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EDUNEX ITB
1Chemical Engineering Study Program β Faculty of Industrial Technology
ENERGY REQUIRMENT AND FRICTION IN
FLUID FLOW
Team Teaching:Dr. Yogi Wibisono Budhi, Dr. Ardiyan Harimawan, Dr. Dendy Adityawarman, Dr. Anggit Raksadjati, Dr. Haryo Pandu Winoto
TK2107 Fluid and Particle Mechanics (3 Credits)
Course Schedule:Tuesday, 13.00 β 14.00 -
Thursday, 10.00 β 12.00 -
Tutorial Schedule:Tuesday, 00.00 β 00.00 -
Wednesday, 00.00 β 00.00 -
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o Energy balance analysis using Bernoulli equation β doesnβt apply for real flows
Pressure drops along the flowInvolves the friction heat
Shaft work
1
Real Fluid FlowβIncompressible and Steady State
Generated by the shear betweenthe moving fluid and stationary
walls
2 Pumps or blower Supplies energy in order to keep the fluid flowing
LiquidThe change of density caused by
pressure can be neglectedIncompressible fluid3
β β
ββ
ββ
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o Gas β pressure drop due to friction can be neglected β gas density can be assumed to be constant β the flow can be assumed as incompressible fluid flow
Real Fluid FlowβIncompressible and Steady State
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Relation between Fluid Pressure Drop and Shear Stress
o friction force leads to the decrease of the pressure along the pipe line
o Straight pipe with constant diameter β pressure at inlet > outlet
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Centrifugal Pump
Gas Blower
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Fluid Flow Friction
o For constant x and position, the change of axial velocity along radial dimension r:
o Due to contact between fluid and stationary wall β the wall surface will give Fw force in the opposite direction with the fluid velocity
o Friction force Fs exists due to position difference between r and r+ r
o Shear Stress
o fluid flow towards x direction, cylindrical coordinate (x-r-)
o The axial velocity at radial position r and r+r dan lim
Ξrβ0
π’π₯|π+Ξr β π’π₯|
Ξr=ππ’π₯ππ
π’π₯|π+Ξrπ’π₯|
Shear Stress
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Newtonβs Lawo Correlate shear stress and
velocity gradiento For Newtonian flow β linear
correlation:
The friction area on fluid layer at layer r and length L is defined as:
π¨π = ππ ππ³ Shear stress is defined as friction force Fs per friction area. For flow that goes to x direction with velocity Ux , Ux velocity changers along radial dimension r, so the shear stress Ο rx
is defined as:
πππ =ππ
ππ ππ³
o πππ = βππππ
ππ
Fluid Flow Friction
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At the pipe center line, r = 0, so the velocity gradient = 0
At the pipe wall,r = R, velocity gradient is maximum, shear stress at the wall surface is defined as:
πππ
ππ= π, πππ = π
ππ = βππππππ
|π=πΉ
Fluid Flow Friction
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Force Balance
πΉπ₯|π₯ = π|π₯π΄|π₯πΉπ₯|π₯+Ξx = π|π₯+Ξxπ΄|π₯ = π|π₯+Ξxππ
2
πΉ = 0
πΉπ₯|π₯ β πΉπ₯|π₯+Ξx β πΉπ = 0
πΉπ = πΉπ₯|π₯ β πΉπ₯|π₯+ΞxπΉπ = π|π₯π΄|π₯ β π|π₯+Ξxπ΄|π₯+ΞxπΉπ = (π|π₯ β π|π₯+Ξx) π΄|π₯
Ξp = π|π₯+Ξx β π|π₯πΉπ|π₯ = πππ₯2ππΞx
π΄π₯ = ππ2
πππ₯2ππΞx = π|π₯ β π|π₯+Ξx ππ2
πππ₯ =π
2βπππ
ππ₯
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Friction Heat
o The friction force in the fluid flow is transformed into friction heat
o The friction heat(Ef) is defined as friction force (Ff) multiplied by the fluid mileage (Ξx):
o Expressed as friction heat rate:
o Friction heat rate per mass flow rate is defined as:
o Friction heat at pipes wall:
o Energy balance (including shaft work and friction):
π¬π = πππ«π±
αΆπ¬π = ππππ
ππαΆπ¬π = ππππ
ππ =αΆπ¬π
αΆπ¦ππ =
βπ«π©π
π
ππ = ππ³
π«
πππ
ππ«π +π«π
π+ π«
ππ
π= ππ β ππ
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Moody/ Darcy-WiesbachFriction Factor
Fanning Friction Factor (fF)
Friction Factor
Friction heat per mass flow unit
ππ =ππ
πππππ
ππ = ππ³
π«
πππππππ
π
πππ
ππ = ππ³
π«ππ
π
πππ
ππ = ππ΄π³
π«
π
πππ
ππ΄ = πππ
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Fanning Friction Factor
Average velocity
Friction Factor Correlation with Laminar Flow
Moody Friction Factor
π =π
πππ
βπ«ππ
π³π«π
ππ =ππ
π΅πΉπ
ππ΄ =ππ
π΅πΉπ
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Experiment by Nikurdase (1933) βfriction factor is affected by Reynolds number and relative pipe surface roughness:
π = π π΅πΉπ
πΊ
π«
Friction Factor
Friction Factor Correlation with Turbulent Flow
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Correlation Equation for Friction Factor
Prandtl Equation
For smooth pipe:
Coolbrook and White Equation
Nikurdase Equation
For very high NRe:
ππ΄ = βπ π₯π¨π π. ππ
π΅πΉπ ππ
βπ
ππ = βπ π₯π¨π π. πππ
π΅πΉπ ππ
βπ
ππ = βπ π₯π¨π πΊ
π. ππ«
βπ
ππ = βπ π₯π¨π π. πππ
π΅πΉπ ππ+
πΊ
π. ππ«
βπ
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Value of πΊ
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Commercial Pipe Sizes
(i) Nominal size D (usually in inch with the symbol β)
(ii) Outside diameter Do (usually in inch)(iii) Schedule number Sch (dimensionless)(iv) Wall thickness, ππ‘β (in inch)(v) Inside diameter Di (in inch)
Commercially, pipe sizes are expressed as parameters below:
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Commercial Pipe Sizes
(cont.)
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Fluid Flow in Straight Pipe Line and Constant Diameter
oVolumetric flowrate
oVariables need to be considered:
αΆβ¨ =π
ππ«ππ
(i) Fluid volume flow rate, αΆβ¨(ii) Internal pipe diameter diameter, D(iii) Pressure drop: βΞp = ππππππ‘ β
πππ’π‘πππ‘
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oPressure drop calculation based on energy balance equation
π1π+1
2π’12 + ππ§1 =
π2π+1
2π’22 + ππ§2 + ππ
π’1 = π’2 = π’
ππ = 4ππΉπΏ
π·
1
2π’2
απ1 β π2
π= 4ππΉ
πΏ
π·
1
2π’2 + π(π§2 β π§1
αβΞp = π1 β π2 = 4ππΉπΏ
π·
1
2ππ’2 + ππ(Ξz
α4ππΉπΏ
π·
1
2ππ’2 = (π1 β π2) + ππ(Ξz
π’ = π·
2ππΉπΏπαΎ(π
1β π2) + π(Ξz)
αΆβ¨ =π
4π·2π’
αΆβ¨ =π
4π·2
π·
2ππΉπΏπαΎ(π
1β π2) + π(Ξz)
4ππΏ
π·
1
2π
αΆβ¨π4π·
2
2
= (π1 β π2) + ππΞz
π· =32ππ αΆβ¨2 πΏ
)π2(π1 β π2 β ππΞz
15
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Exercise
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Solution
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Solution
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Solution
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Friction by Pipe Accessories (Fitting)
Valve
Enlargement
Contraction
Flow Velocity
β¦etc.
Flow Direction
β¦etc.
FITTINGS FUNCTION
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Fitting
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Strainer
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Gate Valve
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Plug Valve
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Globe Valve
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Angle Valve
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Butterfly Valve
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Ball Valve
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(Lift) Check Valve
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(Swing) Check Valve
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o Installation of pipe accessories (fitting) will cause pressure drop of the pipe line
oPressure difference caused by fitting β equivalent with a straight pipe at diameter D that has length at the value of Le β equivalent length
oPressure drop of a fitting is defined as:
Friction Loss by Equivalent Length
βπ«ππ
π= πππ
π³ππ«
ππ
ππππ
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oPressure drop due to fitting installation can be related to the loss of kinetic energy when fluids flow through the fitting
oFitting constant (KL) is expressed as:
oCorrelation:
Friction Loss Due to Kinetic Energy Loss
βπ«ππ
π= π²π³
ππ
π
π²π³ = ππππ³ππ«
π³π =π³ππππ
π«
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Friction Factor due to Geometry Changes
oD1<D2 β u1>u2 β p1<p2
oEnergy loss due to friction:
oThe mass flow rate is constant, thus:
ππ =π1 β π2
π+1
2αΎu1
2β u2
2
ππ = 1 βD14
D24
1
2u12 β
π1 β π2π
πΆπ =π2 β π112πu1
2
ππ = 1 βπ·1π·2
4
β πΆπ1
2u12
πΎπΏπ = 1 βπ·1π·2
4
β πΆπ
ππ = πΎπΏπ1
2u12
π΄π =D14
D24 πππ
)πΎπ π = π(π΄π
Sudden Enlargement:
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Friction Factor for Sudden Enlargement
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Pressure Drop Evaluation for Fluid Flow in the Pipe Systems with Fittings
o A pipe line is constructed by N1 segments of straight pipes with diameter D1. Fitting like valves, elbows, etc are installed between segments. The pressure drop for this pipe line systems is determined using the following equation:
o The pipe line above is connected to second pipe line system with diameter D2 using a connector. The second pipe line system has N2 segment of straight pipe and M2 fittings. The pressure drop for the second pipe line system is determined using the following equation:
πππ·1 =βΞππ
ππ·1
=
π=1
π1
4 ππΏππ
π·1
1
2π’π·12 +
π=1
π1
πΎπΏπ1
2π’π·12
πππ·2 =βΞππ
ππ·2
=
π=1
π2
4 ππΏππ
π·2
1
2π’π·22 +
π=1
π2
πΎπΏπ1
2π’π·22
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oThe friction heat due to diameter change in the pipe line systems (from D1
to D2) is expressed as:
oTotal friction heat:
oThe pressure difference between inlet (point 1) and outlet (point 2) of the pipe line systems is determined using the following equation:
Pressure Drop Evaluation for Fluid Flow in the Pipe Systems with Fittings
βΞππ
ππ·1βπ·2
= πΎπΏπ’π·12
2
πππ‘ =βΞππ
ππ·1
+βΞππ
ππ·1βπ·2
+βΞππ
ππ·2
π1 β π2π
=1
2u22 β
1
2u12 + π π§2 β π§1 + πππ‘
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oConservation of mass:
oFor constant density
oEnergy balance equation for a pipe segment I with diameter Di and length Li is expressed as:
Fluid Flow Calculation for Complex Piping System
π’π = 4ππ
ππ·π2
πππ‘ = 4ππΉπΏππ·π
π’π2
2πβπ§ +βπ
π+ πππ‘ = 0
αΆπ4 = αΆπ2 + αΆπ3
αΆπ4 = αΆπ2 + αΆπ3
where
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oMass balance:
oTotal pressure drop:
Fluid Flow Calculation for Complex Piping System
αΆπ1 = αΆπ2 = αΆπ3 αΆ= π4 = αΆπ8
π1 β π0 = π1 β ππ΄ + ππΆ β ππ· β ππ· β ππ΅ β ππ΅ β π0
Ξπ π‘ =
π
π
Ξπ π
or:
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o Pressure drop calculation:
o Total pressure drop calculation:
ππ΄ β ππΆ + ππ β ππ· + ππ· β ππ΅= ππ΄ β ππΈ + ππΈ β ππΉ + ππΉ β ππ΅= ππ΄ β ππ΅
π1 β π0 = π1 β ππ΄ + ππ΄ β ππ΅ β ππ΅ β π0
o Mass balance:
Fluid Flow Calculation for Complex Piping System
αΆπ1 = αΆπ2 + αΆπ5
αΆπ2 = αΆπ3 + αΆπ4
αΆπ5 = αΆπ6 + αΆπ7
αΆπ4 + αΆπ7 = αΆπ8
αΆπ1 = αΆπ8
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Example
?
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Solusi
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Solusi
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Friction in Non-Circular Pipes
oNon-circular βcross section area of the pipe is not a circle
oEquivalent diameter or hydraulic diameter is used
oThe Reynolds number is defined as:
o For pipes with rectangular cross section area:
π·π =4 π₯ ππππ π π πππ‘πππ ππππ
πππ‘π‘ππ πππππππ‘ππ=4π΄
ππ
ππ π =ππ’π·ππ
π·π =4π΄
π€π=4π·2
4 πΌ βsin 2πΌ2
πΌπ·= π· 1 β
sin 2πΌ
2πΌ
π·π =4π€β
)2(π€ + β
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oFriction factor for non-circular pipes
oDetermination of friction factor uses this following equation:
ofF is calculated using equivalent diameter
oknc (non circular factor) β function of the size and cross section geometry
Friction Factor for Non-Circular Pipes
ππππΉ = πππππΉ
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Friction Factor for Non-Circular Pipes
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Exercise
Natural gas will be transferred from a gas well located in Sengkang to the city of Pare-Pare, South Sulawesi. This well production flowrate is 50
MMSCFD. The pipe length required for this is 70 km long. Sengkang is 300 m higher than Pare-Pare. Natural gas has a molecular weight of 17. The gas temperature in the pipe is assumed to be fixed at 30 oC. The gas inlet pressure of this pipe is 60 kgf/cm2 gauge. Determine the gas outlet
pressure at various pipe diameters of 5, 10, and 15 inches. Graph the relationship between the pipe outlet pressure and the pipe diameter. The
allowable pipe roughness Ξ΅/D is 0.002.
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Thank You