Department of Mechanical Engineering
Massachusetts Institute of Technology
2.20 Marine Hydrodynamics, Fall 2015
Laboratory Assignment
Assigned: Wednesday, November 20, 2015
Lab time: Monday, 11/23/2015 and Tuesday, 11/24/2015
Report Due: Thursday, December 10, 2015
The laboratory assignment requires that you do the following:
1. Read through the details of the lab.
2. Perform the Pre-Lab exercise.
3. Perform the experiment at the time you have signed up.
4. Write a lab report, which is due Tuesday, December 10, 2015. Although the experiments
are performed in a group effort, the lab report should be individual. The lab report
is expected to be type-written, complete yet concise.
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SURFACE WAVE KINEMATICS AND WAVE INDUCED MOTIONS
The laboratory will be performed on Monday (11/23/2015) and Tuesday (11/24/2015) at the
Towing Tank, Room 48-015, x3-4348 during the time slots for which you have signed up. Reports
are to be done individually and are due before the lecture on Thursday, December 10, 2015.
Introduction
This lab is designed to familiarize you with some of the test capabilities of the Towing Tank,
and help you understand important concepts related to two important phenomena in marine
hydrodynamics: dispersive surface water waves and wave induced motions. In this lab, you are
asked to make quantitative measurements of surface wave phase and group speed as a function
of wave frequency, and to observe the dispersion phenomenon of surface waves. You will have
to make quantitative analysis of the response of a inverted pendulum in waves. You will also
observe the phenomenon of vortex-induced vibrations (VIV) of a cylinder phenomenon and its
suppression.
Pre-Lab Preparations
Write a “pre-lab” report of the following pre-lab preparations before the lab. In your final lab
report you should include a copy of your “pre-lab” (in addition to the one turned in on the day
of the lab) along with a short paragraph that discusses the lab preparation.
(Time spent here will certainly save you many times the effort during and after the lab!)
1. Read through the entire lab assignment carefully so that you have a clear idea of what has
to be accomplished. Be familiar with the expected results and calculations so that you can
repeat suspicious measurements or reject spurious data (during the lab).
2. Understand the physical meaning of basic wave properties such as wave length, wave number, period, frequency, phase velocity, group velocity, dispersion relation, etc. You need
to choose three different water depths corresponding to shallow, intermediate, and deep
water. Make plots of the: wave length as a function of frequency (dispersion relation);
phase velocity as a function of frequency; and group velocity as a function of frequency for
these three different water depths. Discuss how does the water depth affect the wavelength,
phase velocity, group velocity for given frequency?
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3. Find the response of a simple harmonic oscillator with harmonic forcing F = F0 cos ωt, i.e.
find the solution x = X0 cos(ωt + φ) of:
M ẍ + B ẋ + Kx = F0 cos ωt
(1)
(i) Find the expression of X0 . (ii) Discuss how will the response amplitude X0 be affected by
M, B, K and F0 ? (iii) If F = 0, how could damping B be determined from measurements
of the motion?
4. Apply the approach in part(3) to the problem of an inverted pendulum: a long buoyant
cylinder moored to the bottom by a wire, as shown in Figure 1. For this case, (i)Calculate
corresponding M , K, and F0 ( in terms of the pendulum geometry). (ii) Discuss the possible
sources of damping for this pendulum. (iii) What non-dimensional quantities govern these
problems?
5. Think through and plan the lab with the other group members. Prepare an action plan
for the lab and tables or graphs to roughly plot the data you anticipate.
Be prepared to discuss with the lab staff your action plan when you enter the lab.
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LABORATORY ASSIGNMENT
Objectives:
The specific objectives of this laboratory assignment are to:
• Measure the frequency, wavelength, phase velocity, and group velocity of various waves
generated by the wavemaker.
• Observe the phenomenon of long wave overtaking short wave due to dispersion effect.
• Measure the natural frequency of an inverted pendulum in calm water.
• Measure the forced response of the inverted pendulum in waves.
• Observe the VIV phenomenon and suppression of VIV using hand-towed cylinders.
Equipment:
The towing tank is a long rectangular basin of water, 35m x 2.5m x 1.5m. At one end of the
tank there is a wave-maker and at the other end there is absorbing “beach”. The wave-maker is
a hydraulically driven vertical paddle with controllable amplitude and frequency. The “beach”
is a region of absorbing material intended to prevent the reflecting of waves from this end of the
tank.
Measurements:
The TA will provide instructions for the operation of the wavemaker. Please follow his instructions. Detailed descriptions how to perform the measurements will be given during the exercise.
1. Part I: Surface Wave Kinematics
(a) Measure the water depth in the tank.
(b) Calibrate wave probes.
(c) Generate a regular wave using wavemaker and measure the wave period, length, phase
velocity and group velocity. Repeat this for 5 different frequencies.
(d) Generate a wave consisting of a short wave followed by a long wave and observe the
difference between the wave passing a location near the wavemaker and that for a
location far away from the wavemaker.
2. Part II: Wave-Induced Motion
We will study the motion of an inverted pendulum in waves. Waves have amplitude A,
wave-length λ and angular frequency ω.
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The inverted pendulum consists of a buoyant horizontal circular cylinder connected with a
wire (at each end) to the bottom of the tank. The ratio of the length and the diameter of
the cylinder is very large so that the cylinder is assumed to be a slender body. The sketch
of the setup is shown on Figure 1.
not to scale
λ, A
SWL
R
m
h
L

wall
wall
bottom
Figure 1: Inverted pendulum setup.
(a) Measure the length of the pendulum. Measure the mass, radius and length of the
cylinder.
(b) Give the pendulum an initial displacement in calm water and then release. Measure
the natural frequency and the response (angular deflection θ) of the pendulum.
(c) Measure the forced response (angular deflection θ) of the system in 3 waves with different frequencies. Be sure to note the wave height at each frequency for normalization
in the post-lab exercise.
(d) For each frequency, observe the wave pattern as the wave passes by the pendulum.
Do you notice any changes due to the presence and motion of the pendulum?
3. Part III: Vortex-Induced Vibration
(a) Tow a hand-held bare cylinder through the water at several different speeds to feel
and observe the VIV motion of the cylinder. How does the frequency of the motion
of the cylinder vary with the forward speed you move it?
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Post-Lab Exercise (To be done individually)
Note that the final results you present in your lab report must be in non-dimensional form.
Tables and graphical plots should be used.
The lab report should include a copy of your pre-lab preparation, the specific procedure of your
group’s experiment, data analysis, and a discussion of your results.
The following results must be analyzed and discussed in your lab report. In addition, you are
encouraged to discuss other hydrodynamic aspects you have observed in the experiments. Any
novel idea and insightful discussion will be given extra credit in the lab grade.
1. Plot the wave length, phase velocity, and group velocity as functions of frequency. Compare
your results with theory and discuss.
2. For the pendulum experiment in calm water, obtain the natural frequency of the pendulum
and the added mass of the cylinder based on the measurements. Compare both results to
the theoretical predictions and try to explain the difference. Plot the measured response θ
as a function of time and calculate the damping of the system. Discuss the possible sources
of damping.
3. For the induced wave motion experiment, plot the non-dimensional response amplitude
operators (RAOs) Lθ/A as a function of non-dimensional frequency. Discuss the results.
Is there a resonant peak?
4. Compare the obtained responses (RAOs) by measurement of the inverted pendulum with
theoretical predictions for long waves. In order to get theoretical solution, you can use
Froude-Krylov approximation to calculate the wave force. For the damping, you can use
the result of measurement.
The lab report should be written in a professional way. It should be type-written and should have
been edited for grammatical and spelling errors. Although it needs to be complete, conciseness
is also emphasized. Unnecessary length will be regarded as a negative factor in the lab grading.
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