwater wavelength and the proper wavelength (Table A5)
Determine design point or calcuate for all phase angles
Calcuate static and dynamic pressures at the despgn point, using approperiate safety factors
Lk
2
gzPS cos
cosh
cosh2
1
kd
zdkgHPD
DS PFSPP
Phase Angle
Deg Rad Depth (m) (z) ‐‐> ‐3 ‐3.5 ‐4 ‐4.5 ‐5
Static Pressure (kPa) ‐‐> 30.17 35.19 40.22 45.25 50.28
0 0 57.21 61.98 66.82 71.74 76.73
30 0.523599 53.58 58.39 63.26 68.19 73.19
60 1.047198 43.69 48.59 53.52 58.50 63.51
90 1.570796 30.17 35.19 40.22 45.25 50.28
120 2.094395 16.65 21.80 26.92 32.00 37.05
150 2.617994 6.75 12.00 17.18 22.30 27.36
180 3.141593 3.13 8.41 13.62 18.75 23.82
210 3.665191 6.75 12.00 17.18 22.30 27.36
240 4.18879 16.65 21.80 26.92 32.00 37.05
270 4.712389 30.17 35.19 40.22 45.25 50.28
300 5.235988 43.69 48.59 53.52 58.50 63.51
330 5.759587 53.58 58.39 63.26 68.19 73.19
360 6.283185 57.21 61.98 66.82 71.74 76.73
Pressure Calculations
Total Pressure (kPa) ‐‐>
NOTE: Using Z of ‐5 m and theata at 0 degrees is sufficient (one calcuation at max pressure location) ‐ highlighted in
green
Lk
2
gzPS cos
cosh
cosh2
1
kd
zdkgHPD
DS PFSPP
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
0 30 60 90 120 150 180 210 240 270 300 330 360
Pressure (kP
a)
Phase angle
Question 4: Wave Pressure
Z = ‐3 m
Z = ‐3.5 m
Z = ‐4 m
Z = ‐4.5 m
Z = ‐5 m
Question A05
Given Value Units
Max Pressure (Pmax) 120 kPa
Resolution (∆P) 0.2 kPa
gravity (g) 9.81 m/s^2
Period (T) 10 s
Depth (z) ‐10 m
Part A
Value Units
Lo 156.13 m
k 0.040243 /m
Value Units
H max 5.78 m
Part B
We do not know the ocean depth, so we can assume this to be deepwater
Fist calcuate the deep water wavelength and wave number
Use the pressure equation for deep water to calcuate the maximum wave height
A pressure sensor with a maximum pressure rating of 120kPa and a resolution of 0.2kPa is to be used to measure ocean
waves with a typical period of 10 seconds. To avoid interfering with ships, it is to be placed at a depth of 10 meters
below the surface.
a) What is the maximum wave height that can be measured with this sensor?
b) What is the resolution in terms of wave height?
Lk
2
maxcos2
PzeH
g kz
Part B
Value Units
∆H 0.06 m
Take the derivative of the pressure equation to relate the change in pressure to the change in height
Lk
2
maxcos2
PzeH
g kz
Question A06
Given Value Units
Depth (z) ‐10 m
Period (T) 7 s
gravity (g) 9.81 m/s^2
Max Hoz. Velocity ‐0.5 m/s
Min Hoz. Velocity 2.5 m/s
Part A
Value Units
Lo 76.50 m
k 0.082129 /m
Value Units Note theata
H1 2.53 m 180
H2 12.66 m 0
Part B
We do not know the ocean depth, so we can assume this to be deepwater
Fist calcuate the deep water wavelength and wave number
Solve the horizontal velocity equations for wave height
A current meter located 10 meters below the surface measures a harmonic ocean current in the horizontal direction with
average minimum and maximum values of ‐0.5 and 2.5 m/s and an average period of 7 seconds.
a) Find the wave height associated with this condition
b) Find the maximum vertical velocity and maximum horizontal and vertical acceleration at the current meter in these
conditions
Lk
2
Value Units Note theata
w (max) 2.50 m/s 90
ax (max) 2.24 m/s^2 90
ay (max) 2.24 m/s^2 270
Use the wave height and approperiate phase to determine the maximum wave velocities and accelerations
Lk
2
Question A07
Period (s) Water Depth (m) Wavelength L (m) Classification
8 25
8 100
8 1000
Period (s) Water Depth (m) Wavelength Lo (m) D/Lo D/L Wavelength L (m) Classification
8 25 99.92 0.250 0.268 93.28 Intermediate
8 100 99.92 1.001 1.001 99.92 Deep
8 1000 99.92 10.008 10.008 99.92 Deep
Use the periods to determine the deepwater wavelengths
Use table A5 to determine the real wavelength and the classification
Compute the wavelength and classify the following waves:
Question A08
Period (s) Deep water wavelength (m) Celerity (m/s) Group celerity (m/s)
4 24.98 6.25 3.12
6 56.21 9.37 4.68
8 99.92 12.49 6.25
12 224.83 18.74 9.37
Use the periods to determine the deepwater wavelengths
Calculate the celerity and group celerity
Compute the deep wavelength and wave celerity for waves with periods of 4, 6, 8, and 12 s.
Question A09
Given Value Units
Length 35 m
Width 1 m
Depth 1.2 m
Part A period 1.1 s
Part A wave height 0.2 m
Part A
Value Units
Lo 1.89 m
Value Units Class
D/Lo 0.64 Deep
Parameter Value Units
A wave tank is 35 m long, 1 m wide and 1.2 m deep. The wave maker generates a wave which is 0.2 m high
and a period of 1.1 s.
a) Calculate the wave celerity, length, group celerity, energy in one wavelength (El) and power.
b) A new wave, 0.15 m high with a period of 1.0 s is created in the wave tank. Determine the water particle
velocity and acceleration at a depth of 0.6 m below the still water level.
c) What is the maximum wave height before breaking for this tank if the wave period is 1.0 s.
Use the period to determine the deepwater wavelengths
Check to ensure this is deepwater (table A5 D/Lo > 0.5)
Calculate the celerity, group celerity, energy and power using governing equations
16
2gHEE kp
Celerity 1.717 m/s
Group celerity 0.859 m/s
Energy 50.28 J/m
Power 43.17 W Note: Efficiency = 1
Part B
Given Value Units
Length 35 m
Width 1 m
Depth 1.2 m
Part B period 1 s
Part B wave height 0.15 m
Depth (z) ‐0.6 m
Value Units
Lo 1.56 m
Value Units Class
D/Lo 0.77 Deep
Use the period to determine the deepwater wavelengths
Check to ensure this is deepwater (table A5 D/Lo > 0.5)
16
2gHEE kp
Value Units Note theata
k 4.024 /m
u (max) 0.042 m/s 0
w (max) 0.042 m/s 90
ax (max) 0.26 m/s^2 90
ay (max) 0.26 m/s^2 0
Part C
Value Units
H/L 0.14
H break 0.22 m
Use the horizontal and vertical velocity and acceleration equations for deep water
Deep water wave will break when H/L = 1/7
Lk
2
Question A10
Period (s) Water Depth (m) Wavelength Lo (m) D/Lo D/L Wavelength L (m) Classification
8 100 99.92 1.001 1.001 99.92 Deep
8 50 99.92 0.500 0.502 99.60 Deep
8 20 99.92 0.200 0.225 88.89 Intermediate
8 5 99.92 0.050 0.094 53.08 Intermediate (near shallow)
Use the periods to determine the deepwater wavelengths
Use table A5 to determine the real wavelength and the classification
A wave with a period of 8 s propagates normal to shore. Evaluate the wavelengths in water depths of 100m, 50 m, 20 m and 5 m.
Question A11
Given Value Units
Depth (d) 3 m
Height (h) 0.4 m
Period (T) 1.2 s
depth (z) ‐1 m
Forward dist. (x) 0.2 m
Part A
a) Sketch the wave pattern entering St. Philips from the North and interacting with the shore – Label the
diagram.
b) Assuming waves at a reduced height make it inside the small boat basin sketch the pattern of waves
there also.
c) Where the slipway and why? What are the groins for?
d) If the small waves entering the St. Philips small boat basin channel (3 m deep) are 0.4 m high and have
a period 0f 1.2 s what will be the wave celerity? What is the energy and power in one wave?
e) Calculate the water particle velocity and pressure at a depth of 1 m below the still water level and 0.2
m ahead of the wave crest.
Part B
Part C
Part D
Value Units Class
Lo 2.25 m
D/Lo 1.334349581 Deep
Parameter Value Units
Celerity 1.874 m/s
Group celerity 0.937 m/s
Energy 201.1 J/m
Power 188.4 W Note: Efficiency = 1
Part E
Value Units
k 2.79 /m
theta 32 deg
u 0.054 m/s
w 0.034 m/s
p 10.16 kPa
First determine the phase angle you are being asked to evaluate from the forward distance, then use the deep water
velocity and pressure equations:
Fist calcuate the deep water wavelengthand determine the actual wavelength (table A5)
The slipway is where the boats are too in the photo. This is the area with lowest wave energy and eaiset access to
the ocean.
Groins are used to keep rubble from filling in the entrance to the harbour.
Calculate the celerity, group celerity, energy and power using governing equations
16
2gHEE kp
Lk
2
16
2gHEE kp
Lk
2
Question B01
Given Value Units
Depth (d) 5 m
Speed (V) 3 m/s
Diameter (D) 2 m
Value Units
A 10.00 m²
F 54 kN
Assuming a drag coefficent of 1.2, calculate the projected area of the cylinder. Then use the drag equation to calcuate the
shear force:
A bridge is being designed to cross a river with a depth of 5 meters a vertically averaged current speed of
3.0m/s during spring runoff. A single central tower is used with a diameter of 2 meters. What is the shear
force exerted by the river? Note: You may neglect the shear force from the bridge deck.
NOTE: From here on small d will be for depth and capital D will be for diameter
NOTE: Here it is assumed that the bridge deck supports zero shear force. Else one would have to consider zero shear in a more complex analysis.
Question B02
Given Value Units
Total height (h) 22 m
Diameter (D) 36 in
Drag Coeff. 0.2
Stock height (z) 2 m
Wind speed (at 10m) 40 knots
Given Value Units
Total height (h) 22 m
Diameter (D) 0.914 m
Drag Coeff. 0.2
Stock height (z) 2 m
Wind speed (at 10m) 20.58 m/s
Value Units
U22 22.50 m/s
Value Units
F 120.31 N
First convert to metric units
Determine the wind velocity at the windstock
Calculate the force on the windstock
A semi‐submersible is fitted with a heli‐deck located 20 meters above the mean waterline for transporting crew on
and off the platform. To aid the pilots in landing in (relatively) high winds, a windsock is to be placed off to the side
and 2 meters above the heli‐deck. The windsock has a diameter of 36 inches and a drag coefficient of 0.2. What is
the force on the windsock if the maximum recorded wind speed on site at a height of 10m is 40 knots.
Note: You are asked to find the force on the windstock only, with a height of 2 m and a diameter of 0.914 m. The height of the platform is needed only in determining the correct wind speed at the wind stock
Question B03
Given Value Units
Steel density 7800 kg/m³
Inner diam. (Di) 0.5 m
Depth 70 m
Wave height 5 m
Period 8 s
Current @ 1 m 1.2 m/s
Frict. Coeff. 0.6
gradient 0.012
Slope 0.687516355 deg 0.011999424 Rad
Part A
Value Units
Lo 99.92 m
Value Units Class
D/Lo 0.70 Deep
Value Units
t 0.004 m Value in green is interated on (change till delta Fw=0)
Do 0.507 m
Value Units
Ue 0 96 m/s
A steel pipeline (density of 7800 kg/m3) is being designed to transport gas across the Strait of Belle Isle. The inner diameter is to
be 0.5m in order to support the desired volume. The water depth across the Strait is typically 70m and the design wave is 5 meters
with a period of 8 seconds. The Labrador Current creates a regular current through the Straits and has been measured 1m off the
bottom to be 1.2 m/s. The bottom is typically sandy with a friction coefficient ranging from 0.55 to 0.65. Approaching the shores,
the bottom has a grad of 1.2 on 100.
a) What is the required outer diameter of pipe such that the pipeline stays in position?
b) After installation, a piece of the pipe is broken after a ship drags anchor over the pipeline. In order to fix the pipeline, a piece of
pipe 50 meters in length is floated into position at a depth of 5 meters. What is the wave loading on the pipe if the ship is traveling
in beam seas (wave direction perpendicular to the pipe)?
Use the period to determine the deepwater wavelengths
Check to ensure this is deepwater (table A5 D/Lo > 0.5)
Therefore these are deep water waves and will not affect the pipelines
Assume a reasonable wall thickness
Calculate the effective velocity
Ue 0.96 m/s
Value Units
Re 4.06.E+05
Cd 0.70
Cl 0.70
Cm 1.15
Cf 0.60
Value Units
Fd 167.90 N
Fl 167.90 N
Value Units
<‐‐Fw calc 439 N
Fw real ‐‐> 439 N
Delta Fw 0 N
Calcuate the drag and lift forces on the pipeline per unit length (note inertial forces are 0)
Calcuate the required force per unit length, determine new thickness, and interate (change first t) until delta Fw= 0)
Assume or calculate drag, lift and inertial coeff.
Note: Goal seek was used to obtain the answer. This is quite small and obviously would need to be
Part B
Additonal Given Value Units
length 50 m
depth (z) ‐5 m
Value Units
k 0.06 /m
Um 1.96 m/s
Value Units
K 30.97 Therefore drag dominated (K>25)
Value Units
Re 8.30E+05
Cd 0.62
Cm 1.8
Horinontal Forces: Theata (deg) Theata (rad) u (m/s) ax (m/s^2) Fx (N) w (m/s) az (m/s^2) Fz (N) F total (N)
0 0.00 1.43 0.00 16567 0.00 1.13 20993 26743
30 0.52 1.24 0.56 22922 0.72 0.98 22323 31996
60 1.05 0.72 0.98 22323 1.24 0.56 22922 31996
90 1.57 0.00 1.13 20993 1.43 0.00 16567 26743
120 2.09 ‐0.72 0.98 22323 1.24 ‐0.56 1929 22406
150 2.62 ‐1.24 0.56 22922 0.72 ‐0.98 ‐14039 26880
180 3.14 ‐1.43 0.00 16567 0.00 ‐1.13 ‐20993 26743
210 3.67 ‐1.24 ‐0.56 1929 ‐0.72 ‐0.98 ‐14039 14171
240 4.19 ‐0.72 ‐0.98 ‐14039 ‐1.24 ‐0.56 1929 14171
Vertical Forces: 270 4.71 0.00 ‐1.13 ‐20993 ‐1.43 0.00 16567 26743
300 5.24 0.72 ‐0.98 ‐14039 ‐1.24 0.56 22922 26880
330 5.76 1.24 ‐0.56 1929 ‐0.72 0.98 22323 22406
360 6.28 1.43 0.00 16567 0.00 1.13 20993 26743
If Re is high ( ie Re > 1.5x10^6) then
Use the wave loading equations to determine the total foce on the pipe:
First calculate the wave numver and the maximum horizontal partical velocity Um
Calculate the Keulegan‐Carpenter Number K = Um*T/D to determine if drag dominate, intetia dominated, or both significant
Determine Drag and Inertia Coefficients.
This is quite small and obviously would need to be thicker in real life. But, this is sufficient for learning purposes.
Lk
2
T
HUm
Lk
2
T
HUm
Question B04
Given Value Units
Depth (d) 5 m
Diameter (D) 0.3 m
Load 500 KN
Current 0.5 m/s
Wave height 2 m
Period 4 s
Part A
Value Units Note
f 1.40 kips/ft^2 Table 3‐7
q 60 kips/ft^2 Table 3‐7
f 67.032 kN/m^2
q 2872.8 kN/m^3
L 4.70 m
Part B
Value Units
Lo 24.98 m
A wharf is being designed that is to be support on vertical piles in a water depth of 5 meters with loose, medium density sand.
Wooden piles with a diameter of 300 mm have been selected based on the layout requiring that each pile support 500 kN. There
is a long shore current of 0.5 m/s combined with 2 meter waves with a period of 4 seconds that are typically driven directly
onshore.
a) How deep should the piles be driven into the sand?
b) What is the expected horizontal wave load?
med dense sand
Find the unit skin friction (f) and unit end bearing capactiy (q) for a loose medium dense sand in Table 3‐7 of notes. Convert for proper units
and fill into the axial bearing capacity formula to solve for L.
Use the period to determine the deepwater wavelengths
Lk
2
T
HUm
Value Units Class
D/Lo 0.200
D/L 0.225 Intermed.
L 22.222 m
Value Units
k 0.28 /m
Um 1.57 m/s
Value Units
K 20.94 Therefore mixed
Value Units
Re 3.93E+05
Cd 0.62
Cm 1.8
Calculate the Keulegan‐Carpenter Number K = Um*T/D to determine if drag dominate, intetia dominated, or both significant
Determine Drag and Inertia Coefficients.
Assume approp. numbers for coeff:
Check to see if deepwater (table A5 D/Lo > 0.5)
First calculate the wave numver and the maximum horizontal partical velocity Um
Lk
2
T
HUm
Theata (deg) Theata (rad) F (N)
0 0.00 625
30 0.52 1037
60 1.05 1142
90 1.57 1138
120 2.09 829
150 2.62 101
180 3.14 ‐625
Value Units 210 3.67 ‐1037
A1 0.118 240 4.19 ‐1142
A2 0.188 270 4.71 ‐1138
300 5.24 ‐829
330 5.76 ‐101
360 6.28 625
Calculate the total force on the vertical cylinder
Question B05
Given Value Units
Depth (d) 60 m
Diameter (D) 10 m
Cd 0.1
Cm 0.2
Wave height 10 m
Period 12 s
Max Load 4500 kN
SF 2.5
Part A
Value Units
Lo 224.83 m
Value Units Class
D/Lo 0.267
D/L 0.280 Intermed.
L 214.286 m
Value Units
k 0.03 /m
Um 2.62 m/s
The company you are working for plans on using a jackup drilling platform for exploratory drilling. The jackup has three truss
style legs with an equivalent diameter of 10m. Based on model test results from the original design, the drag and inertial
coefficients for the legs are 0.1 and 0.2 respectively. The desired drilling location has a water depth of 60m of water. Based on a
statistical analysis of environmental data collected for the region, the design wave for the location is determined to be 10 meters
with a period of 12 seconds.
a) If the maximum lateral base load is 4500 kN, will the jackup be suitable for this site if a safety factor of 2.5 is required to meet
industry standards?
b) Despite the unfavorable drilling conditions, management decides they are willing to compromise and allow the platform to be
moved closer or away from the shore in order to use the available jackup platform. Should the platform be moved into deeper
or shallower water?
Use the period to determine the deepwater wavelengths
Check to see if deepwater (table A5 D/Lo > 0.5)
First calculate the wave number and the maximum horizontal partical velocity Um
Lk
2
T
HUm
Value Units
K 3.14 Therefore inertia dominated
Theata (deg) Theata (rad) F (KN) FxSFx3 (KN)
0 0.00 76 570
30 0.52 433 3250
60 1.05 671 5031
90 1.57 753 5645
120 2.09 633 4747
150 2.62 319 2395
180 3.14 ‐76 ‐570
210 3.67 ‐433 ‐3250
Value Units 240 4.19 ‐671 ‐5031
A1 0.785 270 4.71 ‐753 ‐5645
A2 0.159 300 5.24 ‐633 ‐4747
330 5.76 ‐319 ‐2395
360 6.28 76 570
Part B
Calculate the total force on the vertical cylinder
Note: x SF and x by 3
due to having three
legs!
5645 KN is much greater than the allowed 4500 KN, therefore the safety requirement is not met.
In the force equation wavelength is porportional to force. Wavelengths are reduced in shallower waters, therefore less force on
the structure. Hence the structure should be moved towards shore.
Calculate the Keulegan‐Carpenter Number K = Um*T/D to determine if drag dominate, intetia dominated, or both significant
Question B06
Given Value Units
Depth (d) 15 m
Length 12 m
Diameter (D) 0.15 m
Current 1 m/s
Density 1030 kg/m^3
Viscosity 1.17E‐06 m^2/s
This is a vertical cylinder, therefore just calcuate the drag force:
Value Units
Re 128205
Cd 1.10
F 1022 N
M 6133 N.m
A smooth vertical stainless steel pipe is total submerged in sea water where the water depth is 15 m. The
pipe is 12 meters long with an outside diameter of 0.15 m and fixed at the sea floor. For a uniform current
of 1 m/s evaluate the total force and moment acting at the seafloor (mud line). Note: the density of
seawater is 1030 kg/m³ with a kinematic viscosity of 1.17×〖10〗^(‐6 ) m^2/s .
Question B07
Given Value Units
Depth (d) 60 m
Wave height 5 m
Period 11 s
Diameter (D) 0.9 m
Density 1025 kg/m^3
Viscosity 1.20E‐06 m^2/s
Value Units
Lo 188.92 m
Value Units Class
D/Lo 0.318
D/L 0.330 Intermed.
L 181.818 m
Value Units
k 0.03 /m
Um 1.43 m/s
Value Units
K 17.45 Therefore mixed
Value Units
Re 1.07E+06
Cd 0.62
Cm 1.8
Theata (deg) Theata (rad) F (N) M (N.m)
A fixed jacket structure is located in 60 m water depth and is subject to a 5 m high, 11 s wave. The main legs of the structure are 0.9 m
diameter vertical steel pipes. Calculate and plot the drag, inertia and total force variation for one leg over one wave period. Assume linear
wave theory is valid.
Note: no
Use the period to determine the deepwater wavelengths
Check to see if deepwater (table A5 D/Lo > 0.5)
First calculate the wave numver and the maximum horizontal partical velocity Um
Calculate the Keulegan‐Carpenter Number K = Um*T/D to determine if drag dominate, intetia dominated, or both significant
Determine Drag and Inertia Coefficients.
Assume approp. numbers for coeff:
Calculate the total force on the vertical cylinder
Lk
2
T
HUm
0 0.00 9917 437622
30 0.52 21290 845963
60 1.05 26472 1006168
90 1.57 27704 1035493
120 2.09 21513 787358
150 2.62 6414 189530
180 3.14 ‐9917 ‐437622
210 3.67 ‐21290 ‐845963
240 4.19 ‐26472 ‐1006168
270 4.71 ‐27704 ‐1035493
300 5.24 ‐21513 ‐787358
330 5.76 ‐6414 ‐189530
360 6.28 9917 437622
Value Units
A1 0.141
A2 0.147
A3 0.091
A4 0.112
pi in
Moment
eqn
‐2500000
‐2000000
‐1500000
‐1000000
‐500000
0
500000
1000000
1500000
2000000
2500000
‐40000
‐30000
‐20000
‐10000
0
10000
20000
30000
40000
0 50 100 150 200 250 300 350 400
Moment (N.m
)
Force (N)
Phase
Wave Force and Moment
Force Moment
Question B08
Given Value Units
Depth (d) 15 m
Wave height 1 m
Period 5 s
Diameter (D) 0.3 m
Length of pipe 20 m
Viscosity 1.20E‐06 m^2/s
Value Units
Lo 39.03 m
Value Units Class
D/Lo 0.384
D/L 0.386 Intermed.
L 38.860 m
Value Units
k 0.16 /m
Um 0.63 m/s
Value Units
K 10.47 Therefore mixed
Value Units
Re 1.57E+05
A vertical cylindrical pile is located in 15 m of water and has a diameter of 0.30 m and a length of 20 m. A 1 m wave with a 5 s
period impacts the pile. Evaluate the maximum drag and inertia force on the pile.
Use the period to determine the deepwater wavelengths
Check to see if deepwater (table A5 D/Lo > 0.5)
First calculate the wave numver and the maximum horizontal partical velocity Um
Calculate the Keulegan‐Carpenter Number K = Um*T/D to determine if drag dominate, intetia dominated, or both significant
Determine Drag and Inertia Coefficients.
Assume approp. numbers for coeff:
Lk
2
T
HUm
Cd 0.62
Cm 1.8
Theata (deg) Theata (rad) F (N) Fd (N) Fi (N)
0 0.00 126 126 0
30 0.52 413 94 318
60 1.05 583 31 552
90 1.57 637 0 637
120 2.09 520 ‐31 552
150 2.62 224 ‐94 318
180 3.14 ‐126 ‐126 0
210 3.67 ‐413 ‐94 ‐318
240 4.19 ‐583 ‐31 ‐552
270 4.71 ‐637 0 ‐637
300 5.24 ‐520 31 ‐552
330 5.76 ‐224 94 ‐318
360 6.28 126 126 0
Value Units
A1 0.236
A2 0.135
Calculate the total force on the vertical cylinder (note the Cm component is interia and the Cd is drag)
Question B09
Given Value Units
Outter diameter (D) 0.46 m
Depth (d) 100 m
Wave height 20 m
Period 14 s
gradient 0.01
Slope 0.572939 deg 0.01 Rad
Part A
Value Units
Lo 306.02 m
Value Units Class
D/Lo 0.33
D/L 0.34 Intermediate
L 294.99 m
Value Units
k 0.02 /m
u 1.08 m/s
ax 0.24 m/s^2
Value Units
A concrete coated steel gas pipeline is to be laid between two offshore platforms in 100 m of water where the maximum
environmental conditions include waves of 20 m wave heights and 14s periods. The pipeline outside diameter is 0.46 m and the
clay bottom slope is 1 to 100. Determine the submerged unit weight of the pipe. Assume linear wave theory is valid and that the
bottom current is negligible.
Use the period to determine the deepwater wavelengths
Check to classify the wave type (table A5 D/Lo > 0.5)
Determine the particle velocity and accelaeration (from wave action)
Note: we neglect the
effect of the bottom
current, meaning d=‐z
Calculate the reyonlds number to get the drag and interia coefficients
tkxkd
zdk
T
Hu
cossinh
)(cosh
tkxkd
zdk
T
Hax
sinsinh
)(cosh22
2
Lk
2
Re 4.88E+05
Cd 0.7
Cm 1.5
Value Units
F/V 1536 N/m^3
Value Units Assuming firction factor of 0.6
W 2560 N/m^3
Calculate the friction force resiting the above force with wieght as the unknown, perform a force balance and solve for W:
Assume approp. numbers for coeff:
Determine the force per unit volume:
tkxkd
zdk
T
Hu
cossinh
)(cosh
tkxkd
zdk
T
Hax
sinsinh
)(cosh22
2
Lk
2
Question B10
Given Value Units
Diameter 0.23 m
Length 100 m
Current 1.5 m/s
Value Units
F 31.83 KN
Assuming Cd = 1.2, the drag force is as follows:
A 0.23 m diameter horizontal cross‐member of a steel jacked structure is located near mid‐depth where
the maximum uniform current is 1.5 m/s. Determine the forces on the 100 m long cross member.
Question B11
Part A,B,C
Value Units
Length 50.00 m
Width 10 m
Freeboard 3 m
Avg. Water Depth 5 m
Wave Height 2.00 m
Part D
Assume reasonable values
Sketch the diffraction and refraction
Answer the following for a typical finger pier government wharf in Newfoundland (timber crib, yellow rails,
concrete deck, etc.). Note that breaking waves do not strike these as they are usually sheltered from the open
ocean.
a) Reasonable length, width and freeboard?
b) Average water depth along the length of the pier?
c) Assumed wave height used for design?
d) Sketch of wave pattern around the pier?
e) Sketch and calculate the vertical pressure distribution using Minnikin.
f) What is the total lateral force on the pier?
Part E
Value Units
h 3.32 m
P1 20.1 Kpa
P2 20.1 Kpa
Phyd 50.3 Kpa
Pbottom 70.4 Kpa
Pressure distribution
Part F
Force is just simpley the area of the pressure tringle times the length of the pier
Calculate the pressure distribution using Minnikin (done using simplified approach)
j p y p g g p
Value Units
F 14640 KN
Question B12
Given Value Units
Cd 1.2
Area 9 m²
Height 25 m
Wind Speed 40 m/s
Value Units
U25 44.36 m/s
F 13.82 KN
Shear 13.82 KN
Moment 345.4 KN.m
First correct for the wind elevation, then use the drag equation to determine the force on the lights
A tall light standard is needed to illuminate ferry operations at the end of a new breakwater. If it has a solid
panel (Cd = 1.2) of lights roughly 3m by 3m square, what would be the shear and bending moment at the
base of the light tower if it were 25 m high given that the strongest winds are from the north at 40 m/s?
Question B13
Given Value Units
Cd 0.62
Depth (d) 12 m
Diameter (D) 0.8 m
Wave height 1 m
Period 4 s
Part A
Value Units
Lo 24.98 m
Value Units Class
D/Lo 0.480
D/L 0.482 Intermed.
L 24.896 m
Value Units
k 0 25 /m
If there was an option to place the light standard on a vertical cylinder post/pile in 12 m water off the end of the
breakwater it wouldn’t need to be as high and wind loads would be reduced.
a) What would be the maximum drag‐induced wave moment on this pile if it were 0.8 m in diameter (Cd = 0.62) with a
wave height of 1.0 m with a period of 4s.
b) What force is exerted by a ferry propulsion system during maneuvering if it creates a uniform current of 3 m/s against
the pile with a Cd of 1.2.
c) If sea ice of thickness 30 cm and compressive strength 2 MPa were pushed by the wind against the pile until ice crushing
occurred, what would be the lateral forces and maximum bending moment on the pile assuming it were a rough surface?
What might you do to reduce the ice forces?
Use the period to determine the deepwater wavelengths
Check to see if deepwater (table A5 D/Lo > 0.5)
First calculate the wave number and the maximum horizontal partical velocity Um
k2
H
Um
k 0.25 /m
Um 0.79 m/s
Value Units
K 3.93 Therefore inertia dominated
Calculate the Keulegan‐Carpenter Number K = Um*T/D to determine if drag dominate, intetia dominated, or both significant
Lk
TUm
Theata (deg) Theata (rad) M (N.m)
0 0.00 3179
30 0.52 2384
60 1.05 795
90 1.57 0
120 2.09 ‐795
150 2.62 ‐2384
180 3.14 ‐3179
210 3.67 ‐2384
Value Units 240 4.19 ‐795
A4 0.161 270 4.71 0
300 5.24 795
330 5.76 2384
360 6.28 3179
Part B
Given Value Units
Cd 1.2
Current 3 m/s
Given Value Units
F 53.136 KN
Part C
Given Value Units
Thickness 0.3 m
Comp. strength 2 Mpa
Simply calculate the drag force as a result of the induced current:
Use Croasdale for simple ice crushing Find the indentation factor (roungh surface) and calculate the force:
Calculate the drag induced moment on the vertical cylinder (can neglect A3)
Value Units
I 1.58 /m
F 759.00 KN
M 9108 KN.m
Use Croasdale for simple ice crushing. Find the indentation factor (roungh surface) and calculate the force:
To reduce ice forces, add a cone or wedge at the surface to break ice in flexure
Question B14
Given Value Units
Height 60 m
depth (d) 120 m
Cd 0.6
Diameter (D) 40 m
Wind speed 30 m/s
air density 1.23 kg/m^3
Part A
Value Units
U60 36.73 m/s
F 626 KN
Part B
Given Value Units
Wave height 10 m
Diameter 0.8 m
Period 15 s
W t d it 1025 k / ^3
a) A 60 m high wind turbine is place offshore on a 3 legged lattice structure on 120 m of water. With wind blowing at 30
m/s (at 10 m reference height, 1 min mean sustained) what is the horizontal force produced at the point B from the wind
drag on the rotor. Assume air density is 1.23 kg/m³, Cd = 0.6 (effective), and rotor diameter = 40m.
b) The wind creates waves 10 m high with a 15 s period. Ignoring the cross bracing and wake effects from other legs what is
the maximum lateral force at B due to inertia wave forces on the three legs combined. Assume that the forces on the legs
are in‐phase and the density of water is 1023 kg/m³. (Leg diameter = 0.8 m, Cm = 1.8)
First correct for the wind elevation, then use the drag equation to determine the force on the rotor
Water density 1025 kg/m^3
Cm 1.8
Value Units
Lo 351.29 m
Value Units Class
D/Lo 0.342
D/L 0.349 Intermed.
L 343.8 m
Use the period to determine the deepwater wavelengths
Check to see if deepwater (table A5 D/Lo > 0.5)
Value Units
k 0.02 /m
Um 2.09 m/s
Value Units
K 39.27 Therefore drag dominated
Theata (deg) Theata (rad) F (KN)
0 0.00 0
30 0.52 22
60 1.05 39
90 1.57 45
120 2.09 39
150 2.62 22
180 3.14 0
210 3.67 ‐22
Value Units 240 4.19 ‐39
A1 0.063 270 4.71 ‐45
300 5.24 ‐39
330 5.76 ‐22
360 6.28 0
Therefore the max total force at B (three legs, phase angle at 90 deg) [KN]
134
First calculate the wave number and the maximum horizontal partical velocity Um
Calculate the Keulegan‐Carpenter Number K = Um*T/D to determine if drag dominate, intetia dominated, or both significant
Calculate the inertia induced force on the vertical cylinder (can neglect A2)
Lk
2
T
HUm
Question C01
Given Value Units
Floe diameter 1000 m
Ice thickness 3 m
Water depth 30 m
Width 120 m
Current 2 Knots 1.02888888 m/s
Ice density 920 kg/m^3
Ice crushing pressue 1.80E+06 Pa
Wind speed 80 Knots 41.1555552 m/s
Part A
Value Units
Cm 0.05
F1m 401 MN
Part B
A circular ice floe with a diameter of 1 kilometer and 3.0 meters thick is approaching a Caisson structure
located in a water depth of 30 meters. The Caisson has a square profile with vertical sides and
measures 120m across at the waterline. The current speed is 2 knots and the wind speed is 80 knots.
a) If the ice flow is initially moving at the current speed, determine the limit‐momentum load on the
structure due to the impact of the floe. Assume an effective crush pressure of 1.8MPa.
b) What is the limit force loads as a result of the environmental forces acting the ice floe? Assume drag
coefficients of 3x10‐3 and 5.5x10‐3 for air and water respectively as well as a pack ice pressure of
40kN/m.
c) What will be the load on the structure if the ice begins to crush? Use the analytical method by
Croasdale et. al assuming rough contact and a crushing pressure of 4.5MPa.
d) What will be the load on the structure if the ice begins to buckle? Assume an elastic modulus of 6.0
GPa
e) What will the maximum load on the structure be as a result of the ice floe?
Use the limit momentum equation:
Given Value Units
Drag coeff (air) 3.00E‐03 m
Drag coeff (water) 5.50E‐03 m
Pack ice pressure 40000 N/m
Value Units
A 785398 m^2
F2m 47 MN
Use the limit force equation:
Part C
Given Value Units
Crushing pressure 4.50E+06 Pa
Value Units
I 1.459
p 6564375 Pa
F 2363 MN
Part D
Given Value Units
Elastic Modolus 6.00E+09 Pa
Value Units
k 10055 N/m^3
l 34.9 m
Fb 4095 MN
Part E
During the impact, the structure will experience the momentum loads which will be 401 MN.
However, after the impact, neither crushing nor buckling will occur and hence the load will
be environmentally limited to 47 MN.
Use croasdale analytical formulas to deteremine the force from ice crushing:
Use sodhi formula for buckling:
Question C02
Given Value Units
Period 2 s
Height 0.3 m
Part A
Value Units
Cr 0.10
ξ 1.00
Lo 6.25 m
β 0.22 rad
β 12.36 deg
Here we require the reflected wave (Hr) to be 10% of the incident wave (Hi). This can be maniuplated to determine the
reflection coefficient. Use Cr to find xi from figure 4‐14. Then use this to back calculate the slope.
A beach is being designed for the end of a wave tank. The wave tank will be used to generate waves with a
period of 2 seconds and a height of 30cm.
a) If the beach was made from a plane slope, what would the slope have to be to ensure that the reflected
waves where no more than 10% of the incident waves?
Part B
Value Units
R 0.30 m
Input the above in the wave runup formula and solve for R
Question C03
Given Value Units
Depth 1.8 m
Slope 30 deg 0.523598776 rad
Wave height 3 m
Period 9 s
Value Units
Lo 1 126.47 m
Value Units Class
D/Lo 0.0142
D/L 0.0496 Shallow
L 36.2903 m
Value < 1/7? Class
H/L 0.0827 TRUE Non‐breaking
A rubble mound breakwater is being designed to protect a yacht club. During low tide, the water depth is 1.8
meters. To save money, a fairly steep slope of 30 degrees is chosen for the design and the armor unit is to be
rough angular quarry stone. If the design wave is 3.0 meters with a period of 9 seconds, choose an appropriate
breakwater design.
Calculate the cot(slope) to determine the stability coeff from table 4‐5
First we must determine if the wave will be breaking or non‐breaking.
Use the periods to determine the deepwater wavelengths
Correct for proper wavelength (table A5 D/Lo > 0.5)
Check wave breaking condition
Since its non breaking, only 1 armor uint is required
d
Value Units
Cot(angle) 1.7321
Kd head 2.3
Kd trunk 2.9
Use the main formula to determine the weight of the individual armour units
Value Units
W (head) 38.9 KN
W (trunk) 30.8 KN
Calculate the cot(slope) to determine the stability coeff from table 4 5
Question C04
Given Value Units
fetch 40000 m
Wind speed 40 knots 20.57778 m/s
duration 4 hrs
Value Units
Ua 29.29
First calculate the wind stress
Use the wave prediction plot to determine the expect wave conditions
An offshore platform is located 40 kilometers away from shore. On a given day, the winds are blowing
offshore at a speed of 40 knots. If the wind continues to blow for four hours, what is the expected
wave condition at the site? Is the wave fetch or duration limited? How long will it take for the
maximum wave height to be generated?
Value Units
H(fetch) 3.00 m
H(duration) 3.4 m
Waves are fetch limited and will have a wave height of 3.0 and a corresponding period of 6.6s. This wave height
will be reached after 3.5 hrs.
Question C05
Given Value Units
Current 0.5 m/s
Water depth 20 m
Data Value Units Value Units
Sand density 2650 kg/m^3 B 1.95
water density 1025 kg/m^3
diameter 0.000074 m
viscosity 1.80E‐06 m^2/s
Value Units
Vf 0.00263 m/s
Value Units
dx 3804 m
From table 4‐3, sediment classification, for fine sand 0.074 < d < 0.42 (mm)
First calculate B using the following data
Now calculate the fall velocity (for B < 39)
Use d=vt to determine the distance travelled:
A river transports fine sand into a coastal area. If there is a current running along the shore with a speed of
0.5m/s and the water depth is 20 meters, how far away will the particles settle?
Question C06
Given Value Units
Depth 35 ft
Wave height 3 ft
Dolo specific weight 140 lbs/cubic foot
Value Units
Cot(angle) 2.0000
Kd head 31.8
Kd trunk 16
Use the main formula to determine the weight of the individual armour units
We are told is is a non‐breaking condition
Refere to table 4‐5. Dolos alwars require 2 armour units.
Read of the Kd and cot angle vlaues
A rubble mound breakwater is planned for a depth of 35ft. It has been determined that the
significant wave height for this design is 3 ft with minimal breaking and no damage. Dolos armor
units can be economically used at the proposed site. Assume the specific weight of a concrete
Dolos is 140 lbs/cubic foot. Determine the weight of the armor unit.
Use the main formula to determine the weight of the individual armour units
Value Units
W (head) 35.5 lbs
W (trunk) 70.5 lbs
Question C07
Given Value Units
Depth 11 m
Wave height 1 m
Specific weight 3.3
Value Units
Cot(angle) 2.0000
Kd head 16
Kd trunk 31.8
Use the same kind as used in the first breakwater because they worked and may be cheaper
Told this is non breaking cases. Refer to table 4.5. Assume using rough
Use typical 1 to 2 slope (cot = 1.5) given lack of data
If a second breakwater were planned for Portugal Cove in water depths as shown below but for
significant wave heights of only 1.0 m (no breaking), what kind of armor unit would you use and why?
What slope would you create with them? If you were to design concrete Dolos for this application
determine the weight of each unit if the specific weight of reinforced concrete is 3.3.
Use the main formula to determine the weight of the individual armour units
Value Units
W (head) 83.1 N
W (trunk) 41.8 N
Question C08
Given Value Units
Height 10 m
Wind speed 40 m/s
Wind hight 60 m
Part A
Value Units
U10 32.66848 m/s
Ua 51.72
Value Units
Fetch 160 km
Duration 7.30 hrs
First adjust for wind elevation, the calculate the wind stress
Use the wave perdiction plot to determine the required fetch and duration
How long does it take 10 m significant wave height to develop in open sea when a storm arrives with sustained
wind speeds of 40 m/s measured at 60m above SWL, and what fetch is required?
Question D01
Given Value Units
Depth 12 m
Life 25 yrs
Diameter 0.8 m
Safety factor 1.25
Anode Weight 4.535 kg
Main. Current density 0.00056 A/m^2
Value Units
Current capacity 815.85 A.h/kg
Value Units
A 30.15929 m^2
It 0.0169 A
W (per hour) 2.07E‐05 kg/hr
Wt 5.666996 kg
N 1 249573
Use table 5‐21 to get the current capacity of zinc (and convert to metric)
Calculate the total current, followed by the weight per hour and total weight over the design life. Then determin e the
number of anodes required:
The support post shown in the figure is 12 meters deep and 0.8 m in diameter. The post is to be made of regular
stainless steel – if cathodic protection is to be used how many 10 lb zinc anodes would be required for 25 years of
water zone protection with a safety factor of 1.25, given maintenance current density is 0.56 mA/m^2. Where would
you avoid placing them? In addition to the anodes what else might you do to protect the pile from corrosion?
N 1.249573
Use other protection measures, including painting, non corroding materials, etc
Therefore 2 zinc anodes are required
The anodes should be spread apart as best as possible, but you must ensure they are below the waterline interface
for wave forces, ice, etc.