Pipe Flows – Pipe Systems - Purdue University

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Page 1: Pipe Flows – Pipe Systems - Purdue University

Pipe Flows – Pipe Systems

https://americanvintagehome.com/advice-for-older-homes/need-swap-galvanized-pipes/

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Pipe Flows – Pipe Systems

! "#$+ 𝛼 '()

*$+ 𝑧,

-./= ! "

#$+ 𝛼 '()

*$+ 𝑧,

12− 𝐻5 + 𝐻6

where

𝛼 = 72 𝑅𝑒; < 2300(laminar)1 𝑅𝑒; > 2300(turbulent)

𝐻6 =�̇�6,-2Q'

�̇�𝑔 𝐻5 = T 𝑘1𝑉W1*

2𝑔∀YZ[[\[

𝑘 ≡∆𝑝`)#.(

)𝑘abcZd = 𝑓; f

𝐿𝐷i𝑘ajkZd ∶ Lookupvaluesfromtables.

𝑓;,Ybajkbd =

64𝑅𝑒;

𝑓;,wxdyxY\kw = 𝑓 !𝑅𝑒;,𝜖𝐷, (UsetheMoodyplotorHaalandorColebrookformulas. )

Pipe Flows – Head Losses

ME 309 Comprehensive Exam Formula Sheet Last updated: 2019 Sep 17

Page 6 of 9

Colebrook Formula: Haaland Formula

1f≈ −2.0log10

ε D3.7 + 2.51

ReD f

⎝⎜⎜

⎠⎟⎟

1f≈ −1.8log10

6.9ReD

+ ε D3.7

⎛⎝⎜

⎞⎠⎟

1.11⎡

⎣⎢⎢

⎦⎥⎥

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1 f≈−2.0log

10εD 3.7+

2.51

ReD

f

⎛ ⎝⎜ ⎜

⎞ ⎠⎟ ⎟

1 f≈−1.8log

106.9 Re

D

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⎛ ⎝⎜⎞ ⎠⎟1.1

1⎡ ⎣⎢ ⎢

⎤ ⎦⎥ ⎥

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Pipe Flows – Pipe Systems

Pipe Flows – Head Losses

ME 309 Comprehensive Exam Formula Sheet Last updated: 2019 Sep 17

Page 7 of 9

Average Roughness of Commercial Pipes Material (new) ft mm Riveted steel 0.003-0.03 0.9-9.0 Concrete 0.001-0.01 0.3-3.0 Wood stave 0.0006-0.003 0.18-0.9 Cast iron 0.00085 0.26 Galvanized iron 0.0005 0.15 Asphalted cast iron 0.0004 0.12 Commercial steel or wrought iron 0.00015 0.045 Drawn tubing 0.000005 0.0015 Plastic, glass 0.0 (smooth) 0.0 (smooth)

Table of Minor Loss Coefficients Component K Component K

a. Elbows Regular 90o, flanged 0.3 Regular 90o, threaded 1.5 Long radius 90o, flanged 0.2 Long radius 90o, threaded 0.7 Long radius 45o, flanged 0.2 Regular 45o, threaded 0.4

b. 180o return bends 180o return bends, flanged 0.2 180o return bends, threaded 1.5

c. Tees Line flow, flanged 0.2 Line flow, threaded 0.9 Branch flow, flanged 1.0 Branch flow, threaded 2.0

d. Union, threaded 0.06

h. Sudden Contraction/Expansion:

e. Valves

Globe, fully open 10 Angle, fully open 2 Gate, fully open 0.15 Gate, ¼ closed 0.26 Gate, ½ closed 2.1 Gate, ¾ closed 17 Swing check, forward flow 2 Swing check, backward flow ¥ Ball valve, fully open 0.05 Ball valve, 1/3 closed 5.5 Ball valve, 2/3 closed 210

f. Entrances Re-entrant 0.8 Sharp-edged 0.5 Slightly rounded 0.2 Well rounded 0.04 g. Exits

Re-entrant, sharp-edged, slightly rounded, well-rounded 1

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Pipe Flows – Pipe Systems

Types of Pipe Systems Type I: The desired flow rate is specified and the required pressure drop must be determined. (Easiest

to solve) Type II: The desired pressure drop is specified and the required flow rate must be determined. (Often

requires iteration since the Reynolds number is not known.) Type III: The desired flow rate and pressure drop are specified and the required pipe diameter must be

determined. (Often requires iteration since the Reynolds number and relative roughness are not known.)

Serial Pipe Systems

Parallel Pipe Systems

C. Wassgren Last Updated: 29 Nov 2016 Chapter 11: Pipe Flows

7. Pipe Systems Most pipe flow problems can be classified as being of one of three types:

Type I: The desired flow rate is specified and the required pressure drop must be determined. Type II: The desired pressure drop is specified and the required flow rate must be determined. Type III: The desired flow rate and pressure drop are specified and the required pipe diameter must

be determined. Type I pipe systems are the easiest to solve. Since the flow velocity and diameter are known, calculation of the major loss coefficient, the friction factor in particular, is straightforward. Type II and Type III problems are more challenging to solve since the friction factor is unknown. These types of pipe systems usually require iteration to solve. Notes: 1. There is no unique iterative scheme that must be used to solve Type II and Type III pipe flow

problems. Different people may propose different algorithms. In addition, there is no guarantee that a particular iterative scheme will converge to a solution.

2. When using an iterative scheme, choose an initial flow rate or diameter that is reasonable. Don’t start with an exceedingly small or large value. For example, for a Type II pipe system, choose a starting flow rate that corresponds to the fully turbulent zone region.

3. It’s often worthwhile to first assume that a Type II and Type III flow system is operating in the fully rough zone of the Moody plot. Using this assumption will generally avoid the need for iteration. However, one must verify at the end of the solution that the assumption of fully rough flow was correct. If not, then an iterative solution should be considered.

Serial Pipe Systems Serial pipe systems have multiple pipes that have the same inlet conditions and the same outlet conditions. For these systems one simply applies the EBE separately for each pipe. Parallel Pipe Systems Parallel pipe systems involve pipes that have intersections (aka nodes). These pipe systems are more challenging to solve. The EBE can be used between nodes and between nodes and inlets and outlets. In addition, conservation of mass should be used at each node. The result will be a system of non-linear equations (due to velocity squared terms that appear in the EBE) that must be solved simultaneously. Often these systems of equations are solved computationally using iterative techniques. Interestingly, pipe networks have many similarities with electrical networks, with pipe resistances corresponding to electrical resistances, flow rates corresponding to current, and head differences (due to elevation differences or pumps) corresponding to voltage differences. There are other electrical analogies too. For example surge tanks have properties similar to capacitors, heavy paddle wheels have properties similar to inductors, and ball and check valves act as diodes.

pipe 1 pipe 2 pipe 3

node

1069

C. Wassgren Last Updated: 29 Nov 2016 Chapter 11: Pipe Flows

7. Pipe Systems Most pipe flow problems can be classified as being of one of three types:

Type I: The desired flow rate is specified and the required pressure drop must be determined. Type II: The desired pressure drop is specified and the required flow rate must be determined. Type III: The desired flow rate and pressure drop are specified and the required pipe diameter must

be determined. Type I pipe systems are the easiest to solve. Since the flow velocity and diameter are known, calculation of the major loss coefficient, the friction factor in particular, is straightforward. Type II and Type III problems are more challenging to solve since the friction factor is unknown. These types of pipe systems usually require iteration to solve. Notes: 1. There is no unique iterative scheme that must be used to solve Type II and Type III pipe flow

problems. Different people may propose different algorithms. In addition, there is no guarantee that a particular iterative scheme will converge to a solution.

2. When using an iterative scheme, choose an initial flow rate or diameter that is reasonable. Don’t start with an exceedingly small or large value. For example, for a Type II pipe system, choose a starting flow rate that corresponds to the fully turbulent zone region.

3. It’s often worthwhile to first assume that a Type II and Type III flow system is operating in the fully rough zone of the Moody plot. Using this assumption will generally avoid the need for iteration. However, one must verify at the end of the solution that the assumption of fully rough flow was correct. If not, then an iterative solution should be considered.

Serial Pipe Systems Serial pipe systems have multiple pipes that have the same inlet conditions and the same outlet conditions. For these systems one simply applies the EBE separately for each pipe. Parallel Pipe Systems Parallel pipe systems involve pipes that have intersections (aka nodes). These pipe systems are more challenging to solve. The EBE can be used between nodes and between nodes and inlets and outlets. In addition, conservation of mass should be used at each node. The result will be a system of non-linear equations (due to velocity squared terms that appear in the EBE) that must be solved simultaneously. Often these systems of equations are solved computationally using iterative techniques. Interestingly, pipe networks have many similarities with electrical networks, with pipe resistances corresponding to electrical resistances, flow rates corresponding to current, and head differences (due to elevation differences or pumps) corresponding to voltage differences. There are other electrical analogies too. For example surge tanks have properties similar to capacitors, heavy paddle wheels have properties similar to inductors, and ball and check valves act as diodes.

pipe 1 pipe 2 pipe 3

node

1069