AFD6 Incompressible Flow Application

Applied Fluid Dynamics
AFD6 Incompressible Flow Application
Chemical Engineering Guy
www.ChemicalEngineeringGuy.com

AFD6 Overview

Textbook, Reference and Bibliography

• Chapters:
– 11  System in Series Arrangement
– 12  Systems in Parallel Arrangement
Applied Fluid Mechanics. Robert
Mott 6th Edition

• Section 2: Fluid Mechanics
– NONE 
Unit Operation of Chemical
Engineering. McCabe 7th Edition

AFD6 Block Overview
• Section 1: Series Flow (1 pipe)
– Type of Problems
• Type I  Find a value from M.E.E
• Type II  Find Volumetric Flow Rate
• Type III  Find Pipe Dimensions
• Section 2: Parallel and Branch Flow
– Parallel Flow vs. Branched Flow
– Parallel Flow  2 Pipes
– Parallel (2+) + Branched Flow  (Software)

Section 1: Series Flow (1 pipe)

M.E.E in Series Flow

M.E.E in Series Flow
• We’ve seen some types of single piping
systems
• These type of system are simple to solve, that
is, you just need to isolate a value from the
equation.
• Let’s Call these Problems “Type I” the easy
ones…

Types of Problem in M.E.E
1. Type I : Solve for Pressure, Pump Requirement or any Hieght.
– Flow rate is given.
– Velocities can be calculated.
– Hf is calculated with Velocities (Hf is constant)
2. Type II: Solve for Volumetric Flow Rate
1. We know the Piping Settings.
2. Velocities of the system are not known.
3. Friction can’t be calculated.
4. Propose Velocities
5. Recalculate until iteration error < 5%
3. Type III: Piping Settings are NOT known
1. Flow Rate is given
2. Velocities are not known
3. Propose Piping Size
4. Recalculate until iteration error < 5%

M.E.E. Type I
• Hf depends on friction factor.
– Friction factor if function of Reynolds Number
– Reynold Number is function of Velocity
– You just need Velocity to solve this
• Velocity may be calculated given Volumetric Flow
Rate and Piping Data (diameters)
• After V is calculated
– F.F. may be calculated (only once)
• Solve algebraically and you’re done!

M.E.E. Type I  Exercise
• Check out AFD1, there is plenty of them

What must be the Pressure in A to satisfy the next System?

I’ve got everything but Hf

0.22

Friction due to Shape!
Check out AFD2 and AFD3 for more information!

You got Friction Loss in Wall + Shape…

Need More Problems?
Check out the COURSE
• Courses
Applied Fluid Dynamics
Part 1: Incompressible Flow
You’ll get SOLVED Problems, Quizzes, Slides, and
much more!

M.E.E. Type II
• Velocity may NOT be calculated given Volumetric
• Propose any Volumetric Flow Rate/Velocity
• Calculate for Velocity of this Design
– F.F. may be calculated
– If error < 5% you’re done
– If error > 5% try other Volumetric Flow Rate and Repeat!
• Iteration Based! Be careful!

M.E.E. Type II  Exercise

M.E.E. Type II  Exercise
• Propose  Volumetric Flow Rate
– Calculate Velocity in 2” and 3”
– Calculate Re numbers in 2” and 3”
– Calculate friction factor (f) in each
– Calculate loss of friction in each pipe
– Is Equation 1 = Equation 2?
• Iterate if NOT

M.E.E. Type III
• Velocity may NOT be calculated given Volumetric
• Propose any Piping Sizing
• Calculate for Velocity of this Pipe Design
– F.F. may be calculated
– If error < 5% you’re done
– If error > 5% try other Volumetric Flow Rate and Repeat!
• Iteration Based! Be careful!
• hf is proportional to Diameter  Hf = (1/D)^4

M.E.E. Type III  Exercise

M.E.E. Type III  Exercise
• Propose Diameter in Pipes
– Calculate Velocity in Pipe(s)
– Calculate Re Number in Pipe
– Calculate Relative roughness (e/D)
– Find Friciton Factor
– Calculate Friction Loss in Walls + Fittings + Valves
– Is Equation 1 = Equation 2?
• If NOT, Iterate

End of Section 1: Series Flow (1 pipe)

Section 2: Parallel and Branch Flow

Parallel Flow
• At least 2 pipes
• Arrangement in parallel
– Start in point A
– May pass through many other points
– Finish in point B

Parallel Flow
• The addition of all streams = total stream
QA = Q1 + Q2 + Q3 = QB

Parallel Flow
• The TOTAL friction per pipe is different
– Hf1 is not Hf2 and is not Hf3
• The friction per unit kg is the SAME between Pipes!

Parallel Flow
• Flow will pass through the least frictious
– Low friction  High mass flow
– High friction  low mass flow

Parallel Flow
Inlet
High Friction Outlet
Low Friction Outlet
q= low
q= high

Parallel Flow
• Remember

Parallel Flow
• Fast Cashier 
majority of people
• Slow Cashier 
minority will be here
• Whatever line you
make, you will make
almost the same time

Parallel Flow
Small quantity will go through the
hard path, you will make a lot of time
due to difficulty, but it isnt crowded
Many will take the easy path, but it is crowded
so you can’t actually go fast

Parallel Flow
1= 0.23 kg/s
2= 0.46 kg/s
3= 0.31 kg/s
hf1 = hf2 = hf3 ??
Hf1 = 150 J/s
Hf2 = 300 J/s
Hf3 = 200 J/s

Parallel Flow
Hf1 = 150 J/s
Hf2 = 300 J/s
Hf3 = 200 J/s
1= 0.23 kg/s
2= 0.46 kg/s
3= 0.31 kg/s
hf1 = 150 J/0.23 kg/s = 650 J/kg
hf2 = 300 J/0.46 kg/s = 650 J/kg
hf3 = 200 J/0.31 kg/s = 650 J/kg

Parallel Flow
• Before advancing, please read all previous
material
• Read and re-read the next material, it is kind
of abstract
• In my experience, its better to actually try to
do one problem
• You will understand the problems when
calculaitng and reasoning rather than reading

Parallel Flow
• Before advancing, please read all previous
material
• Read and re-read the next material, it is kind
of abstract
• In my experience, its better to actually try to
do one problem
• You will understand the problems when
calculaitng and reasoning rather than reading
This is a
Theory/Application
Course!

Two Cases
• We know Total Volumetric Flow + Fittings/Valves
– Solve for individual pipes (a and b)
• You know the pressure loss
– Solve for total Flow in pipes (a, b and 1,2)
Numbers are used in internal branches
Letters are used in “start” and “finish” points

Case 1
1. Apply Q1 = Q2 = Qa+Qb
– Qa = AaVa and Qb= AbVb
2. Find Friction loss on each pipe
3. Calculate e/D, f.f., hfs = (terms of unkown velocity) for
each branch
4. Recall that ha = hb; use equations in 3 to do this
5. Solve for a Velocity in terms of other
6. Substitute Equation of 5 in 1 (Solve for V)
7. Solve for the other V
8. Estimate f.f. and hf (from step 2)
– Iterate until error is min.
9. Solve for each Q since V is known

Case 2
1. Calculate dP = Hf
2. Model each friction loss (a and b)
– F.f. and V are unkown
3. Estimate f.f. and specify hf in terms of V
4. Solve Eqn 1+ 3
5. Check Re, V and f.f.
– If error is high  repeat
– If error is low  this is the answer

Parallel Flow Exercise
Height May Be ignored

Branch Flow
• At least 2 pipes
• Arrangement in parallel
– DOES NOT Start only in point A
– May pass through many other points
– DOES NOT finishes only in point B

Branch Flow
Some cases it is difficult to know
where is the flow going!

Branch Flow
• Even the most simple problems are kind of
difficult to solve…
• Typically in a course of Software Engineering
– Will NOT be included in this course!
– Send me an e-mail if you need some stuff!
• If you really need it, I’ll add some extra material
These are solved
using Software!

Complex Piping
• These are too complex to solve “by hand”
• The problem many times is to know where the
flow is going
– Pressures, Velocities, sizes, Heights are no longer
“common sense”
– Basic Principles still apply
– Iteration is needed
• Software is used 
– Spread sheets
– Dedicated Piping Software

Complex Piping

Piping Software

Piping Software
Rohr

End of Section 2: Parallel and Branch Flow

End of AFD6
• By now you should know:
– How to solve incompressible flow problems in series
– Find the most suitable pipe size & volumetric flow
– Understand the basic principle behind parallel pipes
– How to solve parallel pipes
– Understand the difference between parallel and
branched piping systems
– Know the approach when solving complex systems

Questions and Problems
• Check out the SOLVED & EXPLAINED problems
and exercises!
– Don’t let this for later…
• All problems and exercises are solved in the
next webpage
– www.ChemicalEngineeringGuy.com
• Courses
– Momentum Transfer Operations

Contact Information!
• Get extra information here!
– Directly on the WebPage:
• www.ChemicalEngineeringGuy.com/courses
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AFD6 Incompressible Flow Application

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