Lecture 17 Notes - EGN 3353C Fluid Mechanics Lecture 17...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Lecture 17 Bernoulli’s Equation We’ve seen that Bernoulli’s equation results from the energy equation. We can get it another way. Consider the figure at left: s = coordinate following the streamline n = coordinate perpendicular to the streamline The velocity field is given by ( ) ( ) ,, s Vx t V s ts = JG G G 0 n V = by definition 0 Vd s × = J GG Therefore ( ) ( ) t Vs = “drop subscript Let’s consider conservation of linear momentum. Since ( , ) VV s t = , then the substantial derivative is just N N 1 V d V Vt Vs V V V dt t t s t t s ∂∂ =+= +
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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Force balance in streamline direction (ignore friction) Let’s consider steady flow case first so ( ) VV s = only () sin ss dV Fm am V P d AP d P d A W ds θ == =− + (1) but ds m Ad ρ ∀= = and sin sin W mg gdA ds θρ = = dz ds so (1) becomes dA ds dV V ds dP dA gdA dz Dividing by and rearranging gives N 2 1 2 0 dV dP VdV gdz + +=
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This note was uploaded on 08/17/2011 for the course EGN 3353C taught by Professor Lear during the Spring '07 term at University of Florida.

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Lecture 17 Notes - EGN 3353C Fluid Mechanics Lecture 17...

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