Nomenclature

a	sonic speed
A	cross-sectional flow area of a pipe
B	compatibility equations parameter for method of characteristics
C	compatibility equations parameter for method of characteristics
C_d	discharge coefficient
c_p	specific heat, constant pressure
c_v	specific heat, constant volume
C_V	valve coefficient
D	diameter of a pipe
e	specific energy
F	Force
f	friction factor
f_T	turbulent friction factor (used by Crane, 1988)
f_L	laminar friction factor
f_Tr	transition friction factor
F	error value in mass balance
g	gravitational constant
h	internal convection coefficient
h	enthalpy, static
ho	enthalpy, stagnation
H	head
J	Jacobian matrix
k	thermal conductivity
K	loss factor
L	length of a pipe
ṁ	mass flow rate
M	Mach number
n	general constant
N	compressor synchronous speed (rpm)
P	pressure, static
P_o	pressure, stagnation
P_w	wetted perimeter
P	power
q	heat rate to a pipe
Q	volumetric flow rate
r	radius
r	relaxation
R, R’	resistance or gas constant
R_c	coefficient of rigidity
Re	Reynolds Number
s	fan speed
s	entropy
t	time
T	temperature, static
T_o	temperature, stagnation
u	internal energy
v	specific volume
V	volume
V	velocity
w	work
x	distance along pipe centerline
z	elevation
Z	compressibility factor
α, μ, θ	angle
β	diameter ratio
β	coefficient of volume expansion
λ	method of characteristics multiplier
η	efficiency
ν	kinematic viscosity
ε	roughness
γ	specific heat ratio
ρ	density
τ	shear stress
ω	rotational velocity
μ	dynamic viscosity

Subscripts

i	junction or pipe station at which solution is sought
j	junctions with pipes connecting to junction i
R	rated conditions for a compressor, usually BEP
o	stagnation
	infinity, far away, ambient
new	current time for computation
old	most recent time for computation