Object Impact on the Free Surface and Added Mass Effect
2.016 Laboratory Fall 2005
Prof. A. Techet
Introduction to Free Surface Impact
Free surface impact of objects has applications to ocean engineering such as ship
slamming hydrodynamics.
The simplest geometric object to study is a sphere.
The
hydrodynamics are three dimensional, but several basic concepts can be observed using
high speed video sequences.
The main focus of Part A of this laboratory exercise is to determine the
terminal velocity
of a sphere that impacts the free surface of a tank of water at high speeds. When an
object which is falling under the influence of gravity or subject to some other constant
driving force is subject to a resistance (drag force) which increases with velocity, it will
ultimately reach a maximum velocity where the drag force equals the driving force. This
final, constant velocity of motion is called a "terminal velocity", a terminology made
popular by skydivers. For objects moving through a fluid at low speeds so that turbulence
is not a major factor, the terminal velocity is determined by viscous drag.
F
drag
F
buoyancy
=
ρ
gV
F
g
= mg
M
drag
buoyancy
gravity
F
F
F
+
=
2
1
2
drag
d
F
U C A
!
=
(1.1)
The drag force is
(1.2)
where
U
is the speed of the object,
A
is the frontal area of the object, and
C
d
= 0.5 is the
coefficient of drag for a sphere.
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View Full DocumentThe buoyancy force is
buoyancy
F
g
!
=
"
gravity
F
mg
=
(1.3)
and force of gravity is simply
(1.4)
Two photos removed for copyright reasons.
Flow about a sphere in a wind tunnel.
Lab part A:
In this section of the lab you will observe objects impacting the free surface at two speeds
and continuing down into the tank. You are asked to qualitatively consider the behavior
of the sphere at the moment of impact: the splash formation (height and shape), wave
generation, bubble/cavity formation behind the sphere, etc.
You will take high speed
video of the objects and use a software package to determine the position of the ball as a
function of time,
x(t)
. A graduate student will show you how to operate the image
recognition software. You will then use the data to determine the velocity of the ball as a
function of time.
As the ball approaches the bottom of the tank it may reach terminal velocity. Using the
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 Fall '05
 AlexandraTechet
 Fluid Dynamics, Force, Mass, Natural Frequency

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