Darcy / Colebrook-White Equations

[Zahir]

@roach2

Hi

I'd like to see your QuickBasic code, I have a requirement to do a similiar implementation albeit in javascript.

Thanks so much!

Zahir

[nir]

I was confused by the presentation of the Darcy-Weisbach equation in Haested Methods' Computer Applications in Hydraulic Engineering (2002, section 1.4). It gives the Darcy-Weisbach equation as

(1) v = sqrt(8gRS/f)

where v is the flow velocity, g is gravitational acceleration, R is the channel or pipe hydraulic radius, S is the slope, and f is a unitless friction factor that is determined as the solution to the Colebrook-White equation:

(2) 1/sqrt(f) = -2 * log10(k/CR + 2.51/(Re*sqrt(f)))

where k is the roughness scale length of the channel or pipe walls, C is 12 for flow with a free surface and 14.8 for full pipe flow, and Re is the Reynolds number of the flow, Re = 4Rv/\{nu}, where \{nu} is the kinematic viscosity of the fluid. It then says that f must be determined iteratively from (2). But it seems like we could use (1) to express Re in terms of f

(3) Re = 4Rv/\{nu} = 8R*sqrt(2gRS/f)/\{nu}

and cancel out the f on the right hand side of (2), giving a closed-form expression for f:

(4) 1/sqrt(f) = -2 * log10(k/CR + 2.51*\{nu}/(8R*sqrt(2gRS)))


What am I missing?

[Doug Eilertson]

Interesting thread. Here is an equation that is direct and doesn't utilize the iteration method. It was published in the article of the 1984 Chemical Engineering by 'Serghides'.

f = (A7 - ([A8-A7]² / [A9 - 2A8 + A7]))^-2

A7 = -2log(((K/D)/3.7) + (12/Re))
A8 = -2log(((k/D)/3.7) + (2.51A7)/Re)
A9 = -2log(((k/D)/3.7) + (2.51A8)/Re)

note that K in the A7 equation is different than the k in the other two equations.

[aniluvscientist]

Originally Posted by wayneorton

Hi, I want to calculate pipe capacities at certain grades.

Am I correct that I need to calculate f using the Colebrook-White Equation and then substitue it into Darcy's equation?

If so is there a fomulae that solves the Colbrook-White equation in terms of f=..... ? Your comments would be very much appreciated.

Sure . You need to calculate friction factor by solving Colebrook equation. This you can do simply in the convinence of a worksheet like Excel. See COLEBROOK EQUATION (Colebrook) for a description.

[aniluvscientist]

Surely you need to solve Colebrook equation for friction factor f.

This can be done using simply Excel worksheet by making use of circular references. A detailed treatment given in COLEBROOK EQUATION (Colebrook)