Transcript BE105_21_running_on_water

slap, stroke, and protraction
f
impulsetotal  impulseslap  impulsestrok e
impulseslap  mvirtualu peak
impulsestrok e   drag (t ) cosfdt
virtual
mass
hydrodynamic
drag
virtual
mass
impulse =
force dt = mass x velocity
velocity = impact velocity
mass =‘virtual mass’
virtual mass = impulse/velocity
hydrodynamic
drag
h
Drag = CD* (1/2 r u2 S + r g h S)
dynamic
component
Drag coefficient
is constant with depth
and velocity
static
component
=depth
Time for bubble to seal
Step duration of real
lizards
impulseslap  mvirtualu peak
impulsestrok e   drag (t ) cosfdt
Note: most force due to stroke
Could humans do this?
`
no: it would require a
foot velocity of 30 m/sec.
Three important descriptors of fluid motion:
1. velocity, u(x,y)
ux
uy
2. vorticity, w(x,y)
Duy
w
Dx
x
y
u(x,y)
3. circulation, G
Dux
Dy
GSw
Fslap = m U / t
Fstroke = r G A /t
Momentum
of vortex ring
r G A
where m is bolus of
accelerated water, moving at
velocity, u
impulse (F x t) = mass x velocity
A
G = circulation