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Dimensional Analysis & Buckingham Pi Theorem | Fluid Mechanics
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In this video we introduce dimensional analysis and the Buckingham Pi Theorem. In fluid mechanics, there are often many variables, which impact quantities such as flow rate. For example, in a pipe, the volumetric flow rate is dependent on the viscosity, roughness of the pipe, pressure difference, length of the pipe and diameter of the pipe. Instead of doing hundreds of experiments to isolate all these factors we use the Buckingham pi theory, which reduces the amount of variables in our function.
The Buckingham Pi Theorem is done in the following steps: 1. Determine relevant variables, 2. Determine each variables dimension using the MLT system, 3. Determine the number of dimensionless pi groups. 4. Select r repeating variables, 5. Create Pi groups. 6. Solve for all indices, 7. Check pi-groups are dimensionless and 8. Express answer in final form
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