USER INSTRUCTIONS FOR HYDRAULIC SERIES PROGRAM


INTRODUCTION

Please read the user instructions before using the program.

This program was designed for the practicing civil engineer and the
teaching professional.  Data may be entered in English (CFS, GPM,
MGD) or Metric (L/S, M3/S, L/MIN, M3/MIN) units.

The Hazen-Williams, Manning, Kutter, and Darcy-Weisbach equations
were used to solve pressure pipes, gravity pipes, trapezoidal
channels, pipes in parallel, and pipes in series.  Practicing and
teaching professionals continue to debate the relative merits of
these equations.

DIRECTORY AND FILE STRUCTURE

The hydraulic series program consists of HS.EXE and HS.OVR.  HS.EXE
is the main program.  HS.OVR contains the overlay files for each
item on the main menu.  The program was separated into two parts to
reduce memory requirements.

HS.DWC is a textfile of Darcy-Weisbach constants.  READHS is a
textfile containing these instructions.

HS.EXE, HS.OVR, HS.DWC, and READHS are compressed into PKHS.ZIP.

EXECUTE THE HYDRAULIC SERIES PROGRAM

If the hydraulic series program, HS, is installed on directory
C:\HYDR\HS, go to the directory C:\HYDR\HS, type HS and press
Enter, or type C:\HYDR\HS\HS and press Enter from any other
directory.

ON-LINE HELP

A list of recommended roughness values and inside diameters for
various pipe materials, a list of recommended coefficients of
headloss (K) for valves and fittings, and a table listing the
properties of water at various temperatures can be produced by
moving the cursor to appropriate field and pressing 'H'.

UNITS: Change between by pressing 'U'.

PRINT RESULTS

Print results by pressing 'P'.  Computations are saved to a buffer.
The buffer is cleared each time the results are printed, the units
are changed, or the menu is exited.


HS.TXT

A complete record of each session, including all computations, is
saved to HS.TXT and the previous session is backed up to HS.BAK. 
These files can be edited and printed using a word processor of
your choice.

HS.PLT

Each time a graph is generated the results are saved to HS.PLT. 
This file name is used for all the graphs, therefore HS.PLT will 
contain the results of the last graph generated.  HS.PLT may be
retreived by spreadsheet programs.

HS.DWC

This file can be edited to modify the Darcy-Weisbach constants.  Do
not attempt this operation, unless you know what you are doing.

The default values:
               c3       c4      c5
Pressure pipe         2.00     2.52    14.8
Gravity pipe          2.00     2.52    14.8
Trapezoidal Channel   2.03     3.08    12.2  (Corps of Eng)

ACKNOWLEDGEMENTS

Steve Hart, P.E., Civil Engineer, reviewed the program and
recommended several improvements to make it useful to the design
professional.  Henry T. Falvey, Dr.-Ing., suggested the use of
Darcy-Weisbach/Colebrook-White equation for gravity flow
applications.

NOTICE

HS was designed by Istvn Lippai and Mike Finken, National Park
Service, Denver Service Center, 12795 West Alameda Parkway,
Lakewood, Colorado 80228, Phone 303-969-2935, Fax 303-969-2930. 
Persons wishing to make use of this program are free to copy it and
use it.  Every effort was made to find and correct all errors,
however neither the authors nor the Government assume any
responsibility for any use made of this program.

November 8, 1995APPENDIX

SUMMARY

SYMBOLS
FLOW EQUATIONS
   Hazen-Williams
   Manning
   Kutter
   Darcy-Weisbach/Colebrook-White
APPLICATION OF FLOW EQUATIONS
   PRESSURE PIPE
     Hazen-Williams
     Manning
     Kutter
     Darcy-Weisbach/Colebrook-White
   GRAVITY PIPE
     Manning
     Kutter
     Darcy-Weisbach/Colebrook-White
   TRAPEZOIDAL CHANNEL
     Manning
     Kutter
     Darcy-Weisbach/Colebrook-White
   PARABOLIC CHANNEL
     Manning
     Kutter
     Darcy-Weisbach/Colebrook-White
   PIPES IN PARALLEL
     Hazen-Williams Equation
   PIPES IN SERIES
     Hazen-Williams Equation
FIXTURE UNITS vs PEAK WATER DEMAND or PEAK SEWER DISCHARGE


SYMBOLS

ES = English units
SI = Metric units

D  = Diameter
L  = Length
S  = Friction slope = H / L
Y  = Depth
B  = Bottom width
HH = Horizontal projection of side
YY = Vertical projection of side
SS = Side slope = HH / YY
T  = Top width

e = Coefficient C for Hazen-Williams equation
e = Manning n for Manning equation
e = Manning n for Kutter equation
e = Roughness  for Darcy-Weisbach-Colebrook-White Equation

CES = Kutter coefficient of roughness in ES units
CSI = Kutter coefficient of roughness in SI units

A  = Area
P  = Perimeter
R  = Hydraulic radius
V  = Velocity
H  = Headloss
Q  = Discharge = A * V

f  = Friction factor
g  = Gravitational acceleration
Re = Reynolds number


FLOW EQUATIONS

Hazen-Williams Equation

ES:  Vfps = 1.318 * C * R^(0.63) * S^(0.54)   (Rft)

SI:  Vm/s = 0.849 * C * R^(0.63) * S^(0.54)   (Rm)


Manning Equation

ES:  Vfps = (1.486 / N) * R^(2/3) * S^(1/2)   (Rft)

SI:  Vm/s = (1.000 / N) * R^(2/3) * S^(1/2)   (Rm)


Kutter Equation

                (1.81 / N) + 41.67 + (0.0028/S)
ES:  CES = 
            1 + [N / R^(1/2)] * [ 41.67 + (0.0028/S)]


                (1 / N) + 23 + (0.00155/S)
SI:  CSI = 
            1 + [N / R^(1/2)] * [ 23 + (0.00155/S)]


ES: Vfps = CES * (R * S)^(1/2)    (Rft)

SI: Vm/s = CSI * (R * S)^(1/2)    (Rm)

Darcy-Weisbach/Colebrook-White Equation

   Darcy-Weisbach-Colebrook-White constants:
                    c3       c4      c5
     Pressure pipe         2.00     2.52    14.8
     Gravity pipe          2.00     2.52    14.8
     Trapezoidal Channel   2.03     3.08    12.2  (Corps of Eng)


H = f * (L/D) * V^2 / (2*g)

f is determined as follows:

Implicit equation for f (transitional and turbulent flow):

  1/(f) = c3 * log10{(e/R)/c5 + c4 / [Re * (f)]}  or

  1/(f) = c3*log10(c5/4) - 
           c3*log10 {e/(4*R) + c4*(c5/4)/[Re * (f)]}

Explicit equation for f (laminar flow):

  f = 64 / Re

Explicit approximation of f (turbulent flow - by Don J. Wood):

  f =  a + b / Re^c

  a = 0.094 * [e / (4 * R)]^(0.225) + 0.53 * [e / (4 * R)]

  b = 88 * [e / (4 * R)]^(0.44)

  c = 1.62 * [e / (4 * R)]^(0.134)

After an initial estimate of f is obtained using Wood's
approximation, the implicit equation for f is solved using the
Newton-Raphson method.


APPLICATION OF FLOW EQUATIONS


PRESSURE PIPE
     Hazen-Williams
     Manning
     Kutter
     Darcy-Weisbach/Colebrook-White

A set of 15 distinct pairs was produced from the set of variables

{Q,D,L,H,e,V} -> {{Q,D}
                  {Q,L} {D,L}
                  {Q,H} {D,H} {L,H}
                  {Q,e} {D,e} {L,e} {H,e}
                  {Q,V} {D,V} {L,V} {H,V} {e,V}}.

Enter 4 variables to compute the remaining two variables.  {L,H},
{L,e}, and {H,e} can not be computed because both elements of
these pairs occur only in one of the equations.  Minor loss is a
special case.


GRAVITY PIPE
     Manning
     Kutter
     Darcy-Weisbach/Colebrook-White

A set of 15 distinct pairs was produced from the set of variables

{Q,D,S,e,V,Y} -> {{Q,D}
                  {Q,S} {D,S}
                  {Q,e} {D,e} {S,e}
                  {Q,V} {D,V} {S,V} {e,V}
                  {Q,Y} {D,Y} {S,Y} {e,Y} {V,Y}}.

Enter 4 variables to compute the remaining two variables. {S,e}
can not be computed because both elements of this pair occur only
in one of the equations.  {D,Y} is not computed because it has a
very small region of solution.


TRAPEZOIDAL CHANNEL
   Manning
   Kutter
   Darcy-Weisbach/Colebrook-White

A = (B * Y) + (SS * Y^2)

P = B + 2 * [Y^2 + (SS * Y)^2]^(1/2)

R = A / P

If the side slope, SS is zero, the channel shape is rectangular.
If the bottom width, B is zero, the channel shape is triangular.

A set of 21 distinct pairs was produced from the set of variables

{Q,B,SS,S,e,V,Y} -> {{Q,B}
                     {Q,SS}{B,SS}
                     {Q,S} {B,S} {SS,S}
                     {Q,e} {B,e} {SS,e} {S,e}
                     {Q,V} {B,V} {SS,V} {S,V} {e,V}
                     {Q,Y} {B,Y} {SS,Y} {S,Y} {e,Y} {V,Y}}.

Enter 4 variables (5 variables if bottom width and side slope is
entered) to compute the remaining two variables.  {S,e} can not
be computed because both elements of this pair occur only in one
of the equations.  {B,SS}, {B,Y}, {B,V} and {SS,Y} are not computed
because they have very small regions of solution.


PARABOLIC CHANNEL
   Manning
   Kutter
   Darcy-Weisbach/Colebrook-White

Trapezoidal earth channels tend to erode and assume a parabolic
shape.
The parabolic channel is very efficient.

y = [Y / T^2] * x^2

A = (2/3) * (T * Y)

a = (4 * Y) / T

b = (a^2 + 1)^(1/2)

P = (T/2) * b + [T^2 / (8 * Y)] * ln(a + b)

R = A / P

A set of 15 distinct pairs was produced from the set of variables

{Q,T,S,e,V,Y} -> {{Q,T}
                  {Q,S} {T,S}
                  {Q,e} {T,e} {S,e}
                  {Q,V} {T,V} {S,V} {e,V}
                  {Q,Y} {T,Y} {S,Y} {e,Y} {V,Y}}.

Enter 4 variables to compute the remaining two variables. {S,e}
can not be computed because both elements of this pair occur only
in one of the equations.  {T,Y} is not computed because it has a
very small region of solution.


PIPES IN PARALLEL
  Hazen-Williams Equation

The head loss of every pipe in parallel is equal.

The sum of the discharges of individual pipes is equal to the
discharge of the equivalent pipe.

  Qe = Q1 + Q2 + ... + Qn

  He = H1 = H2 = ... = Hn


PIPES IN SERIES
  Hazen-Williams Equation

The discharge of every pipe in series is equal.

The sum of the head losses of individual pipes in series is equal
to the head loss of the equivalent pipe.

  Qe = Q1 = Q2 = ... = Qn

  He = H1 + H2 + ... + Hn
