Page 6-20
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 (
ε
/D,Re)
The Darcy-Weisbach equation is used to calculate the energy loss (per unit
weight), h
f
, in a pipe flow through a pipe of diameter D, absolute roughness
ε
,
and length L, when the flow velocity in the pipe is V. The equation is written as
. The quantity
f
is known as the friction factor of 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 =
ρ
VD/
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
ε
/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
F
, is defined as 4 times the Darcy-
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.
g
V
D
L
f
h
f
2
2
⋅
⋅
=
Summary of Contents for 50G
Page 1: ...HP g graphing calculator user s guide H Edition 1 HP part number F2229AA 90006 ...
Page 130: ...Page 2 70 The CMDS CoMmanDS menu activated within the Equation Writer i e O L CMDS ...
Page 206: ...Page 5 29 LIN LNCOLLECT POWEREXPAND SIMPLIFY ...
Page 257: ...Page 7 20 ...
Page 383: ...Page 11 56 Function KER Function MKISOM ...
Page 715: ...Page 21 68 Whereas using RPL there is no problem when loading this program in algebraic mode ...
Page 858: ...Page L 5 ...