FLUID FLOW. Note that the balance is per unit mass. In differential form:

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1 Mechanical Energy Balance FLUI FLOW gδz ρ V Δ Wo F potential expansion ketic work added/ sum o energy work energy change subtracted by riction change pumps or losses compressors Note that the balance is per unit mass. In dierential orm: ( g dz V dv δf δ ) ρ W o ChE esign I

2 Mechanical Energy Balance FLUI FLOW ivide by, (L is the length o the pipe) Tot ρg dz ρv dv δf ρ δl δw ρ δl o or: Tot elev accel rict W o δ δl is usually ignored, as the equation applies to a pipe section. The above equation is an alternative way o writg the mechanical energy balance. It is not a dierent equation ChE esign I

3 Potential energy change: Mechanical Energy Balance φ dz dz g g sφ Friction Losses: Fanng equation: df V This equation applies to sgle phase luids. The riction actor is obtaed rom the Moody iagram (see PT page 487). ChE esign I

4 Mechanical Energy Balance Friction actor equations. (Useul or computers and Excel) 16 Re Lamar Flow a Re Smooth pipes: a 0. Iron or steel pipes: a log 10 ε Re Colebrook equation or turbulent low. Equivalent length o valves and ittgs. Pressure drop or valves and ittgs is accounted or as equivalent length o pipe. See PT&W or a table contag these values (page 490). ChE esign I

5 Mechanical Energy Balance - Fluid Flow Scenario I Need pressure drop known pipes (pump or compressor is not present.) Incompressible Flow a) Isothermal (ρ is constant) Tot ρ g dz V δf δl or a ixed ρ V constant dv 0 dv Integral orm: Δp ρ g ΔZ L L b) Nonisothermal It will not he a big error i you use ρ(t erage ) ChE esign I V e F

6 Mechanical Energy Balance - Fluid Flow Compressible Flow a) Relatively small change T (known) For small pressure drop (somethg you can check ater you are done) can use Bernoulli and anng equation as ollows V g dz v d g 1 V dz dv v v v V Velocity Mass low (Kg/hr) Note: ChE esign I V δf δf v v Speciic volume (m 3 /Kg)1/ρ Cross sectional area v

7 Mechanical Energy Balance - Fluid Flow Compressible Flow. Relatively small change T (known) g 1 dv δf dz v v v v Now put tegral orm g dz v v dv V 1 ssume: T T T ρ ρ( T, P ) ρ( T, P ) ( T, P ) ( T, P ) ChE esign I

8 Mechanical Energy Balance - Fluid Flow Compressible Flow. Relatively small change T (known) The tegral orm will be: Recall: ρ gδz p v v Z RT M V ln V L M: Molecular weight Then: v Z RT pm and v M Z RT p M Z RT ( p p ) ChE esign I

9 Mechanical Energy Balance - Fluid Flow Compressible Flow. Relatively small change T (known) Substitute the tegral orm: ρ g Δz M Z RT ( p p ) V ln V L Sce: we get V V Z Z T T p p p Z RT L ZT p p ln ρ g Δz M ZT p 1 ChE esign I

10 Mechanical Energy Balance - Fluid Flow Compressible Flow. Relatively small change T (known) This is an equation o the orm: p F ( p ) lgorithm: a) ssume (1) p b) Use ormula to get a new value c) Contue usg p F ( ( ) p ) ( i 1) i p F ( (1) ) () p ( i 1) ( i) until p p ε ( i) p OR BETTER: Use Solver EXCEL, or even use PRO II, or any other luid low simulator. ChE esign I

11 Mechanical Energy Balance - Fluid Flow Compressible Flow. Relatively small change T (known) The above algorithm can be applied or cases where p p p For longer pipes, break the pipe to smaller sections ChE esign I

12 Burstg pressure o a pipe P S b PIPIN STRENTH T t m m m Mean iameter t m Wall Thickness S t Tensile Strength (properties o material and abricate) P b Burstg pressure P P b P - P P ChE esign I

13 PIPIN STRENTH Sae Workg Pressure P S S S t We substitute with a sae workg stress, S s < S T Range o S s psi (T < 50 o F) m m (Low end) butt-welded lap-welded (High end) Schedule o a Pipe (merican Standard ssociation) There are 10 Sch numbers: 10, 0, 30, 40, 60, 80, 100, 10, 140, 160 ChE esign I

14 PIPIN STRENTH Schedule o a Pipe (merican Standard ssociation) You speciy a pipe by givg the diameter and the Schedule et pressure side, P (psia) P S P α 1000 P S ; S S > Characteristic o pipe (6500 SS 9000 psi) Pick lower possible Sch standard. Sch > a ChE esign I