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Topics:    Scenarios  Common Questions   Equations    Minor Loss Coefficients

Piping Scenarios:

Common Questions                                          Back to Calculation 
I took fluid mechanics a long long time ago.  What is head?  Why does it have units of length?  Head is energy per unit weight of fluid (i.e. Force x Length/Weight = Length).  The program on this page solves the energy equation (shown below); we call energy "head."
Why is Pressure=0 for a reservoir?  A reservoir is open to the atmosphere, so its gage pressure is zero.
Why is Velocity=0 for a reservoir?  This is a common assumption in fluid mechanics and is based on the fact that a reservoir has a large surface area.   Therefore, the liquid level drops very little even if a lot of liquid flows out of the reservoir.  A reservoir may physically be a lake or a large diameter tank.
What is a "main" and a "lateral"?  A "main" is a large diameter supply pipe that has many smaller diameter "laterals" branching off of it.   In fluid mechanics, we set V=0 for the main since it has a large diameter (relative to the lateral) and thus a very small velocity.  To further justify the V=0 assumption, the main's pressure is typically high, so the velocity head in the main is negligible.  The main is drawn such that it is coming out of your computer monitor.
Can I model flow between two reservoirs using either Scenario B or E?  Yes, you can.  If using Scenario E, just set P₁-P₂=0.  Scenario B automatically sets P₁-P₂=0.
Can I model flow between two mains using either Scenario B or E?  Only if the pressure is the same in both mains.
How do I model a pipe discharging freely to the atmosphere?  Use Scenario A, C, or F.  Since P₂=0 (relative to atmospheric pressure), P₁-P₂ that is input or output will be P₁.
What are minor losses?  Minor losses are head (energy) losses due to valves, pipe bends, pipe entrances (for fluid flowing from a tank to a pipe), and pipe exits (fluid flowing from a pipe to a tank), as opposed to a major loss which is due to the friction of fluid flowing through a length of pipe.  Minor loss coefficients (K_m) are tabulated below.   For our program, all of the pipes have the same diameter, so you can add up all your minor loss coefficients and enter the sum in the Minor Loss Coefficient input box.
Why do I sometimes get the message, "Infeasible Input"?  The governing equations for fluid flow must be satisfied.  Fluids must flow from higher energy to lower energy; driving head must always be > 0.  Pipe roughness, fluid viscosity, pipe diameter, and velocity must be such that the Reynolds number is <=10⁸ and other conditions shown with the equations below are satisfied.  It is possible to enter values that are not physically or mathematically feasible.
I'm confused about pumps.  Only input Pump Head if the pump is between points 1 and 2.  Otherwise, enter 0 for Pump Head.  Pump Head, H_p, is also known as total dynamic head.
Your program is great!  What are its limitations?  Pipes must all have the same diameter.  Pump curves cannot be implemented.
What is Driving Head?  See below.

Steady State Energy Equation            Back to Pipe Design Calculation         References
(Uses the Darcy Weisbach friction loss (major loss) equation.  The friction factor is found using the Colebrook equation which represents the Moody diagram.)

Driving Head (DH) = left side of the first equation
g = acceleration due to gravity = 32.174 ft/s² = 9.8066 m/s²
S = weight density, v=kinematic viscosity
Pump Power = SQH_p.  Note that 1 horsepower = 550 ft-lb/s
Fluid density and viscosity may be entered in a wide choice of units.  Some of the density units are mass density (g/cm³, kg/m³, slug/ft³, lb(mass)/ft³) and some are weight density (N/m³, lb(force)/ft³).   There is no distinction between lb(mass)/ft³ and lb(force)/ft³ in the density since they have numerically equivalent values and all densities are internally converted to N/m³.  Likewise, fluid viscosity may be entered in a wide variety of units.  Some of the units are dynamic viscosity (cP, poise, N-s/m2 (same as kg/m-s), lb(force)-s/ft² (same as slug/ft-s) and some are kinematic viscosity (cSt, stoke (same as cm²/s), ft²/s, m²/s).   All viscosities are internally converted to kinematic viscosity in SI units (m²/s).   If necessary, the equation Kinematic viscosity = Dynamic viscosity/Mass density is used.
Other variables are defined above in the calculation above.

All of our calculations utilize double precision.  Newton's method (a numerical method) is used to solve the Colebrook equation accurate to 8 significant digits.   A cubic solver (numerical method) is used for "Solve for V, Q," "Q known. Solve for Pipe Diameter," and "V known. Solve for Pipe Diameter."   More than one solution is possible for these three calculations since there could be a result in the laminar range and the turbulent range.  There may even be two possible results in the laminar range for "Solve for V, Q" if scenario D or G is selected.   All of the possible solutions are computed and output.  If you have selected "Q known. Solve for Pipe Diameter," and scenario D or G, you must enter K_m >=1.  All calculations are analytic (closed form) except as mentioned here.

Table of Minor Loss Coefficients (K_m is unit-less):   References  Back to Calculation

© 1999-2001 LMNO Engineering, Research, and Software, Ltd. (All Rights Reserved)
Additional density and viscosity units added January 16, 2001

LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd.   Athens, Ohio  USA   (740) 592-1890
LMNO@LMNOeng.com    http://www.LMNOeng.com