Lecture 25 Notes - EGN 3353C Fluid Mechanics Lecture 25...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Lecture 25 Buckingham PI Theorem ± Recall dynamic similarity between a model and a prototype requires that all dimensionless Π variables must match. Æ How do we determine the ' s Π ? Use the method of repeating variables Æ 6 steps Step 1 : Parameters are dimensional, nondimensional variables, and dimensional constants. n includes the dependent variable. Make sure that any listed independent parameter is indeed independent of the others, i.e., it cannot be expressed in terms of them. (e.g., don’t include radius r and area 2 A r π = , since r and A are not independent.) Step 3 : As a first guess, set reduction j equal to the number of primary dimensions represented in the problem. The expected number of ' s Π comes from the Buckingham Pi theorem: 1 knj = −≥ . Step 4 : Since the repeating parameters have the potential to appear in each Π , be sure to choose common parameters (see Table 7–3). Step 5 : [ ] 000 1 ... k mLt Π== . Can often be done by inspection. Step 6 : N 12 3 4 dependent independent parameters parameter , , ,..., k f ⎛⎞ ⎜⎟ Π Π Π Π ⎝⎠ ±²²²³ ² ²²´
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Example Pressure in a bubble. 1. List the parameters in the problem: ( ) , s Pf R σ Δ= . 3 n = 2. List the primary dimensions of each.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

Lecture 25 Notes - EGN 3353C Fluid Mechanics Lecture 25...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online