Lecture 05 Notes

# Lecture 05 Notes - EGN 3353C Fluid Mechanics Static...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida 3 ± Static equilibrium of above element leads to N 21 specific weight s PPP gz γ ρ Δ =−= Δ (*) P Δ∝ (and is usually negligible in gases for small changes in depth) If point 1 is taken at the “free surface” open to the atmosphere then 2 atm PP P g h == + o Leads to definition of gage pressure gage Pg h = (amount pressure is above local atmospheric pressure) o Similar concepts for absolute and vacuum pressures From (*), 0 lim z Pd P g zd z Δ→ Δ Δ ( sign comes from z direction positive upward so that dP <0 when dz >0) General Vector Form: p g ∇= G G or ˆˆ Pi j k P g k xy z ⎛⎞ ∂∂ + + = ⎜⎟ ⎝⎠ G . Can you see that this reduces to

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida 4 () 0 only 0 P PP x x z P y y =→ ≠ = Pd P g zd z ρ == We can integrate 2 21 1 P P P gdz Δ= − = if we know ( ) z and ( ) gz If const and gc o n s t ( ) 12 Pg z z g z Δ =− = Δ ± Reasonable for small depth changes For stratified fluids w/ const g , ( ) N 2 2 2 1 HO SG z d z Δ= Example : 321 ρρ >> Why?
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Lecture 05 Notes - EGN 3353C Fluid Mechanics Static...

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