Nomenclature

A

cross-sectional flow area of a pipe

cp

specific heat, constant pressure

CD

discharge coefficient

CV

valve coefficient

CHW

Hazen-Williams factor

D

diameter of a pipe

f

friction factor

fT

turbulent friction factor (used by Crane, 1988Crane Co., Flow of Fluids Through Valves, Fittings, and Pipe, Technical Paper No. 410, Crane Co., Joliet, IL, 1988.)

fL

laminar friction factor

fTr

transition friction factor

F

error value in mass balance

Fr

Froude number

g

gravitational constant

h

convection coefficient

h

enthalpy

H

head

HGL

hydraulic gradeline (same as head)

J

Jacobian matrix

k

thermal conductivity

K

loss factor

K

constant for Power Law fluid

Ksprinkler

fire sprinkler loss factor

L

length of a pipe

mass flow rate

n

general constant

n

constant for Power Law fluid

Nu

Nusselt Number

P

pressure, static

Ph

heated perimeter

Po

pressure, stagnation

Pw

wetted perimeter

q

heat rate to a pipe

Q

volumetric flow rate

q"

heat flux

r

radius

r

relaxation

R, R’

resistance

Rc

coefficient of rigidity

Re

Reynolds Number

Rh

Hydraulic radius (equal to radius divided by 2)

s

pump speed

S

Submergence

S

Hydraulic gradeline gradient

Sy

yield stress

T

temperature

U

overall heat transfer coefficient

V

velocity

x

distance along pipe centerline

z

elevation

a, m, q

angle

b

diameter ratio

e

roughness

n

kinematic viscosity

ρ

density

μ

dynamic viscosity

Subscripts

i

junction at which solution is sought

j

junctions with pipes connecting to junction i

o

stagnation

infinity, far away, ambient