92fd59f0-8c55-48b8-8ecb-4192391c3c38 46 3 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Colebrook friction factor R,D,ε

t0 1 time :

In water works, we use two ε values ε=0.00003, ε=0.0001 roughness factor. PONT-A-MOUSSON p. 214

Colebrook memo m ε 0.00003<ε>0.0001 ≡ m D Pipe ID(m) ≡ f friction factor [dimensionless] ≡ R Reynolds [dimensionless] ≡ ε D 12 mat in the same units system ≡ f 0.02 : initial guess all cases ≡ 61 line

Colebrook formula 1 f sqrt / 2.0 ε 3.7 D * / 2.51 R f sqrt * / + log10 * - ≡

f R D ε Find 1 f sqrt / 2.0 ε 3.7 D * / 2.51 R f sqrt * / + log10 * - ≡ f 0 0.05 solve :

Colebrook plot wrt [D(m), ε(m), Re] Colebrook D 0.14633 : ε 0.00005 : R 10000100000020000 range : i 1 R rows range f i el f R i el D ε Find : for R f augment 51 line :

Project specs R 240000 : D 0.14633 : ε 0.00005 : 31 line

On-line Colebrook

On-line  Colebrook [f] f R D ε Find 0.018

1 time t0 - 0.5 s *

Colebrook plot wrt [D(m), ε(m)] vs Reynolds

Colebrook 0.018 2 1 sys

Δp[Pa] in rectilnear piping Pa Δp f m D / kg m 3^/ ρ * V 2^m s / (* (* m L * ≡

π 4 / 3.6 * (1 -^0.353678

Supplement Project Demo

Q 100 : MassFlow rate T/hr ≡ μ 1 : Viscosity Centipose [cp] ≡ ρ 1000 : kg/m^3 @ nominal ops ≡ f f R D ε Find : L 100 : rectilinear (m) ≡ D 0.14633 : Pipe ID [m] ≡ mWC 1 : meter WC ≡ PkWhr 1 : PumpPower kW/hr ≡ h Δp .000102 * : Pa to mWC ≡ Pa 1 : Pa-> Pascal ≡ ms 1 : m/s ≡ 111 line

Pipe Reynolds e+6 R 0.3537 Q D μ * ρ * / * : 0.24

Nominal speed [m/s] V 0.3537 Q * ρ D 2^* / : ms 1.7

Pumping kW/hr PkWhr Q h * 367 / ≡

Conclude the project in Pa
..... linear losses..... Δp f D / ρ V 2^* 2 / (* L * : Pa 16429

3600 9.8067 / 367 ≡

f 0.018

Recommanded speed: Water: 0.1 .. 2.5 [m/s] Superheated steam: 35 ... 100 [m/s]

h mWC 1.68

PkWhr Q h * 367 / : PkWhr 0.46

Accidents in piping result in local singular losses. Head potential is simply consummed. Darcy 'J' is rarely used.

Darcy J head loss m/m of pipe length J 6.378 109 -^* f D 5^/ * Q ρ / (2^* : 31 line

M x/y 016203045609012018020 0.18 0.22 0.25 0.29 0.31 0.32 0.33 0.30 40 0.36 0.43 0.50 0.56 0.61 0.63 0.63 0.63 60 0.42 0.47 0.58 0.68 0.72 0.76 0.76 0.75 100 0.42 0.49 0.59 0.70 0.80 0.87 0.85 0.86 510 mat :

col row M Spline A M 112 M cols submatrix : B M 2 M rows 11 submatrix : C M 2 M rows 2 M cols submatrix : j 1 A length 2 range CC j el B C 1 C rows j j submatrix row linterp : for A transpose CC col linterp 51 line :

col row M Spline

6010 M Spline 0.8

705 M Spline 0.68