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MAE-403 - AIR CONDITIONING Static Regain Method: lower the velocity for next section, to “regain” friction and localized losses, so that ALL outlets have the SAME STATIC PRESSURE. This is best accomplished by the use of a computerized spreadsheet. losses r losses losses P V C V P V V P P P V P V P + = = = + + = + 2 2 : or 2 2 : so : want we 2 2 2 1 2 2 1 2 2 1 2 2 1 1 2 2 2 ρ ρ ρ ρ ρ ρ 2/24/2005 1

Static Regain

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Page 1: Static Regain

MAE-403 - AIR CONDITIONING

Static Regain Method: lower the velocity for next section, to “regain” friction andlocalized losses, so that ALL outlets have the SAME STATIC PRESSURE.

This is best accomplished by the use of a computerized spreadsheet.

lossesr

losses

losses

PVCV

PVV

PP

PVPVP

∆+=

∆=−

=

∆++=+

22

:or22

:so

: wantwe22

21

2

21

22

12

21

1

22

2

ρρ

ρρ

ρρ

2/24/2005 1

Page 2: Static Regain

MAE-403 - AIR CONDITIONING

60

x 1

5

30 x 15

150 l/s 150 l/s

150 l/s 150 l/s

440 cm

170 cm 440 cm

375 cm

40 cm

200 cm

4

56 7 8

215 cm

3

180 cm

2/24/2005 2

Page 3: Static Regain

MAE-403 - AIR CONDITIONING

STATIC REGAIN METHOD EXAMPLE - uses hydraulic diameterρ = 1.2 kg/m3 Cr = 0.75 ε = 0.09 mm ν = 1.6E-05 m2/s ∆P

Sect. Descr. Air Flow W x H Veloc Dh Re fprime f F.Loss Length Co Pdyn Loss Sum Sect.l/s cm x cm m/s cm Pa/m m Pa Pa Pa

3-4 straight 600 60 x 15 6.67 24.0 1.00E+05 0.01982 0.01982 2.203 2.15 - - -4.74 -4.74 3-44-5 wye-br 300 30 x 15 6.67 - - 0.25 26.67 -6.67 -11.40 4-55-6 straight 300 30 x 15 6.67 20.0 8.33E+04 0.02075 0.02075 2.767 1.80 - - -4.98 -16.38 5-6

Diffuser 150 60 x 60 -20.83 -37.21 Diffuser 0.00%

Section 7-8 is now designed to give the same static pressure at the diffuser (or as close as we can).

7-8 straight 150 15 x 15 6.67 15.0 6.25E+04 0.02230 0.02230 3.964 4.40 - - -17.44 -33.82 11-12Diffuser 150 60 x 60 -20.83 -54.65 Diffuser

ALT to 7-8regain 150 20 x 15 5.00 8.75 -7.63 regain

7-8 straight 150 20 x 15 5.00 17.1 5.36E+04 0.02264 0.02264 1.981 4.40 - - -8.72 -16.35 11-12Diffuser 150 60 x 60 -20.83 -37.18 Diffuser -0.09%

2/24/2005 3

Page 4: Static Regain

MAE-403 - AIR CONDITIONING

60

x 1

5

30 x 15

150 l/s 150 l/s

150 l/s 150 l/s

440 cm

170 cm 440 cm

375 cm

40 cm

200 cm

4

56 7 8

215 cm

3

180 cm

20 x 15

2/24/2005 4

Page 5: Static Regain

MAE-403 - AIR CONDITIONING

formulas

Veloc.= (Air Flow)/(WxHx10)Dh=4x(WxH)/(2*(W+H)) Eq. 24 Ch 32Re=VelocxDh/νfprime=0.11x(ε/Dh+68/Re)^0.25 Eq 21 Ch 32f: IF fprime >= 0.018 THEN f=fprime ELSE f=0.85xfprime+0.0028F.Loss=f x r x Veloc^2/(2xDh)Loss=L x F.LossorLoss=Co x PdynPdyn = r x V^2/2Regain = Cr x r x (Vout^2 - Vin^2)/2

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Page 6: Static Regain

MAE-403 - AIR CONDITIONING

A computer program to solve Colebrook's Formula in Excel follows.

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Page 7: Static Regain

MAE-403 - AIR CONDITIONINGOption Explicit'Calculates friction factor using Colebrok's formula'Uses ASHRAE Hndbk of Fundamentals 1997 Ch.2 eq.(29b) corrected'according to Shames, Mechanics of Fluids, 3rd. ed. eq.(9-18)Static Function ffriction#(Vdot As Double, W As Double, _

H As Double, nu As Double, eps As Double)Dim iter As Integer, itlim As Integer, a As IntegerDim Area As Double, Per As Double, Dh As Double, Vel As Double, _

Re As Double, fold As Double, f1 As Double, Df1 As Double, _tol As Double, invsqrtf As Double, conv As Double, _arg As Double, incr As Double, f As Double, _Vdotlocal As Double, Wlocal As Double, _Hlocal As Double, Log10 As Double, _epslocal As Double

Log10 = Log(10#)Vdotlocal = Vdot / 1000# 'l/s -> m3/sWlocal = W / 100# ' cm -> mHlocal = H / 100# ' cm -> mepslocal = eps / 1000# ' mm -> mtol = 0.0000000001itlim = 100Area = Wlocal * HlocalPer = 2# * (Wlocal + Hlocal)

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Page 8: Static Regain

MAE-403 - AIR CONDITIONING

Dh = 4# * Area / PerVel = Vdotlocal / AreaRe = Vel * Dh / nufold = 0.01iter = 0

100 iter = iter + 1f = foldinvsqrtf = 1# / Sqr(f)arg = (epslocal / Dh + 9.35 * invsqrtf / Re)f1 = invsqrtf - 1.14 + 2# * Log(arg) / Log10Df1 = -(0.5 + 9.35 / (Re * arg * Log10)) * (invsqrtf ^ 3)incr = f1 / Df1f = f - incrfold = fIf (iter > itlim) Thena = MsgBox("iterations: limit exceeded!", 0, "error!")Return

End IfIf (Abs(incr) > tol) Then GoTo 100ffriction = f

End Function

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Page 9: Static Regain

MAE-403 - AIR CONDITIONING

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Page 10: Static Regain

2/24/2005 10

MAE-403 - AIR CONDITIONING

Neck Ve locity (m /s) 2 2.5 3 3.5 4 4.5 5 6 7 8Velocity Pressure, Pa 2.5 4 5.5 7.75 10 12.5 15.5 22.5 30.4 40

Total Pressure 3.81 5.84 8.64 11.68 15.24 19.30 23.88 34.29 46.48 60.71

6Flow Rate , l/s 37 46 56 65 74 83 93 111 129 148NC -- -- -- -- -- 19 22 28 33 37Throw m .75,.50,.25 0.3/0.6/1.2 0.3/0.6/1.2 0.6/0.9/1.5 0.6/0.9/1.8 0.6/1.2/2.1 0.9/1.2/2.1 0.9/1.2/2.1 1.2/1.5/2.4 1.2/1.8/2.7 1.5/2.1/2.7

Total Pressure 4.064 6.35 9.40 12.70 16.51 20.83 25.91 37.08 50.55 66.04

8Flow Rate , l/s 66 83 99 115 132 148 165 198 231 263NC -- -- -- -- 19 22 26 31 36 40Throw .75,.50,.25 0.6/0.6/1.5 0.6/0.9/1.8 0.6/1.2/2.1 0.9/1.2/2.4 0.9/1.5/2.7 1.2/1.8/2.7 1.2/1.8/3.0 1.5/2.1/3.3 1.8/2.4/3.6 2.1/2.7/3.6

Total Pressure 4.826 7.62 11.18 15.24 19.81 24.89 30.99 44.45 60.45 78.99

10Flow Rate , l/s 103 129 154 180 206 232 257 309 360 412NC -- -- -- 17 21 25 28 34 39 43Throw .75,.50,.25 0.6/0.9/1.8 0.9/1.2/2.4 0.9/1.5/2.7 1.2/1.8/3.0 1.2/1.8/3.3 1.5/2.1/3.6 1.5/2.4/3.6 1.8/2.7/3.9 2.4/3.3/4.2 2.7/3.3/4.5

Performance Data - 24 x 24 / 600 x 600 Face Size - METRIC

Listed Size

Diff

user

Dat

a

Page 11: Static Regain

MAE-403 - AIR CONDITIONING

2/24/2005 11

60

x 1

5

30 x 15

150 l/s 150 l/s

150 l/s 150 l/s

440 cm

170 cm 440 cm

375 cm

40 cm

200 cm

4

56 7 8

215 cm

3

9

10

11

12 13 14

180 cm

20 x 15

Page 12: Static Regain

MAE-403 - AIR CONDITIONING

4 wye-st 300 30 x 15 6.67 - - 0.13 26.67 -3.47 -8.20 44-9 straight 300 30 x 15 6.67 20.0 8.33E+04 0.02075 0.02075 2.767 0.40 - - -1.11 -9.31 4-9

9-10 straight 300 30 x 15 6.67 20.0 8.33E+04 0.02075 0.02075 2.767 3.75 - - -10.37 -19.68 9-1010-11 elbow 300 30 x 15 6.67 - - 0.12 26.67 -3.20 -22.88 10-1111-12 straight 300 30 x 15 6.67 20.0 8.33E+04 0.02075 0.02075 2.767 2.00 - - -5.53 -28.42 11-12

Diffuser 150 60 x 60 -20.83 -49.25 Diffuser 32.34%ALT to 4-12

4 wye-st 300 30 x 15 6.67 - - 0.13 26.67 -3.47 -8.20 44-9 straight 300 30 x 15 6.67 20.0 8.33E+04 0.02075 0.02075 2.767 0.40 - - -1.11 -9.31 4-9

regain 300 0 x 15 #DIV/0! #DIV/0! #DIV/0! regain9-10 straight 300 0 x 15 #DIV/0! 0.0 #DIV/0! #DIV/0! #DIV/0! #DIV/0! 3.75 - - #DIV/0! #DIV/0! 9-1010-11 elbow 300 0 x 15 #DIV/0! - - 0.12 #DIV/0! #DIV/0! #DIV/0! 10-1111-12 straight 300 0 x 15 #DIV/0! 0.0 #DIV/0! #DIV/0! #DIV/0! #DIV/0! 2.00 - - #DIV/0! #DIV/0! 11-12

Diffuser 150 60 x 60 -20.83 #DIV/0! Diffuser #DIV/0!

13-14 straight 150 17.50 x 15 5.71 16.2 5.77E+04 0.02245 0.02245 2.723 4.40 - - -11.98 #DIV/0! 13-14Diffuser 150 60 x 60 -20.83 #DIV/0! Diffuser #DIV/0!

ALT to 13-14regain 150 0 x 15 #DIV/0! #DIV/0! #DIV/0! regain13-14 straight 150 0 x 15 #DIV/0! 0.0 #DIV/0! #DIV/0! #DIV/0! #DIV/0! 4.40 - - #DIV/0! #DIV/0! 13-14

Diffuser 150 60 x 60 -20.83 #DIV/0! Diffuser #DIV/0!

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Page 13: Static Regain

MAE-403 - AIR CONDITIONING

Assignment: Use the spreadsheet and the drawing posted, and complete the design of the rest of the duct system using Static Regain.

Due: next class

2/24/2005 13