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Similitude in open channel flow (calculation of the prototype velocity by the model velocity)

작성자 Uploader : a.c.e. 작성일 Upload Date: 2019-09-09변경일 Update Date: 2019-10-05조회수 View : 300

Similitude in open channel flow

In the open channel flow, the relationship between the model and the prototype can be established and the values ​​measured in the model can be converted to values ​​on a real scale.

The dimensionless number applied to the open channel flow is Froude Number, which is F = V / (g * L)^(1/2).

Since the Froude Numbers of the model (m) and of the prototype (p) must be the same, the following relation holds.

Vm^2  / (gm*Lm) = Vp^2 / (gp*Lp)

Lm, Lp : lengths of model and prototype  

Solving this for velocity (V), the gravitational acceleration (g) is the same both for the model and for the prototype, thus :

gm = gp

Then,

Vp = Vm*(Lp/Lm)^(1/2)

In general, the ratio (λ) of lengths of the prototype and the model  is defined as  λ = Lp / Lm and this is called the similitude ratio.

Vp = Vm*λ^(1/2)

Meantime, since the time (t) is L/V, tm = Lm/Vm and tp = Lp/Vp, then;

tp = tm* Lp/Lm * Vm/Vp = tm*λ^(1/2)
(tm, tp : time in model and in prototype)


*** 참고문헌[References] ***

FLUID MECHANICS Eighth Edition, KOREAN STUDENT EDITION, Victor L. Streeter, E. Benjamin Wylie, McGRAW-HILL, 1986.
Vp = Vm*(Lp/Lm)^(1/2)
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변수명 Variable 변수값 Value 변 수 설 명 Description of the variable


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