1.

Segment V7.1: Reynolds Number
(Related to Textbook Section 7.6 - Common Dimensionless Groups in Fluid Mechanics)

Important dimensionless groups can frequently be given useful physical interpretations. For example, the Reynolds number is an index of the ratio of inertia forces to viscous forces in a moving fluid.

For a rotating tank containing a very viscous fluid, which gives a small Reynolds number, viscous forces are dominant. Thus, when the tank is suddenly stopped fluid particles also suddenly stop due to the dominance of viscous forces over inertia forces. Correspondingly, when a low viscosity fluid is in the tank, which gives a much higher Reynolds number, inertia forces are dominant. When the tank suddenly stops the fluid particles continue to move.

2.

Segment V7.2: Environmental Models
(Related to Textbook Section 7.8.1 - Theory of Models)

Scale models are widely used in fluid mechanics. It is essential that such models be designed and operated with careful consideration given to the necessary similarity requirements.

Plume dispersion in a building complex is studied using scale models located in a large environ-mental wind tunnel. Spires at the tunnel entrance and roughness elements on the floor of the tunnel are used to create the necessary flow similarity in the test section. The effect of wind speed and direction on the dispersion of a plume can be determined for the geometrically scaled model. (Video courtesy of Cermak Peterka Petersen, Inc.)

3.

Segment V7.3: Model of Fish Hatchery Pond
(Related to Textbook Section 7.8.3 - Practical Aspects of Using Models)

Sometimes it is not obvious which of the numerous details of the geometry of a fluid flow system need to be accurately modeled. In such a case, it is desirable, whenever possible, to run some validation tests in which model data are compared with any available corresponding prototype data.

Model tests of a fish hatchery pond were conducted to determine how to improve the water quality and flow characteristics in the pond. A scale model that appropriately modeled the basic pond geometry including the outlet and inlet flows was used. A comparison of model and prototype flows validated the model. The model was then used to study possible design changes.

4.

Segment V7.4: Wind Engineering Models
(Related to Textbook Section 7.9.2 - Flow Around Immersed Bodies)

Wind induced flow characteristics around buildings can be efficiently studied using modeling techniques.

The complicated wind patterns in a scale model of a building complex are studied in a large environ-mental wind tunnel by injecting smoke near the building of interest. Spires at the tunnel entrance and roughness elements on the floor of the tunnel are used to create the necessary flow similarity in the test section. Regions of high and low pressure can be determined by strategically located pressure taps. Large scale wind patterns can also be studied in this type of wind tunnel as illustrated with the model of the city of Hong Kong subjected to winds coming over nearby Victoria Peak. (Video courtesy of Cermak Peterka Petersen, Inc.)

5.

Segment V7.5: Wind Tunnel Train Model
(Related to Textbook Section 7.9.2 - Flow Around Immersed Bodies)

To maintain exact similarity between model and prototype flows in a wind tunnel, the model and prototype Reynolds numbers must be equal. This is usually not possible to achieve. Fortunately, flow characteristics are often not strongly influenced by the Reynolds number over the range of interest.

The flow past a train with a cross wind is studied by observing the flow of smoke injected near a model in a wind tunnel. Although the model Reynolds number is less than that for the prototype, the complex flow characteristics observed for the model should also occur for the prototype. (Video courtesy of the National Research Council of Canada and the Institute for Aerospace Research.)

6.

Segment V7.6: River Flow Model
(Related to Textbook Section 7.9.3 - Flow with a Free Surface)

To maintain exact similarity between model and prototype flows in a wind tunnel, the model and prototype Reynolds numbers must be equal. This is usually not possible to achieve. Fortunately, flow characteristics are often not strongly influenced by the Reynolds number over the range of interest.

The unwanted collection of debris against bridge piers or at pipe inlets in rivers can cause consider-able damage. Appropriate information obtained from carefully conducted model experiments can be used in the design of such structures to reduce the problems involved. (Video courtesy of the U.S. Army Engineer Waterways Experiment Station.)

7.

Segment V7.7: Boat Model
(Related to Textbook Section 7.9.3 - Flow with a Free Surface)

Model experiments are used to determine characteristics of the flow past vehicles. Although the experiments use small scale models, the required experimental apparatus is not necessarily small or inexpensive.

Flow past a barge in a shallow channel is studied by means of the scale model shown. Although all dimensionless parameters (Reynolds, Froude, Weber numbers, etc.) are not the same for the model as for the prototype, a carefully designed experiment may provide the desired information. In this case, the flow near the channel bottom as the barge passes overhead is made visible by the motion of small particles on the bottom. (Video courtesy of U.S. Army Engineer Waterways Experiment Station.)