Abstract
1. Prof. Prandtl, in his paper presented to the Second International Congress for Technical Mechanics, Zurich, 1926, shows that if certain assumptions are made, it is possible to obtain the equations of motion for the turbulent region behind a body, placed in a uniform stream, in such a form that they can be integrated. Taking the case, where the undisturbed stream is parallel to the axis of
x
, he show that the interchange of momentum between the fluid particles, due to turbulence, may be allowed for by introducing into the equations of motion a term representing the "apparent stress" in the form
l
2
(∂
u
/∂
y
)
2
, where
u
is the mean velocity at any point parallel to 0
x
,
y
is distance from the axis of
x
and
l
is a length called by Prandtl "Mischungsweg" (mixing distance) or "mean free path"; it is not constant but varies from point to point. A form related to this was found by G. I. Taylor in his paper on "Eddy motion in the atmosphere." It has been pointed out by Jeffreys that if A is the "apparent viscosity," the term introduced into the equation of motion by Taylor is A ∂
2
u
/∂
y
2
, whereas Prandtl introduces the term ∂/∂
y
(A ∂
u
/∂
y
); further the difference between these tow terms represents the momentum lost during migration owing to the differences of pressure. Taylor takes this loss into account. Prandtl assumes that for a first approximation the pressure may be treated as constant and hence no momentum is lost during migration and we get the form ∂/∂
y
(A ∂
u
/∂
y
).
Cited by
43 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献