Full resolution (JPEG) - On this page / på denna sida - Sidor ...
<< prev. page << föreg. sida << >> nästa sida >> next page >>
Below is the raw OCR text
from the above scanned image.
Do you see an error? Proofread the page now!
Här nedan syns maskintolkade texten från faksimilbilden ovan.
Ser du något fel? Korrekturläs sidan nu!
This page has never been proofread. / Denna sida har aldrig korrekturlästs.
100
ilinger. Den kunde ogsaa bestem mes. naar mail kjendte
den gjennemsnitlige Hastighed af Vandet over og under
Grændsetladen. Man vilde da have Betingelsen for Vandets
Continuitet udtrykt derved, at ile ovre Strømningers
Tversnit forholder sig til de nedre Strømningers Tversnit som
disses Middelhastighed til de forstes, og af Tversnittenes
indbyrdes Størrelse kunde Beliggenheden af Gramdselinieii
mellem begge bestemmes.
At linde Middelhastigheden af Vandet i de øvre og
nedre Strømme, eller Forholdet mellem begge, lader sig
neppe gjøre med nogen synderlig Tilnærmelse til
Nøjagtighed. Ydre og indre Frietion spiller lier en Rolle, hvis
Virkning ikke lader sig bestemme. Vi kunne imidlertid
ved Forsøg finde Grændser, inden hvilke Opgavens Løsning
maa ligge.
Tamlte vi os. som i Fig. 2, at et vertiealt Snit
gjennem Havet har Formen af en Parabel, hvis Toppunkt ligger
i Havets dybeste Punkt. B, saa ville vi søge den Dybde,
i hvilken GrændseHaden N’ N’ vil ligge, dersom
Gjenneinsnits-Hastigheden i de øvre Lag var l’ og i de nedre Lag r. I
saa Fald maatte Fladerunimene T T N’ N’ og N’ N’ B
forholde sig som r til l’.
Kaldes Maximuriisdybden H, Dybden af Gramdsetladen
h, og Havets halve Bredde i Overfladen A. i GrændseHaden
a. saa har man
2 2
det ovre Fladeruni = " HA — ~ t H—h) a
It might also be determined if we knew the average
velocity of the water above and below the limiting surface.
We should then have the condition of the water’s
continuity expressed by the cross-section of the upper currents
having to the cross-section of the lower the same ratio
as the mean velocity of the latter has to that of the
former; and from the relative areas of the cross-sections,
the position of the limiting line between both might be
determined.
To find the mean velocity of the water in the upper
and lower currents, or their ratio to each other, will
hardly admit of being effected with any reasonable approach
to correctness. Here, outer and inner friction play a part,
the influence of which cannot be determined. Meanwhile,
we can. on repeated trial, find limits within which the
solution of the problem must lie.
Now. if we imagine, as shown in fig 2. a vertical
section through the sea having the form of a parabola, the
vertex of which is at the deepest point of the ocean-bed,
B, we shall seek the depth at which the limiting surface,
jfc’ N’, will lie. assuming the average velocity in the upper
strata to be V and in the lower strata r. Hence the
areas T T N’ N’ and N’ N’ B must have the same ratio as
r to V.
Calling the maximum depth H, the depth ol’ the
limiting surface h, and half the breadth of the sea at the
surface at the limiting surface a, we have
If A— (11 Jn a r
altsaa =., •
(II—h) a 1
Indføres Relationen = °
the lower
H A — (H— k) a
hence TT , =
i H h) a
Now, since H=JI _h.
*=!-( ’’
u~ r i
Sættes U— 2000 Favne, saa faar man
for ’=1 h =0.370 // =740 Favne
2 0.237 474
3 0.174 349
4 0.138 27(5
5 0.1 lø 229.
Da Middelhastigheden i det nedre Fladeruin maa være
mindre end i det ovre. saa bliver den allerstørste Dybde,
i hvilken vi kunne søge Grændsetladen, 740 Favne.
Naar man ser hen til, af i det nedre Tversnit den
horizontale Hastighed er Nul rundt hele Tversnittets
Omkreds, medens den i det ovre Tversnit kun paa 3 Sider
er Nul, nemlig i Axen, i Grændsetladen og ved Randen,
men i Overfladen har et absolut Maximum, i Forbindelse
med, at Gradienterne i de nedre Lag tilhøre den Axen
nærmestliggende Del af Systemet, hvor disse overhovedet ere
mindre, medens de i Overfladen voxe med Afstanden fra
„=’"( T+,-1" *
Putting H — 2000 fathoms, we get
for ’ =1 h = 0.370 H = 740 fathoms
2 0.237 474
3 0.174 349
4 0.138 27(5
5 0.115 229
Since the average velocity in the lower area, must
be less than’in the upper, the greatest depth at which we
can seek the limiting surface will be 740 fathoms.
If we consider that in the lower cross-section the
horizontal velocity is nil at the entire perimeter of the
section, whereas in the upper cross-section it is nil
on three sides only, viz., in the axis, at the limiting
surface, and at the margin, but at the upper surface has
an absolute maximum, besides that the gradients in the
lower strata belong to the part of the system nearest the
axis, where these on the whole are less, whereas at the
<< prev. page << föreg. sida << >> nästa sida >> next page >>
