engi 8751 - coastal engineering - solutions - 2010 - v2

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


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


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


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


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


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


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 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


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


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



16

2gHEE kp


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 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)?



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.


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



Assume approp. numbers for coeff:

Check to see if deepwater (table A5 D/Lo > 0.5)


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?



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


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.


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


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


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








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


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


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.







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.


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:


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?




k2

H

Um

k 0.25 /m

Um 0.79 m/s

Value Units

K 3.93 Therefore inertia dominated


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



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



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.


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


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.


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.


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.

engi 8751 - coastal engineering - solutions - 2010 - v2

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