ERDC/CHL CETN-IV-26
June 2000
A = inlet throat cross-sectional area
Vmax = average maximum velocity at inlet throat
The tidal prism scale ratio is given by the prototype-to-model ratio of Equation 4, i.e.,:
N p = NV N T N A
(5)
where NV, NT, and NA are the velocity scale, tidal period time scale, and cross-sectional area
scale, respectively.
Froude Scaling. Noting for Froude-scaled models NV = NT, NA = (NL)2, and NL = (NT)2, the
prism scale can be expressed in terms of just the time scale. Thus, the model results can be
scaled to prototype area and prism using the Froude-scale equations:
b g4
b g6
Ap = Am N T
Pp = Pm N T
(6)
and
where once again the subscripts p and m represent prototype and model, respectively. Model
tidal periods were used to establish the time scale, and the corresponding length scales were then
fixed by the Froude scale. (Resulting prototype length scales ranged between 50 ≤ NL ≤ 1,388.)
The Froude-scaled experiment results are shown as x-symbols (Mayor-Mora 1977) and plus-
signs (CIRP data) on Figure 1. All but one value are outside Jarrett's 95 percent confidence
limit, with cross-sectional areas smaller then would be expected for the scaled-up tidal prism.
This is logical because the model sediment diameter was much larger than required for Froude
scaling, so it was not as easily scoured from the model inlet.
New Scaling Relationship. Scaling the small-scale model results to prototype using the
scale relationship given in this technical note uses the same tidal prism scale given by
Equation 5. But instead of Froude velocity scaling, Equation 2 is substituted for NV in
Equation 5, yielding
N p = N d /8 N T N 17/8
3
(7)
L
e
The relationship between the length and time scales is found from the identity NV = NL/NT or:
N L = N d /7 N T/7
3
8
(8)
e
where NV is given by Equation 2. Substituting Equation 8 into Equation 7 results in the
following relationships for scaling area and prism to prototype scale:
b g2 = Am e N d j6/7 b N T g16/7
e j b N T g24/7
9/7
Ap = Am N L
Pp = Pm N de
(9)
and
e
The model sediment grain size was 0.34 mm in Mayor-Mora's (1977) experiments, and the CIRP
experiments used grain sizes of 0.13 mm and 0.26 mm. Because 0.34 mm is typical for real tidal
inlets, this value was chosen as the prototype grain size. Therefore, Nde was unity for Mayor-
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