Modeling and Similitude: Example Problems
Try to solve these problems before watching the solutions in the screencasts.
Example Problem 1
A newly-designed blimp will move at 15 mph through the air. To decide on what engines to use, you need to predict the drag force on the blimp. To do so, you place a 1:9 scale model in moving water in the laboratory.
a. Determine the water velocity needed to ensure similar flow characteristics.
b. The measured drag force on the model at this water flow rate is 700 lb. Estimate the drag on the prototype blimp and the power needed to move the blimp through the air.
Example Problem 2
A model of a glacier is built using ice (SG of 0.92). Experimentation with the model reveals that it takes 5.5 hr for an object to move from point A to point B within the model glacier. Data collected from the actual glacier indicates the density of the glacier is similar to that of glycerin (SG of 1.26) but the viscosity is 1 million times more viscous than the model fluid. How long would it take an object to go from a scaled length of point A to point B in the actual glacier?