REE 307 Fluid Mechanics II. Lecture 1. Sep 27, Dr./ Ahmed Mohamed Nagib Elmekawy. Zewail City for Science and Technology


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1 REE 307 Fluid Mechanics II Lecture 1 Sep 27, 2017 Dr./ Ahmed Mohamed Nagib Elmekawy Zewail City for Science and Technology
2 Course Materials drahmednagib.com 2
3 COURSE OUTLINE Fundamental of Flow in pipes Losses in valves and connections. Analysis of pipe networks (Pipes in Series Pipes in Parallel  Branching Pipes Networks of Pipes) The Boundary layer The Differential and Integral Equations of the Boundary Layer The Displacement and Momentum Thickness Approximate Solutions of The Incompressible Laminar and Boundary Layers Unsteady Flow in Conduits (Oscillation of Liquid in a UTube, Water Hammer Phenomena, Surge tanks). The NavierStokes equations, Stokes' hypothesis 3
4 References Munson, Fundamental of Fluid Mechanics, 7th Edition White F. M., Fluid Mechanics, 8th Edition Cengel Y., Fluid Mechanics Fundamentals and Applications, 3rd Edition Menon, Gas Pipeline Hydraulic Gary Z. Waters, "Analysis and control of unsteady flow in pipelines,
5 Prerequisite Course: Fluid Mechanics  ENGR 207 Classification of fluids  Definition of viscosity surface tension  Hydrostatic pressure Buoyancy  Bernoulli s equation and its application for ideal fluid  stream lines velocity and acceleration in two dimensional flow Differential Analysis of fluid flow (continuity equation NavierStokes equations)  Moody diagram  Incompressible Flow through Networks of Pipes Unsteady Flow in Conduits 5
6 Fundamentals of Flow in Pipelines 1. Incompressible flow through pipes 2. Branching Pipe system 3. Network pipe system 4. Unsteady flow 5. Compressible Flow in Pipes. 6
7 Revision Fluid Mechanics Mechanics Fluid Statics Compressible Dynamics Incompressible Kinematics 7
8 Revision Mechanics Statics: Concerned with the analysis of loads on physical system in static equilibrium Dynamics: Concerned with the effect of forces on the motion of objects Kinematics: Concerned with the spacetime relationship of a given motion without considering the origins of forces 8
9 Revision Fluid Liquids take the shape of the container and have a free surface Gases: take the shape of the container but have no free surface 9
10 Revision Fluids can sustain tension, compression, but can not withstand shear stresses, and therefore it is subjected to a continuous deformation. Solids bear tension, compression and shear stresses, and a deformation occurs in matter in case of failure: 1. Fracture 2. Yield 10
11 Revision Fluids Gases (compressible fluids) dρ dp 0.0 Liquids (Incompressible fluids) dρ dp = 0.0 At lower Mach numbers (<0.3), Gases could be considered an incompressible fluid. 11
12 Revision Fluid Mechanics Fluid Statics Fluid Kinematics Fluid Dynamics Aerostatics Aerodynamics (Gas Dynamics) Hydrostatics Hydrodynamics Hydraulics 12
13 Revision 13
14 Revision Continuity Equation m. = constant A V = constant Momentum Equation Fluid Dynamics P ω + Z + V2 2g = const F = ma 14
15 Revision Fluid Properties Density (ρ), Viscosity (υ), Surface tension (σ) Flow Properties Pressure (P), Velocity (V) 15
16 Revision Assumptions 1. Incompressible Flow 2. 1D Flow 3. Single Phase Flow 4. Steady Flow t Fluid Property = 0 16
17 Revision Pressure Pressure = Force/Area psi = ponds per square inch Pa = pascals = N/m 2 bar = 10 5 pascals atm = pascals 0 psi gauge pressure= 14.7 psi absolute 17
18 Revision Pressure Pressure ls also reported as height a liquid (water or mercury) will rise in A column with that pressure at the base of the column. ft or m water in or mm mercury 18
19 Friction Loss in pipes 19
20 Head Loss Equations Head loss equations are empirical relationships that predict head loss in pipes (or other conveyances). The four most common equations are: o DarcyWeisbach: Most accurate and flexible but relatively difficult to apply. o HazenWilliams: Most commonly used in water network modeling. o Colbrook: Most commonly used in network modeling. o Manning: Widely used for wastewater, drainage and open channel flow. 20
21 DarcyWeisbach h l = flv2 2gd h l = 0.8 flq2 gd 5 h = head loss f = friction factor L = length d = diameter V= velocity g = acceleratlon due to gravity Friction factor depends on pipe roughness and Reynolds Number, Re = VD/υ Friction factor can be estimated from a Moody diagram. However, the difficulty wlth the use of the Darcy Weisbach equation ls that the frlction factor ls not constant for a given pipe. 21
22 Moody Chart 22
23 HazenWilliams h = kl d 1.16 V C 1.85 h = head loss d = diameter ( ft or m) k= 6.79 for V in m/s, D in m k= 3.02 for V in ft/s, D in ft V= velocity C= HazenWilliams factor L = length 23
24 HazenWilliams h = kl d 1.16 V C 1.85 C can be estimated from field measurements. The table on the next page provides initial estimates for C for pipes of different material, age and diameter. These estimates should be used with care and field checked when possible. Cfactors range from 150 for very smooth pipes to 20 for very rough pipes. For rough pipes at high velocity, the Cfactor can vary significantly and should be field tested. 24
25 HazenWilliams 25
26 Manning Equation V = C o R2 Τ 3 h L 0.5 /n C o = 1.49 for English units and 1.0 for metric units V= velocity (ft/s or m/s) R = Hydraulic Radius = Cross sectional area / wetted perimeter (ft or meters) h = head loss ( ft or m) L = length n = Manning s roughness coefficient as follows 26
27 Manning Equation n = Manning s roughness coefficient as follows 27
28 Comparison of friction equations Darcy Weisbach Manning HazenWilliams All fluids Water only Water only Difficult to get f Easy to get n Easy to get C Good for all Roughness Rough flow Smooth flow Not commonly used Commonly used Commonly used 28
29 Minor Losses Minor losses caused by fittings, bends, valves Described by coefficient K In h = KV 2 /2g Where, K = minor loss coefficient h = head loss due to minor loss See following table for K representative values 29
30 Minor Losses Coefficient Table [K] 30
31 Minor Losses Coefficient Table [K] 31
32 Minor Losses Coefficient [K] fr valves For valves, a flow coefficient C v is frequently given which defines the flow (gpm) that will pass through a valve at a pressure drop of 1 psi. C v can be converted to K, the minor loss coefficient: K = 888D4 C v 2 D is diameter in inches. C v is a function of D, while K is independent of D. 32
33 Minor Losses Minor loss can also be given in terms of equivalent length of pipe that would give same head loss. (L/D) = K/f Where, L = length added to account for minor loss D = pipe diameter f = Darcy Weisbach friction factor 33
34 The Energy and Hydraulic Gradient Lines The Energy Line is a line that represent the total head available to the fluid The Hydraulic Grade Line is a line that represent the total head available to the fluid minus the velocity head 34
35 Pipeline Design Why do we need to study pipelines? Pipelines affect daily lives in most parts of the world. Modern people's lives are based on an environment in which energy plays a predominant role. Oil and gas are major participants in the supply oj ener9y, and pipelines are the primary means by which they are transported. 35
36 Major factors that affect pipeline system design: Fluid properties Design conditions Supply and demand magnitude/locations Codes and standards Route, topography, and access Environmental impact Economics Hydrological impact Seismic and volcanic impacts Materiai Construction Operation Protection Longterm integrity 36
37 Classification of Pipelines: 37
38 Classification of Pipelines: 38
39 How to design a pipeline? 1. Select pipe material 2. Select/Design pipe diameter 3. Select pipe thickness 4. Select pumping/ compressor unit 5. Select primover (Electric motor/ diesel engine/ gas turbine) 39
40 1. Selecting pipe material When we select the material we must not that: 1. No chemical reaction between pipe material and fluid material (erosion, corrosion) 2. Low roughness 3. Low cost 40
41 2. Selecting pipe diameter V = Q A Where V ranges between 1 and 3 m/s, because: 1. At high velocities (high pressure drop, high friction loss) 2. At low velocities (Deposition of suspending material in the pipe) 41
42 3. Selecting pipe thickness t = PD 2S t Where t = Maximum required thickness, mm P= Maximum allowable working pressure, Mpa D= Outside diameter of cylinder, mm S t = Maximum allowable stress value at the operating temperature of the metal 42
43 4. Selecting pipe thickness Power required by the pump determined by: 1. Power loss 2. Starting pressure head 3. Flow properties Where Power = ωqh η 43
44 5. Selecting Primover Electric motor, Gas turbine, Steam turbine, Diesel engine,.. etc Selecting the primover depends on: 1. Speed 2. Used source of energy 3. Size 44
45 Branched Pipe System Pipe in Series Pipe in Parallel 45
46 Branched Pipe System Supply at several points 46
47 Branched Pipe System Three Tank Problem 47
48 Branched Pipe System Three Tank Problem 48
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