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Pipe_f.Loss is specially developed to feature 2-K Method for a single pipe friction loss (pressure drop) calculations. Note that Pipe_f.Loss does not calculate total system (pump) head. If you need to calculate total dynamic head (i.e., pump head), see Easy Pipe Friction (ePF) Loop program for Windows.

It's a plug-and-use Windows PC program, thus creating a mobile design environment (ShowMe!) for the practising engineers & designers in today's mobile world.

Highlights:

• built-in selections for valves & fittings losses using 2-K Method developed by Hooper

• 4 options (Colebrook, Swamee, etc) for solving friction factor f

• design as easy as "Select & Click" with full built-in database, conversion calculators, guides, etc

• save/open project, save results to Rich Text File (.rtf) for formatting & printing

• fully mobile “plug-and-use” program with no setup requirement

• in SI & IP units

Feature . . . 2-K Method for Minor Loss Calculations 

The 2-K method is a technique developed by Hooper B.W. to predict the head loss in an elbow, valve or tee. The 2-K method is advantageous over other method especially in the laminar flow region. The 2-K method takes the following forms of equation:

a) for valve & fitting,  K = (K1/Re) + K2(1+(1/ID))

where

K1 = K for the fitting at Re (Reynolds number) = 1, laminar flow 

K2 = K for a large fitting at Re = infinity, turbulent flow

ID = internal pipe diameter in inch

b) for entrances & exits,  K = (K1/Re)+K2. Here, the constant K2 is the "classic" K.

for details, refer to (1) "The Two-K Method Predicts Head Losses in Pipe Fittings" by Hooper B.W.,  Chemical Engineering, August 24, 1981; (2) "Fluid Flow Handbook" by Jamal M. Saleh (Editor), McGraw-Hill, 2002.

User guide and a calculation example using 2-K method can be downloaded here. 

Solver for solving Friction Factor, f  . . . don't be confused 

note: The friction factor, f, mentioned here is Darcy friction factor, not Fanning friction factor. Darcy f = 4 x Fanning f - don't be confused!

a) Laminar Flow: Friction factor is solved by the equation f = 64/Re, where Re=Reynolds number.

b) Turbulent Flow: Solving friction factor for turbulent flow can be tedious and complex. There are numerous equations, both implicit & explicit forms, available for solving friction factor.

Implicit equation requires iteration process and it is best to let a computer program to perform it. The most popular and common one is the Colebrook equation. However, it is to note that there are numerous forms of Colebrook equation available - main and modified forms. In the Pipe_f.Loss program, 4 friction factor equations are included as follows:

Head Loss & Pressure Drop: Darcy-Weisbach equation 

Calculation Example: 2-K Method Minor Losses  (in English units) 

Consider a 16-in (ID = 15.624-in) Sch 40S stainless steel system. The system contains 100 ft of pipe, 6 long-radius (R/D=1.5) 90o elbows, 2 side-outlet tees, 2 gate valves (β=0.9) and an exit into a tank. The fluid has dynamic viscosity of 1 cP, density of 62.43 lb/ft³, and the flow rate is 13.314 ft³/s. What is the head loss through this system?

The following is the results computed by Pipe_f.Loss program:

Pipe friction Loss  calculations

Fluid Data

Fluid = Water @ 20 °C (68 °F)

Density, ρ = 62.43 lb/ft³

Dynamic viscosity, µ = 1 cP = 0.000672 lb/ft.s

Kinematic viscosity, v = 1.08E-05 ft²/s

Flow rate, Q = 13.314 ft³/s

Mass flowrate, q = 831.19 lb/s

Pipe Data

Material = Stainless Steel

Roughness, ε = 5E-05 ft

Relative roughness, ε/D = 3.84E-05

Diameter, D = 15.624 in

Length, L = 100.00 ft

Flow Area, A = 1.3314 ft²

Velocity, V = 9.9998 ft/s

Friction Factor

Reynolds nos, Re = 1,209,624

Flow regime = Turbulent

Friction factor, ƒ = 0.012192 - solved by Swamee (Explicit Eqn 2)

Minor Losses

<Valves & Fittings>

Qty=6       K1=800    K∞=0.2     Elbows, 90, Long-radius(R/D=1.5), all types

Qty=2       K1=800    K∞=0.8    Tees, Used as elbow, Standard, flanged/welded

Qty=2       K1=500    K∞=0.15   Valves, Gate/Ball/Plug, Reduced trim, B=0.9

Total Kf = 3.305

<Entrance & Exit>

Qty=1       K1=0        K∞=1        Exit, projecting / sharp-edged / rounded

Total Ke = 1.000

Head Loss and Pressure Drop

Head loss for Pipe, ΔHp = 1.455 ft (K = 0.936)

Head loss for Minor losses, ΔHm = 6.687 ft

Total Head loss , ΔH = 8.142 ft

Total Pressure drop, ΔP = 3.53 psi (0.243 bar)      

Compare the above results with  Hazen-Williams and Darcy-Weisbach equations with equivalent length Le and resistance coefficient K method . . . on Android.

For multiple Series pipes + loop ring main pipe network, see  ePF Loop (easy Pipe Friction) on Windows.