Oggi in treno...

[Zhurlo]

... riflettevo sulla possibilità di determinare la velocità della carrozza in base all'angolo che le gocce di pioggia formano quando vengono in conttatto con il vetro ... ma non sono arrivato a grandi conclusioni


... Ne è passato di tempo da Fisica 1!

[Fenomeno85]

Originariamente inviato da Zhurlo
... riflettevo sulla possibilità di determinare la velocità della carrozza in base all'angolo che le gocce di pioggia formano quando vengono in conttatto con il vetro ... ma non sono arrivato a grandi conclusioni


... Ne è passato di tempo da Fisica 1!

che palle io sto facendo fisica sperimentale a + b ... ma sta roba è fatta per i complessati

~§~ Sempre E Solo Lei ~§~

[kaioh]

Originariamente inviato da Zhurlo
... riflettevo sulla possibilità di determinare la velocità della carrozza in base all'angolo che le gocce di pioggia formano quando vengono in conttatto con il vetro ... ma non sono arrivato a grandi conclusioni


... Ne è passato di tempo da Fisica 1!

devi sapere anche la direzione del vento, la velocità di caduta , come si comportano gli attriti acqua-vetro,....

[FastFreddy]

Originariamente inviato da Zhurlo
... riflettevo sulla possibilità di determinare la velocità della carrozza in base all'angolo che le gocce di pioggia formano quando vengono in conttatto con il vetro ... ma non sono arrivato a grandi conclusioni

Dormire come tutti gli altri no, eh????

[Zhurlo]

Originariamente inviato da kaioh
devi sapere anche la direzione del vento, la velocità di caduta , come si comportano gli attriti acqua-vetro,....

certo, la direzione e l'intensità del vento non è da sottovalutare, io direi di facilitare il problema considerandola non presente

la velocità di caduta si può supporre trascurabile, così come il peso e la dimensione delle goccie di pioggia. l'atrito acqua-vetro invece non ha nessuna implicazione nel problema... se ho capito bene quello che intendi dire

[shadylane]

Originariamente inviato da Zhurlo
certo, la direzione e l'intensità del vento non è da sottovalutare, io direi di facilitare il problema considerandola non presente

be a questo punto se trascuri la direzione e l'intensità dl vento non potrai mai determinare la velocità del treno, poichè le gocce cadranno sempre perpendicolari al terreno, ed in particolare parallele al vetro, e come ben noto due linee parallele non si incontrano mai.

[a2000.1]

Originariamente inviato da Zhurlo
... riflettevo sulla possibilità di determinare la velocità della carrozza in base all'angolo che le gocce di pioggia formano quando vengono in conttatto con il vetro ... ma non sono arrivato a grandi conclusioni

... Ne è passato di tempo da Fisica 1!

velocità relativa, velocità di trascinamento ....
settling velocity of liquid drops in gases ....

eh karino ... fisica 1 non basta ... ma ti daro' una ricetta semplice e compatta.
usare la seguente formula:

vt = 25*tg(alfa)

alfa è l'angolo tra l'asse verticale e la direzione (di attacco) delle gocce
vt è la velocità del treno in km/h

[RaouL_BennetH]

Originariamente inviato da a2000.1
velocità relativa, velocità di trascinamento ....
settling velocity of liquid drops in gases ....

eh karino ... fisica 1 non basta ... ma ti daro' una ricetta semplice e compatta.
usare la seguente formula:

vt = 25*tg(alfa)

alfa è l'angolo tra l'asse verticale e la direzione (di attacco) delle gocce
vt è la velocità del treno in km/h

Ma questi dati da dove li prenderebbe? non sono tutte incognite?

[giannipas]

Ciao !
Mah!, secondo me la velocità di caduta non è certo trascurabile.....bisognerebbe calcolarla considerando che dopo un certo tempo, indipendentemente dall'altezza di partenza, diventa costante infatti la goccia viene "frenata" dall'attrito con l'aria.
Calcolata questa, basta applicare la relazione trigonometrica che lega i cateti di un triangolo rettangolo con l'angolo compreso: tg(alfa)=velocità del treno/velocità di caduta della goccia.
Misurando alfa si calcola facilmente la velocità del treno.

Ciao !!!!!!!!

[Bilancino]

Quando sono sul treno cerco posti con bonazze.......

Ciao

[Zhurlo]

Originariamente inviato da a2000.1
velocità relativa, velocità di trascinamento ....
settling velocity of liquid drops in gases ....

eh karino ... fisica 1 non basta ... ma ti daro' una ricetta semplice e compatta.
usare la seguente formula:

vt = 25*tg(alfa)

alfa è l'angolo tra l'asse verticale e la direzione (di attacco) delle gocce
vt è la velocità del treno in km/h

il 25 da dove salta fuori?

[Zhurlo]

Originariamente inviato da giannipas
Ciao !
Mah!, secondo me la velocità di caduta non è certo trascurabile.....bisognerebbe calcolarla considerando che dopo un certo tempo, indipendentemente dall'altezza di partenza, diventa costante infatti la goccia viene "frenata" dall'attrito con l'aria.
Calcolata questa, basta applicare la relazione trigonometrica che lega i cateti di un triangolo rettangolo con l'angolo compreso: tg(alfa)=velocità del treno/velocità di caduta della goccia.
Misurando alfa si calcola facilmente la velocità del treno.

Ciao !!!!!!!!

Ho sbaglito termine... pensavo di risolvere il problema senza utilizzare la velocità di caduta della goccia! in questo caso la parola esatta sarebbe costante e non trascurabile. grazie per lo spunto

anche se non mi convince tanto

[a2000.1]

Originariamente inviato da Zhurlo
il 25 da dove salta fuori?

da qui:


PARTICLE DYNAMICS
GENERAL REFERENCES: Brodkey, The Phenomena of Fluid Motions, Addison-
Wesley, Reading, Mass., 1967; Clift, Grace, and Weber, Bubbles, Drops and Particles,
Academic, New York, 1978; Govier and Aziz, The Flow of Complex
Mixtures in Pipes, Van Nostrand Reinhold, New York, 1972, Krieger, Huntington,
N.Y., 1977; Lapple, et al., Fluid and Particle Mechanics, University of
Delaware, Newark, 1951; Levich, Physicochemical Hydrodynamics, Prentice-
Hall, Englewood Cliffs, N.J., 1962; Orr, Particulate Technology, Macmillan,
New York, 1966; Shook and Roco, Slurry Flow, Butterworth-Heinemann,
Boston, 1991; Wallis, One-dimensional Two-phase Flow, McGraw-Hill, New
York, 1969.
DRAG COEFFICIENT
Whenever relative motion exists between a particle and a surrounding
fluid, the fluid will exert a drag upon the particle. In steady flow, the
drag force on the particle is
FD = (6-227)
where FD = drag force
CD = drag coefficient
AP = projected particle area in direction of motion
r = density of surrounding fluid
u = relative velocity between particle and fluid
The drag force is exerted in a direction parallel to the fluid velocity.
Equation (6-227) defines the drag coefficient. For some solid bodies,
such as aerofoils, a lift force component perpendicular to the liquid
velocity is also exerted. For free-falling particles, lift forces are
generally not important. However, even spherical particles experience
lift forces in shear flows near solid surfaces.
CDAPru2
}2
TERMINAL SETTLING VELOCITY
A particle falling under the action of gravity will accelerate until the
drag force balances gravitational force, after which it falls at a constant
terminal or free-settling velocity ut, given by
ut =!§ (6-228)
where g = acceleration of gravity
mp = particle mass
rp = particle density
and the remaining symbols are as previously defined.
Settling particles may undergo fluctuating motions owing to vortex
shedding, among other factors. Oscillation is enhanced with increasing
separation between the mass and geometric centers of the particle.
Variations in mean velocity are usually less than 10 percent. The
drag force on a particle fixed in space with fluid moving is somewhat
lower than the drag force on a particle freely settling in a stationary
fluid at the same relative velocity.
Spherical Particles For spherical particles of diameter dp, Eq.
(6-228) becomes
ut =!§ (6-229)
The drag coefficient for rigid spherical particles is a function of particle
Reynolds number, Rep = dpru/m where m = fluid viscosity, as shown
in Fig. 6-57. At low Reynolds number, Stokes’ Law gives
CD = Rep < 0.1 (6-230)
which may also be written
FD = 3pmudp Rep < 0.1 (6-231)
and gives for the terminal settling velocity
ut = Rep < 0.1 (6-232)
In the intermediate regime (0.1 < Rep < 1,000), the drag coefficient
may be estimated within 6 percent by
CD =1 211 + 0.14Rep
0.702 0.1 < Rep < 1,000 (6-233)
In the Newton’s Law regime, which covers the range 1,000 < Rep <
350,000, CD = 0.445, within 13 percent. In this region, Eq. (6-227)
becomes
ut = 1.73!§ 1,000 < Rep < 350,000 (6-234)
Between about Rep = 350,000 and 1 ´ 106, the drag coefficient drops
dramatically in a drag crisis owing to the transition to turbulent flow
in the boundary layer around the particle, which delays aft separation,
resulting in a smaller wake and less drag. Beyond Re = 1 ´ 106, the
drag coefficient may be estimated from (Clift, Grace, and Weber):
CD = 0.19 - Rep > 1 ´ 106 (6-235)
Drag coefficients may be affected by turbulence in the free-stream
flow; the drag crisis occurs at lower Reynolds numbers when the free
stream is turbulent. Torobin and Guvin (AIChE J., 7, 615–619 [1961])
found that the drag crisis Reynolds number decreases with increasing
free-stream turbulence, reaching a value of 400 when the relative
turbulence intensity, defined as Ïuww¢ww/UwR is 0.4. Here Ïuww¢ww is the rms
fluctuating velocity and UwR is the relative velocity between the particle
and the fluid.
For particles settling in non-Newtonian fluids, correlations are
8 ´ 104
}
Rep
gdp(rp - r)
}}
r
24
}
Rep
gdp
2 (rp - r)
}}
18m
given by Dallon and Christiansen (Preprint 24C, Symposium on
Selected Papers, part III, 61st Ann. Mtg. AIChE, Los Angeles, Dec.
1–5, 1968) for spheres settling in shear-thinning liquids, and by Ito
and Kajiuchi (J. Chem. Eng. Japan, 2[1], 19–24 [1969]) and Pazwash
and Robertson (J. Hydraul. Res., 13, 35–55 [1975]) for spheres settling
in Bingham plastics. Beris, Tsamopoulos, Armstrong, and Brown
(J. Fluid Mech., 158 [1985]) present a finite element calculation for
creeping motion of a sphere through a Bingham plastic.
Nonspherical Rigid Particles The drag on a nonspherical particle
depends upon its shape and orientation with respect to the direction
of motion. The orientation in free fall as a function of Reynolds
number is given in Table 6-8.
The drag coefficients for disks (flat side perpendicular to the direction
of motion) and for cylinders (infinite length with axis perpendicular
to the direction of motion) are given in Fig. 6-57 as a function of
Reynolds number. The effect of length-to-diameter ratio for cylinders
in the Newton’s law region is reported by Knudsen and Katz (Fluid
Mechanics and Heat Transfer, McGraw-Hill, New York, 1958).
Pettyjohn and Christiansen (Chem. Eng. Prog., 44, 157–172
[1948]) present correlations for the effect of particle shape on freesettling
velocities of isometric particles. For Re < 0.05, the terminal
or free-settling velocity is given by
PARTICLE DYNAMICS 6-51
FIG. 6-57 Drag coefficients for spheres, disks, and cylinders: Ap = area of particle projected on a plane normal to direction of motion; C = overall
drag coefficient, dimensionless; Dp = diameter of particle; Fd = drag or resistance to motion of body in fluid; Re = Reynolds number, dimensionless;
u = relative velocity between particle and main body of fluid; m = fluid viscosity; and r = fluid density. (From Lapple and Shepherd, Ind.
Eng. Chem., 32, 605 [1940].)
TABLE 6-8 Free-Fall Orientation of Particles
Reynolds number* Orientation
0.1–5.5 All orientations are stable when there are three or
more perpendicular axes of symmetry.
5.5–200 Stable in position of maximum drag.
200–500 Unpredictable. Disks and plates tend to wobble, while
fuller bluff bodies tend to rotate.
500–200,000 Rotation about axis of least inertia, frequently
coupled with spiral translation.
SOURCE: From Becker, Can. J. Chem. Eng., 37, 85–91 (1959).
*Based on diameter of a sphere having the same surface area as the particle.
ut = K1 (6-236)
K1 = 0.843 log 1 2 (6-237)
where y = sphericity, the surface area of a sphere having the same volume
as the particle, divided by the actual surface area of the particle;
ds = equivalent diameter, equal to the diameter of the equivalent
sphere having the same volume as the particle; and other variables are
as previously defined.
In the Newton’s law region, the terminal velocity is given by
ut =!§ (6-238)
K3 = 5.31 - 4.88y (6-239)
Equations (6-236) to (6-239) are based on experiments on cubeoctahedrons,
octahedrons, cubes, and tetrahedrons for which the
sphericity y ranges from 0.906 to 0.670, respectively. See also Clift,
Grace, and Weber. A graph of drag coefficient vs. Reynolds number
with y as a parameter may be found in Brown, et al. (Unit Operations,
Wiley, New York, 1950) and in Govier and Aziz.
For particles with y < 0.67, the correlations of Becker (Can. J.
Chem. Eng., 37, 85–91 [1959]) should be used. Reference to this
paper is also recommended for intermediate region flow. Settling
characteristics of nonspherical particles are discussed by Clift, Grace,
and Weber, Chaps. 4 and 6.
The terminal velocity of axisymmetric particles in axial motion
can be computed from Bowen and Masliyah (Can. J. Chem. Eng., 51,
8–15 [1973]) for low–Reynolds number motion:
ut = (6-240)
K2 = 0.244 + 1.035S - 0.712S2 + 0.441S3 (6-241)
where Ds = diameter of sphere with perimeter equal to maximum
particle projected perimeter
V¢ = ratio of particle volume to volume of sphere with
diameter Ds
S = ratio of surface area of particle to surface area of a
sphere with diameter Ds
and other variables are as defined previously.
Hindered Settling When particle concentration increases, particle
settling velocities decrease because of hydrodynamic interaction
between particles and the upward motion of displaced liquid. The suspension
viscosity increases. Hindered settling is normally encountered
in sedimentation and transport of concentrated slurries. Below
0.1 percent volumetric particle concentration, there is less than a 1
percent reduction in settling velocity. Several expressions have been
given to estimate the effect of particle volume fraction on settling
velocity. Maude and Whitmore (Br. J. Appl. Phys., 9, 477–482 [1958])
give, for uniformly sized spheres,
ut = ut0(1 - c)n (6-242)
where ut = terminal settling velocity
ut0 = terminal velocity of a single sphere (infinite dilution)
c = volume fraction solid in the suspension
n = function of Reynolds number Rep = dput0r/m as given
Fig. 6-58
In the Stokes’ law region (Rep < 0.3), n = 4.65 and in the Newton’s law
region (Rep > 1,000), n = 2.33. Equation (6-242) may be applied to
particles of any size in a polydisperse system, provided the volume
fraction corresponding to all the particles is used in computing terminal
velocity (Richardson and Shabi, Trans. Inst. Chem. Eng. [London],
38, 33–42 [1960]). The concentration effect is greater for nonspherical
and angular particles than for spherical particles (Steinour, Ind.
Eng. Chem., 36, 840–847 [1944]). Theoretical developments for
low–Reynolds number flow assemblages of spheres are given by Happel
and Brenner (Low Reynolds Number Hydrodynamics, PrenticegDs
2(rp - r)
}}
18m
V¢
}
K2
4ds(rp - r)g
}}
3K3r
y}
0.065
gds
2(rp - r)
}}
18m
Hall, Englewood Cliffs, N.J., 1965) and Famularo and Happel
(AIChE J., 11, 981 [1965]) leading to an equation of the form
ut = (6-243)
where g is about 1.3. As particle concentration increases, resulting in
interparticle contact, hindered settling velocities are difficult to predict.
Thomas (AIChE J., 9, 310 [1963]) provides an empirical expression
reported to be valid over the range 0.08 < ut /ut0 < 1:
ln 1 2= -5.9c
Liquid Drops in Gases Liquid drops falling in stagnant gases
appear to remain spherical and follow the rigid sphere drag relationships
up to a Reynolds number of about 100. Large drops will deform,
with a resulting increase in drag, and in some cases will shatter. The
largest water drop which will fall in air at its terminal velocity is about
8 mm (0.32 in) in diameter, with a corresponding velocity of about
9 m/s (30 ft/s). Drops shatter when the Weber number defined as
We = (6-253)
exceeds a critical value. Here, rG = gas density, u = drop velocity, d =
drop diameter, and s = surface tension. A value of Wec = 13 is often
cited for the critical Weber number.
Terminal velocities for water drops in air have been correlated by
Berry and Prnager (J. Appl. Meteorol., 13, 108–113 [1974]) as
Re = exp [-3.126 + 1.013 ln ND - 0.01912(ln ND)2] (6-254)
for 2.4 < ND < 107 and 0.1 < Re < 3550. The dimensionless group ND
(often called the Best number [Clift, et al.]) is given by
ND = (6-255)
and is proportional to the similar Archimedes and Galileo numbers.
Figure 6-61 gives calculated settling velocities for solid spherical
particles settling in air or water using the standard drag coefficient
curve for spherical particles. For fine particles settling in air, the
Stokes-Cunningham correction has been applied to account for
particle size comparable to the mean free path of the gas. The correction
is less than 1 percent for particles larger than 16 mm settling in air.
Smaller particles are also subject to Brownian motion. Motion of
particles smaller than 0.1 mm is dominated by Brownian forces and
gravitational effects are small.
Wall Effects When the diameter of a settling particle is significant
compared to the diameter of the container, the settling velocity is
reduced. For rigid spherical particles settling with Re < 1, the correction
given in Table 6-9 may be used. The factor kw is multiplied by the
settling velocity obtained from Stokes’ law to obtain the corrected set-
4rDrgd3
}3
m2
rGu2d}
s
m}r
d
m}m
w
4}3
tling rate. For values of diameter ratio b = particle diameter/vessel
diameter less than 0.05, kw = 1/(1 + 2.1b) (Zenz and Othmer, Fluidization
and Fluid-Particle Systems, Reinhold, New York, 1960, pp.
208–209). In the range 100 < Re < 10,000, the computed terminal
velocity for rigid spheres may be multiplied by k¢w to account for wall
effects, where k¢w is given by (Harmathy, AIChE J., 6, 281 [1960])
k¢w = (6-256)
For gas bubbles in liquids, there is little wall effect for b < 0.1. For
b > 0.1, see Uto and Kintner (AIChE J., 2, 420–424 [1956]), Maneri
and Mendelson (Chem. Eng. Prog., 64, Symp. Ser., 82, 72–80 [1968]),
and Collins (J. Fluid Mech., 28, part 1, 97–112 [1967]).

[ChristinaAemiliana]

Le formule dove sono?

[a2000.1]

ci sono anche quelle ...

ma perchè, se leggibili cambia qualcosa ?

[a2000.1]

comunque crì come vedi torniamo sempre a problemi di "two phase flow"

sarà un caso ?