# Function For Pipe Flow: Darcy; Function Fanning - HP 50g User Manual

Graphing calculator.

In the next example we will use the DARCY function for finding friction factors in
pipelines. Thus, we define the function in the following frame.
Special function for pipe flow: DARCY ( /D,Re)
The Darcy-Weisbach equation is used to calculate the energy loss (per unit
, in a pipe flow through a pipe of diameter D, absolute roughness ,
weight), h
f
and length L, when the flow velocity in the pipe is V. The equation is written as
L
V
h
f
f
D
2
it has been found to be a function of the relative roughness of the pipe, /D,
and a (dimensionless) Reynolds number, Re. The Reynolds number is defined as
Re = VD/ = VD/ , where
the fluid, respectively, and
The calculator provides a function called DARCY that uses as input the relative
roughness /D and the Reynolds number, in that order, to calculate the friction
factor f. The function DARCY can be found through the command catalog:
For example, for /D = 0.0001, Re = 1000000, you can find the friction factor
by using: DARCY(0.0001,1000000). In the following screen, the function
NUM () was used to obtain a numerical value of the function:
The result is f = DARCY(0.0001,1000000) = 0.01341...
The function FANNING( /D,Re)
In aerodynamics applications a different friction factor, the Fanning friction
factor, is used. The Fanning friction factor, f
Weisbach friction factor, f. The calculator also provides a function called
FANNING that uses the same input as DARCY, i.e., /D and Re, and provides
the FANNING friction factor. Check that FANNING(0.0001,1000000) =
0.0033603589181s.
2
. The quantity f is known as the friction factor of the flow and
g
and
are the density and dynamic viscosity of
is the kinematic viscosity of the fluid.
, is defined as 4 times the Darcy-
F
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