NCEES Fundamentals of Engineering (FE) Examination Review Fluid Mechanics, Hydraulics and Hydrologic Systems
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1 NCEES Fundamentals of Engineering (FE) Examination Review Fluid Mechanics, Hydraulics and Hydrologic Systems Instructor: Dr. Marcio H. Giacomoni 1
2 Introduction The FE examination is an 8-hour suppliedreference examination: 120 questions in the 4-hour morning session 2 minutes per question 60 questions in the 4-hour afternoon session. 4 minutes per question 2
3 FE Supplied-Reference Book It can be downloaded at: y-materials/download-fesupplied-referencehandbook/ It is very important to be familiar with the Reference book To know exactly where each topic is located 3
4 Morning Session 120 questions divided in 12 topic sections X. Fluid Mechanics (7% - 8 to 9 questions) A. Flow measurement B. Fluid properties C. Fluid statics D. Energy, impulse, and momentum equations E. Pipe and other internal flow 4
5 Afternoon Session 60 questions divided in 9 sections II. Hydraulics and Hydrologic Systems (12% - 7 to 8 questions) A. Basic hydrology (e.g., infiltration, rainfall, runoff, detention, flood flows, watersheds) B. Basic hydraulics (e.g., Manning equation, Bernoulli theorem, open-channel flow, pipe flow) C. Pumping systems (water and wastewater) D. Municipal water distribution systems E. Reservoirs (e.g., dams, routing, spillways) F. Groundwater (e.g., flow, wells, drawdown) G. Sewer collection systems (storm and sanitary) 5
6 UNITS The FE examination uses both the International System of Units (SI) and the US Customary System (USCS). See page 19 of the FE Supplied-Reference Book In the USCS system of units, both force and mass are called pounds. Therefore, one must distinguish the pound-force (lbf) from the poundmass (lbm). 6
7 UNITS 7
8 Important Constants Constant Symbol SI USCS Acceleration of Gravity g 9.81 m/s² ft/s² Atmospheric Pressure P atm kpa 14.7 lbf/in² or psia Vapor Pressure P v 2.34 kpa 0.34 lb/in² or psia Water Density ρ 1000 Kg/m³ lbm/ft³ Sea Water Density ρ sea 1025 Kg/m³ 64 lbm/ft³ Air Density ρ air 1.2 Kg/m³ lbm/ft³ Specific Weight of Water γ 9810 N/m³ 62.4 lbf/ft³ 8
9 Properties of Water (Page 70) FE REVIEW Fluid Mechanics, Hydraulics and Hydrologic Systems FALL
10 Properties of Water (Page 70) FE REVIEW Fluid Mechanics, Hydraulics and Hydrologic Systems FALL
11 CONVERSION FACTORS (page 20) Dynamic Viscosity Kinematic Viscosity 11
12 CONVERSION FACTORS (page 20) 12
13 Fluid Mechanics (Page 62 to 72) FE REVIEW Fluid Mechanics, Hydraulics and Hydrologic Systems FALL
14 Density, Specific Volume, Specific Weight, and Specific Gravity (Page 62) If 10 m³ of a liquid weights 60 kn, calculate its specific weight, density and specific gravity. V = 10 m 3, W = 60 kn Specific weight, g = W/V = 60 kn/10 m 3 = 6 kn/m 3 = 6000 N/m 3 Density, r = g/g = 6000 N/m 3 /9.81 kn/m 3 = kg/m 3 Specific gravity, s.g. = g/g w = 6 kn/m 3 /9.81 kn/m 3 =
15 Stress Pressure and Viscosity (Page 62) 15
16 Principles of Fluid Mechanics Viscosity Is the measure of a liquid resistance to shear or angular deformation Is a measure of fluid s resistance to flow Dynamic Viscosity (μ mu) τ = μ dv fluid) dy v (Shear stress between two thin sheets of Units: N.s or centipoise (cp) 1 cp = 1 N.s m 2 m 2 v
17 Viscosity τ t = μ dv dy = F A dv dy = v δ F A = μ v δ 17
18 Surface Tension and Capillarity (Page 62) 18
19 The Pressure Field in a Static Liquid (Page 62) 19
20 Pressure and Pressure Forces in Static Fluids Hydrostatic Forces: The hydrostatic force on any submerged plane surface is equal to the product of the surface area the pressure acting at the centroid of the plane surface F = γysinθda = γsinθ yda = γsinθy c A A A F = γh c A 20
21 Pressure and Pressure Forces in Static Fluids Hydrostatic Forces: 21
22 Example Determine the hydrostatic force and the location of the center of pressure on the 25 m long dam shown in the Figure The face of the dam is at an angle of 60º. Assume 20ºC. 22
23 Example F = γh c A γ = 9.79 kn m 3 A = 25 m 5 sin60 h c = 2.5 m m = m2 L = 25 m F = 9.79 kn m 3 2.5m 167.2m2 = 4092 kn y = 5/sin60 h c = 2.5 m 23
24 Forces on Submerged Surfaces and the Center of Pressure (Page. 63) 24
25 Forces on Submerged Surfaces and the Center of Pressure (Page 63) 25
26 Archimedes Principle and Buoyancy (Page 63) 26
27 One Dimensional Flows (Page 63) 27
28 One Dimensional Flows (Page 64) 28
29 One Dimensional Flows (Page 64) 29
30 Reynolds Number (Page 65) 30
31 Hydraulics and Energy Grade Lines (Page 65) 31
32 Steady, Incompressible Flow in Conduits and Pipes (Page 65) Z =200 m Q =? Z =180 m 32
33 Steady, Incompressible Flow in Conduits and Pipes (Page 65) 33
34 Steady, Incompressible Flow in Conduits and Pipes (Page 65) 34
35 Moody Diagram (Page 71) FE REVIEW Fluid Mechanics, Hydraulics and Hydrologic Systems FALL
36 Steady, Incompressible Flow in Conduits and Pipes (Page 65) 36
37 Steady, Incompressible Flow in Conduits and Pipes (Page 65) 37
38 Pump Power Equation (Page 66) 38
39 Flow in Noncircular Conduits (Page 65) 39
40 Flow in Noncircular Conduits (Page 65) 40
41 Flow in Noncircular Conduits (Page 65) 41
42 Minor Losses in Pipe Fittings, Contractions and Expansions (Page 65-66) 42
43 Performance of Components (Fans, Pumps and Compressors) Mechanical Engineering (Page 241) 43
44 Example 44
45 Centrifugal Pump Characteristics (Page 241) 45
46 The Impulse-momentum Principle (Page 66) 46
47 The Impulse-momentum Principle (Page 66) 47
48 The Impulse-momentum Principle (Page 66) 48
49 Jet Propulsion (Page 66) 49
50 Multipath Pipeline Problems (Page 67) 50
51 Multipath Pipeline Problems (Page 67) 51
52 Fluid Measurements (Page 67) 52
53 Manometers (Page 68) 53
54 Manometers (Page 68) 54
55 Barometers (Page 68) A weather broadcaster states that the barometer reads inches of mercury and is steady. Calculate the atmospheric pressure in psi if the specific gravity of mercury is 13.6 p atm = lbf ft³ p atm = p v + γ mer h p atm = p v + SG γ w h 1 144in 2 /ft p atm = lbf in2 = psi in 12in/ft 55
56 Venturi Meters (Page 68) 56
57 Orifices (Page 68) 57
58 Submerged Orifices (Page 68) 58
59 Orifice Discharging Freely into Atmosphere (Page 69) 59
60 Dimensional Homogeneity and Dimensional Analysis (Page 69) 60
61 Similitude (Page 69) 61
62 Dimensional Analysis: Reynolds and Froude Numbers R e = VLρ μ = VL ν F r = Reynolds number represents the ratio of inertial force to viscous force It is useful in pressure conducts and groundwater hydraulics The Froude number represents the ratio of inertial force to gravitational force Useful in open channel flow in which gravitational forces tend to dominate. V gl 62
63 Dimensional Analysis 63
64 Similitude 64
65 Hydraulics and Hydrologic Systems (Pages 159 to 161) 65
66 Hydrology NRCS (SCS) Rainfall-Runoff 66
67 Hydrology Rational Formula 67
68 Hydrology Rational Formula 68
69 Rational Formula 69
70 Hydrology Unit Hydrograph 70
71 Groundwater Darcy s Law 71
72 Groundwater Well Drawdown 72
73 Sewage Flow Ration Curves 73
74 Sewage Flow Ration Curves 74
75 Sewage Flow Ration Curves 75
76 Sewage Flow Ration Curves 76
77 Sewage Flow Ration Curves 77
78 Hydraulic-Elements Graph for Circular Sewers V f, Q f, A f and R f Are velocity, flow, area and hydraulic radius for full pipe 78
79 Hydraulic-Elements Graph for Circular Sewers 79
80 Hydraulic-Elements Graph for Circular Sewers V f, Q f, A f and R f Are velocity, flow, area and hydraulic radius for full pipe 80
81 81
82 Open-Chanel Flow Specific Energy Compute the critical depth for a 8-ft wide rectangular channel with a discharge of 100 cfs. Q 2 g = A3 T = T y 3 T = 8 y = 83 T T 3 = T = /3 8 2 = 1.61ft 82
83 Open-Chanel Flow Specific Energy 83
84 Open-Chanel Flow Specific Energy 84
85 Open Channel Flow Uniform Flow 85
86 Open Channel Flow Uniform Flow 86
87 Flow Classification Uniform Flow Non-Uniform Flow Steady Flow Unsteady Flow 87
88 Open Channel Flow Weir Formulas 88
89 Open Channel Flow Hazen-Williams Eq. 89
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