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diffuser

# diffuser - V 1 2 2 p 1 ρ gz 1 = α V 2 2/2 p 2 ρ gz 2 h...

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Roman aqueduct customers received water continuously (no shut off valve). To get more water, they often put a nozzle at the exit. (0) (2) (1)

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Roman aqueduct customers received water continuously (no shut off valve). To get more water, they often put a nozzle at the exit. How much does Q change with diffuser? (0) (2) α V 0 2 / 2 + p 0 / ρ + gz 0 = α V 2 2 /2 + p 2 / ρ + gz 2 + h Δ Total h Δ Total = h f + Σ h m = [V 1 2 /(2)][f(L/D 1 ) + K entrance + K diffuser ] (1) Not units of length
Without diffuser (2) (0) (1) α V 0 2 / 2 + p 0 / ρ + gz 0 = α V 2 2 /2 + p 2 / ρ + gz 2 + h Δ Total h Δ Total = h f + Σ h m = [ V 1 2 /(2)][f(L/D 1 ) + K entrance + K diffuser ]

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(1) α V 0 2 / 2 + p 0 / ρ + gz 0 = α V 2 2 /2 + p 2 / ρ + gz 2 + h Δ Total Without diffuser V 1 = V 2 ; K diffuser = 0 (2) 0 1 (0) 0 z o = [V 2 2 /(2g)] + [V 1 2 /(2g)][f(L/D 1 ) + K ent ] 2m = [V 1 2 /(2g)] (1 + f(2/.03) + 0.5)
(1) (2) (0) 2m = [V 1 2 /(2g)] (1 + f(2/.03) + 0.5) or f = (1.8 log [( ρ V 1 D/µ)/6.9]) -2 (Eq. 6.39) Solve for V and then calculate Q no diffuser Moody Plot – guess Re D and get f, calculate V, check Re D – if not close use that Re D and repeat….

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(2) (0) α V 0 2 / 2 + p 0 / ρ + gz 0 = α V 2 2 /2 + p 2 / ρ + gz 2 + h Δ Total What changes for the diffuser case? (1)

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Unformatted text preview: V 1 2 / 2 + p 1 / ρ + gz 1 = α V 2 2 /2 + p 2 / ρ + gz 2 + h Δ Total (2) 1 (0) z o = [V 2 2 /(2g)] + [V 1 2 /(2g)][f(L/D 1 ) + K ent + K diff ] 2m = (0.36V 1 ) 2 /(2g) + [V 1 2 /(2g)] (K diff + f(2/.03) + 0.5) V 2 = V 1 (3/5) 2 (1) (2) (0) 2m = (0.36V 1 ) 2 /(2g) + [V 1 2 /(2g)] (K diff + f(2/.03) + 0.5) f = (1.8 log [( ρ V 1 D/µ)/6.9])-2 With proper choice of diffuser Q with diffuser can result in 33% increase Moody Plot – guess Re D and get f, calculate V 1 , check Re D – if not close use that Re D and repeat…. V 1nodiffuser = [2gz o /(1 + K entrance )] 1/2 V 1diffuser = [2gz o /{( A 1 /A 2 ) 2 + K entrance + K diffuser }] 1/2 No pipe at exit so f = 0 0.25 0.3 .55 < 1 so V 1diffuser > V 1nodiffuser Does diffuser reduce energy “losses”? Does diffuser increase V 1 ? Is V 2 faster than V 1diffuser ? Is V 2 faster than V 1nodiffuser ?...
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