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

Cd

discharge coefficient

cp

specific heat, constant pressure

cv

specific heat, constant volume

CV

valve coefficient

D

diameter of a pipe

e

specific energy

F

Force

f

friction factor

fT

turbulent friction factor (used by Crane, 1988)

fL

laminar friction factor

fTr

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

mass flow rate

M

Mach number

n

general constant

N

compressor synchronous speed (rpm)

P

pressure, static

Po

pressure, stagnation

Pw

wetted perimeter

P

power

q

heat rate to a pipe

Q

volumetric flow rate

r

radius

r

relaxation

R, R’

resistance or gas constant

Rc

coefficient of rigidity

Re

Reynolds Number

s

fan speed

s

entropy

t

time

T

temperature, static

To

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

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