fluid_mechanics

368 Chapter 7 ■ Dimensional Analysis, Similitude, and Modeling
F I G U R E 7.8 A scale hydraulic model
(1:197) of the Guri Dam in Venezuela which is used
to simulate the characteristics of the flow over and
below the spillway and the erosion below the spillway.
(Photograph courtesy of St. Anthony Falls
Hydraulic Laboratory.)
V7.19 Dam model
models. Although this approach eliminates surface tension effects in the model, it introduces geometric
distortion that must be accounted for empirically, usually by increasing the model surface
roughness. It is important in these circumstances that verification tests with the model be performed
1if possible2 in which model data are compared with available prototype river flow data. Model
roughness can be adjusted to give satisfactory agreement between model and prototype, and then
the model subsequently used to predict the effect of proposed changes on river characteristics 1such
as velocity patterns or surface elevations2.
For large hydraulic structures, such as dam spillways, the Reynolds numbers are large so that
viscous forces are small in comparison to the forces due to gravity and inertia. In this case, Reynolds
number similarity is not maintained and models are designed on the basis of Froude number similarity.
Care must be taken to ensure that the model Reynolds numbers are also large, but they are
not required to be equal to those of the prototype. This type of hydraulic model is usually made
as large as possible so that the Reynolds number will be large. A spillway model is shown in Fig.
7.8. Also, for relatively large models the geometric features of the prototype can be accurately
scaled, as well as surface roughness. Note that e m l / e, which indicates that the model surfaces
must be smoother than the corresponding prototype surfaces for l / 6 1.
F l u i d s i n t h e N e w s
Ice engineering Various types of models have been studied in
wind tunnels, water tunnels, and towing tanks for many years. But
another type of facility is needed to study ice and ice-related problems.
The U.S. Army Cold Regions Research and Engineering
Laboratory has developed a unique complex that houses research
facilities for studies related to the mechanical behavior of ice and
ice–structure interactions. The laboratory contains three separate
cold-rooms—a test basin, a flume, and a general research area. In
the test basin, large-scale model studies of ice forces on structures
such as dams, piers, ships, and offshore platforms can be performed.
Ambient temperatures can be controlled as low as 20 °F,
and at this temperature a 2-mm per hour ice growth rate can be
achieved. It is also possible to control the mechanical properties of
the ice to properly match the physical scale of the model. Tests run
in the recirculating flume can simulate river processes during ice
formation. And in the large research area, scale models of lakes
and rivers can be built and operated to model ice interactions with
various types of engineering projects. (See Problem 7.73.)
E XAMPLE 7.8
Froude Number Similarity
GIVEN The spillway for the dam shown in Fig. E7.8a is 20 m
wide and is designed to carry 125 m 3 /s at flood stage. A 1:15 model
is constructed to study the flow characteristics through the spillway.
The effects of surface tension and viscosity are to be neglected.
FIND
(a) Determine the required model width and flowrate.
(b) What operating time for the model corresponds to a 24-hr period
in the prototype?
F I G U R E E7.8a