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lecture9_hydraulicsIIIandEMmachines_1

lecture9_hydraulicsIIIandEMmachines_1 - LECTURE 9 Hydraulic...

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LECTURE 9 Hydraulic machines III and EM machines © 2002 MIT PSDAM LAB

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2.000 DC Permanent magnet electric motors Topics of today’s lecture: Project I schedule revisions Test Bernoulli’s equation Electric motors Review I x B Electric motor contest rules (optional contest) Class evaluations © 2002 MIT PSDAM LAB
Σ Project schedule updates Approx START WHAT DUE PTS 07 March Project mgmt spread sheet 12 March HMK 6: 1 page concept & equations + SIMPLE 1 page explanation 19 March Gear characteristics 1 page explanation 19 March CAD files & DXF files 14 March [ 20 ] 02 April [ 80 ] 02 April [ 10 ] 09 April (via zip disk) [ 90 ] : 200 © 2002 MIT PSDAM LAB

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BERNOULLI’S EQUATION © 2002 MIT PSDAM LAB
Streamlines Streamline : Line which is everywhere tangent to a fluid particle’s velocity. Stream Line V A V B z g For a steady flow, stream lines do not move/change A stream line is the path along which a fluid particle travels during steady flow. For one dimensional flow, we can assume that pressure (p) and velocity (v) have the same value for all stream lines passing through a given cross section v 2 1 Bernoulli’s equation for steady flow, constant density: 2 + ρ p ⋅+ g z = Constant © 2002 MIT PSDAM LAB

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Bernoulli derivation For two cross section (ends of control volume) located dx apart: Something in Something out = Something in + d(Something) dx dx dx dv dx v out = v in + dx dA A out = A in + dx dx Differntial changes with dx p out = p in + dp dx dx dz dx z out = z in + dx © 2002 MIT PSDAM LAB
Bernoulli derivation Stead flow momentum equation for Control Volume From F = m a following a fluid mass dv v v + dx m C in v in + Σ F on CV = m C out v out dx For a stead, there is no stored mass dx m C in = m C out = m C m C v in + Σ F on CV = m C v out Σ F on CV = m C ( v out - v in ) dv v out = v in + dx dx Σ F on CV = ρ A v dv dx dx © 2002 MIT PSDAM LAB

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Bernoulli derivation Pressure force: dx ] ) dA / dx A + ( d x ] [ ) dP / dx z d x ) dA / dx p A [p + ( p( © 2002 MIT PSDAM LAB
Bernoulli derivation Gravity: z g m dz m g dx = − F x © 2002 MIT PSDAM LAB

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Bernoulli derivation Summation of pressure and gravity forces: ~ 0 Σ F on CV = + dx dA p - A p - dx dx dA p A p dx A dp dx ( terms dx ) 2 m g dz dx dx Σ F
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