HP 48gII User Manual Page 222

Graphing calculator.

2
L
V
h
f
. The quantity f is known as the friction factor of
written as
f
D
2
g
the flow and it has been found to be a function of the relative roughness of the
pipe, ε/D, and a (dimensionless) Reynolds number, Re. The Reynolds number
is defined as Re = ρVD/µ = VD/ν, where ρ and µ are the density and
dynamic viscosity of the fluid, respectively, and ν = µ/ρ is the kinematic
viscosity of the fluid.
The calculator provides a function called DARCY that uses as input the relative
roughness ε/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(ε/D,Re)
In aerodynamics applications a different friction factor, the Fanning friction
factor, is used. The Fanning friction factor, f
, is defined as 4 times the Darcy-
F
Weisbach friction factor, f. The calculator also provides a function called
FANNING that uses the same input as DARCY, i.e., ε/D and Re, and
provides the FANNING friction factor. Check that
FANNING(0.0001,1000000) = 0.0033603589181s.
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