setting was evolved which completely eliminated the necessity for sills of any kind in the pool.

HYDRAULIC TURBINES

Model studies for obtaining a more efficient draft tube for the turbines of Wheeler Dam on the Tennessee River were made in the Denver laboratory. A stationary runner was constructed with fixed vanes which could be set at any angle to induce the whirl in the draft tube. Such tests yield only comparative results, and are chiefly valuable in providing qualitative information as to the relative value of proposed designs. It is assumed that the draft tube which gives the better results in the model will also give optimum performance in the prototype.

Draft tube experiments are now being made on a model of one of the turbines for Grand Coulee Dam. This is a complete working model with movable runner, governor, and generator. Direct observation of the flow within the scroll case and the draft tube is made possible by the use of transparent pyralin in all the outer walls. A side view of the model may be seen in figure 6.

MISCELLANEOUS TESTS

The tests which have been sited thus far have related to hydraulic structures of considerable size. Models of minor structures and other features difficult to classify have included canal chutes with stilling pools, ejectors, roller gates, a silt scraper for the All-American canal desilting works, seepage under the Imperial Dam which will be founded on a porous foundation, silt movement in the Colorado River above Imperial Dam (fig. 7), circular and rectangular sluiceway entrances, a fish trap proposed for the Columbia River immediately downstream from Grand Coulee Dam, and many others.

Models based on the so-called "electric-analogy" were used to supplement some of the tests. The electric-analogy utilizes the flow of electrical current through an electrolyte, shaped to resemble the hydraulic structure, for determining the idealized streamline flow through the structure. It is applicable only to certain types of problems in which boundary conditions are easily established. For such problems its simplicity and rapidity make it an extremely useful tool.

PRESENT LABORATORY OPERATIONS

Because practically every problem studied in the Bureau of Reclamation laboratories relates to the specific design of an actually proposed structure, the work of the laboratories has become a highly specialized field of hydraulics. Since complete similitude between models and their prototypes is impossible of attainment, the laboratory staff must be thoroughly familiar with the model limitations and with the corrections that should be applied to obtain results applicable to field conditions. To avoid the effects of viscous friction, which cannot be represented to scale, care must be exercised to prevent the construction of models on too small a scale. Again, to compensate for differences in wall

and bottom friction, it is sometimes necessary to exaggerate model slopes.

The use of models has proved so advantageous in indicating opportunities for reducing costs and improving hydraulic properties that the work of the laboratories is now recognized as a regular part of hydraulic design. At the present time, the three laboratories are engaged in testing or constructing models of twenty different features relating to ten major projects. However, opposed to the tendency toward an increasing use of models is the fact that the accumulating experience, in many cases, obviates the necessity for further experiments; so that any attempt to predict the future expansion of the work would be unwarranted.

FOLLOWING the arch dam model testing program carried on by the Engineering Foundation Committee in cooperation with the Bureau- of Reclamation and the University of Colorado, the Bureau has extended the program to include a comprehensive study of gravity dams as well as some special problems in connection with both arch and gravity dams. The initial program for the procedure of this work was described in the 1929 edition of this publication, and other articles have appeared in the Engineering News Record, Vol. 108, No. 14, and Vol. 113, No. 23. This article will give a brief account of the early tests and a review of the later and current work on structural model tests.

MODEL THEORY

The general theory of models and their relationships to the prototypes involves a rather complicated mathematical treatment, but when these relationships are applied to the specific problems of model dams, they reduce to fairly simple terms. The general model requirements and the relationships of model to prototype will be presented in order that the reader may readily understand the descriptions of the various model studies which follow:

1. One of the important requirements of a structural model of a dam is that upon application of the loads, the resulting strains and deformations must be of magnitudes susceptible of measurement with available laboratory equipment. Since the model must necessarily be constructed to a fairly small scale, it will ordinarily require a higher specific gravity of loading or a greatly reduced stiffness than the prototype in order to comply with this requirement. Often it is necessary to combine both these properties.

2. The model must be a true scalar representation of the prototype.

3. The loading of the model must be proportional to the loadings of the prototype.

4. If the model represents a massive structure where the stress distribution is influenced by the volume changes occurring under strain, Poisson's ratio must be the same for model and prototype. However, if only a cross section of the structure is being investigated giving a model under twodimensioned stress, the stress distribution is independent of Poisson's ratio.

5. If the effect of both live load and gravity forces are to be investigated, the ratio of specific gravities of the dam and loading medium must be the same for both model and

prototype. If the effect of external forces only are to be investigated the results are not affected by the specific gravity of the model, providing the action of the structure is elastic.

6. The model material must be homogeneous, isotropic and obey Hooke's Law.

7. Foundations and abutments for the model must be sufficiently extensive to allow freedom to deform in a manner similar to the prototype.

If these requirements are fulfilled the ratios between stresses and deformations in the dam and in the model will be as follows:

n

With a scale ratio between model and prototype equal to 1:n and a specific gravity of loading for the model equal to G times that of water, the unit liquid pressure at the base of the dam will be times that for the model. This ratio G will also apply to stress conditions. If the modulus of elasticity of the material in the dam is equal to E, and in the model equal to Em, the ratio between the unit strain in the model and in the dam will be the ratio of the unit stresses multiplied by the ratio of the two moduli of elasnEm ticity, or These strains are acting over lengths for the GE damn times the corresponding lengths for the model. The total deformation for the dam expressed as the deflection at a certain point will therefore be n times the ratios of the unit strains compared to the total deformation for the model. The ratio between the deflections of the dam n2 Em and the deflection of the model will be GEa

EARLY EXPERIMENTS

While the relations between model and prototype are simple and direct, there is seldom an opportunity to check the model results against direct measurements on the prototype, except in special cases. The most important phase of the model studies therefore was to obtain experimental data which would aid in developing and checking mathematical analyses which would apply to both model and prototype.

The first objective in the model testing program was to develop apparatus and a technique of procedure, and to prove that a model would give satisfactory results. With this much accomplished, sufficient information was avail

able to design and build a practical model of Boulder Dam, the eventual objective of the early investigations.

It was quite fitting therefore, that the first model should be constructed of the Stevenson Creek Test Dam, on which the model measurements could be checked against similar measurements on the actual dam as well as computed mathematically for both. The model was constructed to a one-twelfth scale, giving a model 5 feet high, 2 inches thick at the top, 721⁄2 inches thick at the bottom and 11 feet 8 inches long at the crest. Concrete, mixed from the same aggregate as the real dam, was used to build the model. The model was loaded with a film of mercury, contained in a rubber bag which fit the upstream face and was held in place by a steel plate securely braced against the walls of the testing pit. Dial gages attached to a rigid concrete reference post were used to measure radial deflections on the downstream face. Measurements of changes of chord length and strains at the downstream face were also made. These measurements checked very closely with the measurements taken on the real dam and also with the deflections calculated by the trial load method of arch dam analysis.

The following conclusions were reached from these tests: 1. A properly constructed small scale model can be relied upon to produce strains and deformations similar to its prototype.

2. Mercury is a satisfactory loading medium where the effects of hydrostatic pressure only are being investigated. 3. The trial-load method gives accurate results for the thin-arch dam.

The next step in the program was to build an arch-dam model where a considerable portion of the load was carried by gravity action. Such a test would supply the necessary data to check the trial-load method for this type of structure. Accordingly a model of the Gibson Dam was constructed. This dam was considerably different from the Stevenson Creek Dam since it was built in a relatively wide valley whereas the Stevenson Creek Dam was located in a narrow V-shaped canyon. The Gibson model was 2 feet 10%1⁄2 inches high, 2% inches thick at the top, and 15% inches thick at the bottom, with a crest length of 13 feet 6 inches. This model was constructed of concrete and loaded with mercury in the same manner as in the Stevenson Creek model tests. The procedure of the tests was also practically the same as the Stevenson Creek tests, except that a temperature test was run on the Gibson model. The temperature of the model was first raised by running hot water over the faces. When a fairly uniform high temperature had been reached, it was allowed to cool, after which the temperature was lowered further by running ice water over the faces. Continuous observations of radial deflection and temperature were taken throughout the temperature cycle. The behavior of this model was entirely satisfactory and the agreement with the calculated deflections obtained from the trial-load analysis was excellent. In the analysis of

It was evident from the deflection measurements on the Gibson model that a concrete model of Boulder Dam, with its greatly increased cross section, would be entirely too stiff to obtain measurable deflections. Boulder Dam, having a heavy cross section and a relatively short span compared to its height, would therefore require a model to be constructed of a much more flexible material than concrete. After a careful study of many possible materials, it was concluded that the most satisfactory material was produced from a mixture of commercial plaster and diatomaceous earth (Celite) combined with the proper amount of water. Other possible materials were celluloid and rubber. After this preliminary investigation indicated that the plaster-celite mixture had desirable properties, an extensive study was made, using various brands of commercial plasters with different proportions of celite and water.

The results of this study are summarized as follows: 1. Average proportions. One part celite, 2 parts plaster, 3% parts water, all by weight. The exact proportions must