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Lecture 23 Notes

# Lecture 23 Notes - EGN 3353C Fluid Mechanics Chapter 7...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Chapter 7: DIMENSIONAL ANALYSIS AND MODELING Lecture 23 ± dimension Æ measure of a physical quantity without numerical values (e.g., length) ± unit Æ assigns a number to that dimension (e.g., meter) ± 7 fundamental dimensions from which all other secondary dimensions can be expressed in terms of o Fluid dynamics usually just concerned with m, L, t, and T.

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Example : Write the dimensions of electrical voltage in terms of primary dimensions. [] [] -2 -1 2 -3 -1 force velocity Power = Voltage×Current Vo Power Current = mLt Lt I= ltage mtI = L ⎡⎤ ⎢⎥ ⎣⎦ ±²³ ± Law of Dimensional Homogeneity Æ Every additive term in an equation must have the same dimensions o Each term must also have the same units o Recommendation : Write out all units when performing calculations in order to avoid errors. Example : Various Forms of Bernoulli’s Equation 1. N N N 2 static hydrostatic total pressure pressure pressure q = dynamic pressure 1 2 t p Vg z P ρρ ++ = Æ total pressure form Æ each term has primary dimensions of [ ] [ ] -2 2 -1 -2 mL P = Forc tL = m L eA re t a= Æ each term must have the same units (e.g., Pa)
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Lecture 23 Notes - EGN 3353C Fluid Mechanics Chapter 7...

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