Civil Engineering Capsule PDF (UPSSSC SSC)

Youth Competition Times Civil Engineering CAPSULE Useful for All Competitive AE/JE Exam : UPPSC AE UKPSC AE BPSC AE CGPSC AE MPPSC AE RPSC AE UPSSSC SSC JE DMRC JE LMRC JE JMRC JE BMRC JE DSSSB JE UP Jal Nigam UKSSSC JE RSMSSB JE MPPEB SUB ENGINEER HPSSC JE HSSC JE Punjab J...

Youth Competition Times Civil Engineering CAPSULE Useful for All Competitive AE/JE Exam : UPPSC AE UKPSC AE BPSC AE CGPSC AE MPPSC AE RPSC AE UPSSSC SSC JE DMRC JE LMRC JE JMRC JE BMRC JE DSSSB JE UP Jal Nigam UKSSSC JE RSMSSB JE MPPEB SUB ENGINEER HPSSC JE HSSC JE Punjab JE CGPEB SUB ENGINEER BSSC JE DRDO JE ISRO JE UPPCL AE/JE UPRVUNL AE/JE JVUNL JE SAIL JE GAIL JE BHEL JE NTPC JE DFCCIL COAL INDIA LTD. JE RRB JE etc. Chief Editor Mr. Anand Mahajan Compiled & Written by Er. Maneesh Kr. Yadav Er. Pradeep Kumar Gupta Er. Sanjeet Maurya, Er. Rohit Singh Computer Graphics by Balkrishna, Charan Singh Editorial Office Youth Competition Times 12, Church Lane Prayagraj-211002 Mob. : 9415650134 Email : [email protected] website : www.yctbooks.com Publisher Declaration Edited and Published by A.K. Mahajan for YCT Publications Pvt. Ltd. and printed by Roop Printing Press, Prayagraj. In order to publish the book, full care has been taken by the editor and the publisher, still your suggestions and queries are welcomed. Rs. : 60/- In the event of any dispute, the Judicial area will be Prayagraj.  INDEX Building Material -------------------------------------------------------------3 Concrete Technology ------------------------------------------------------ 10 CPM & PERT --------------------------------------------------------------- 12 Building Construction and Maintenance Engineering ------------------ 13 Fluid Mechanics & Hydraulic Machine --------------------------------- 15 Strength of Materials ------------------------------------------------------- 28 Applied Mechanics --------------------------------------------------------- 34 Soil Mechanics ------------------------------------------------------------- 36 Highway Engineering ------------------------------------------------------ 43 Railway Engineering ------------------------------------------------------- 48 Bridge Engineering --------------------------------------------------------- 50 Airport Engineering -------------------------------------------------------- 51 Tunnel Engineering -------------------------------------------------------- 52 Reinforced Cement Concrete --------------------------------------------- 53 Steel Structure--------------------------------------------------------------- 58 Structure Analysis ---------------------------------------------------------- 62 Building Estimate, Costing & Evaluation------------------------------- 64 Public Health Engineering ------------------------------------------------ 68 Surveying Engineering ---------------------------------------------------- 70 Irrigation & Hydrology Engineering ------------------------------------ 77 Civil Engineering Capsule 2 YCT  Civil Engineering Capsule BUILDING MATERIALS Rock minerals- Quartz, Mica, Gypsum, Dolomite, Amphibole, Calcite, Feldspar etc. Hardness of stone based on Moh's scale- Talc 1 Scratched Gypsum 2 by the finger nail Calcite 3 Scratched Fluorite 4 by Apatite 5 knife Feldspar 6 Scarcely scratched Quartz 7 by knife Topaz 8 Not scratched Corundum 9 by Diamond 10 knife Properties of Minerals- Measurement of the capability of some minerals to split along Cleavage certain planes parallel to the crystal faces Colour of the mineral in powder Streak form Shine on the surface due to Classification of Rocks on the Basis of Mineral Lustre reflection of light of a mineral Available- Classification of Rocks- Name of Rock Example Mono mineralic Rocks Quartzite, Marble & (Composed of only one Gypsum mineral) Granite, Trap, Basalt, Shale, Polymineralic Rocks Sand Stone, Shale, Slate Metamorphism of Rocks- Original Rock Metamorphic form Granite Gneiss Syenite Gneiss Sand Stone Quartzite Lime Stone Marble Marl Marble Dolomite Marble Shale Slate Mud Stone Slate Dolerite/Basalt Schist Civil Engineering Capsule 3 YCT  Explosive Material Used in blasting- Descriptive Elasticity (kg/cm2) Name of Chemical Composition Explosive Very stiff rock 8×105 - 16×105 Nitroglycerine (93%) + Gun- cotton (7%) Stiff rock 4×105 - 8×105 Blasting Use-In deep wells, underground Gelatine Medium stiffness rock 2×105 - 4 ×105 works, in wet conditions. Less stiffness rock 1×105 - 2×105 Gun Cotton Cotton with the solution of Yielding rock 0.5×105 - 1×105 (Most (HNO3+H2SO4) High yielding rock 0.25×105 - 0.5×105 powerful) Use-where demolitions are required Nitroglycerine (75%) + Fine sand (25%) Max. bearing Dynamite Types of rock/soil Use- Both under water capacity (tonne/m2) and surface blasting Lime stone 400 Potassium nitrate (65%) + Sulphur Schist and shale 300 Blasting/ (25%) + Charcoal powder 20% Clay shale 100 Gun powder Use-In quarrying large blocks Compacted sand stone 45 Potassium Chlorate (79%) + Nitro Loose graval 25 Rock-a- benzol (21%) Soft clay 10 Rock Use-Under water and damp situation Compressive strength of different types of stones- blasting Compressive strength Stone crusher and equipment- Stone Crusher Type Equipment (in MPa) Trap 350-380 Primary Jaw, Impact and Gyratory Gneiss 206-370 crusher and Hammer mill Secondary Roll crusher, Cone crusher Basalt 150-185 Ball mill, Roll mill and Rod Slate 75-207 Tertiary mill Dolerite 90-150 Specific Gravity of Various Types of Stone- Syenite 90-150 Name of Stone Specific gravity Granite 75-127 Sand Stone 2.65 - 2.95 Lime stone 54 Marble 2.7 - 2.85 Sand stone 64 Granite 2.65 - 2.79 Use of various types of stone- Basalt 2.6 - 3 Name of Rock Use Slate 2.72 - 2.89 Railway ballast, Roofing, Laterite 2 - 2.2 Granite Abutment, Pier and Sea walls Lime Stone 2 - 2.75 Marble Ornamental work Gniess 2.5 - 2.7 Lime Stone Manufacture of cement Slate Flooring, roofing Various types of test and purpose for stone- Quartzite Retaining wall Type of Test Determine for Basalt Marine work, Rubble masonry Abrasion Test wearing resistance Manufacture of Hydraulic (By Dorry Testing Kankar lime Machine) Tools Used in Quarrying of Stone- Attrision Test Hardness, Toughness and Jumper To make hole (By Deval Testing rate of wearing resistance Scraping spoon For Cleaning hole Machine) Dipper For making deep hole Crushing Strength Compressive strength Priming Needle To make space for fuse Test (By C.T.M) (IS : 1121-1974) For tamping of explosive Length- 600 mm Smith's Test Soluble minerals/ Muddy matter Tamping Rod Brard's Test Frost resistance Dia (φ)- 16 mm Acid Test Weather resistance Steps for Blasting- Crystallization Test Durability Boring→ Cleaning→ Charging→ Tamping→ Firing (IS : 1126-1974) Quantity of Explosive- Hardness Test Hardness N = [L.L.R(in m)]2 ×1.5 (in gm.) (Moh's Scale) [L.L.R(in m)]2 Impact Test Toughness = (By Page Impact 0.008 Machine) [L.L.R(in cm)]2 Water Absorption % Voids (≯5% for good = 61 Test (IS 1124-1974) stone) Civil Engineering Capsule 4 YCT  Dorry Testing Machine Test- Friction Factor Type of Rock Frog 10 cm × 4 cm × 1 or 2 cm 0-14 Soft rock Stock Board 21 cm × 10 cm × 6 cm 14-17 Medium hard (To make frog) > 17 Hard rock Pallet Board 30 cm × 12 cm × 1 cm (To dry the brick) Impact Test- Sequence for the Preparation of Brick Earth- Toughness coefficient Toughness Unsoiling → Digging → Weathering→ 19 or More Very tough Blending →Tempering/Kneeding 16 to 17 Moderate tough Burning Zone of Bricks- 16 or below Poor tough Burning Temperature- 900 - 1200°C Attrision Test- Dehydration Oxidation Vitrification Friction Co-efficient Quality of Stones Zone Zone Zone 400-650°C 650-900°C 900-1200°C 2% Good Efficiency of Kiln- 3% Medium Ist Class Remark 5% or More Useless Types of kiln Brick Common Brick Size- outcome Brick Usual size Nominal Pazawah 50-60% – Classification size Allahabad kiln 60-70% Intermittent " " " Bull's Trench kiln 70-80% Semicontinuous 3 3 Conventional/ 9"× 4 × 2 9"× 4 1 × 3" Hoffman's kiln 80-90% Continuous Traditional/ 8 4 2 Class of Brick on the Basis of Strength- user size (23×11.2×7.0) (23×11.4×7.6) IS : 10719557-1970 cm cm Class Comp. Strength Standard/ Grade A ≮ 105 kg/cm2 Modular/ (19×9×9) cm (20×10×10) Normal size cm Grade AA ≮ 140 kg/cm2 Ingredients of Good Brick Earth- Grade B ≮ 70 kg/cm2 Ingredients % in brick Silica (SiO2) 50 - 60 Grade C ≮ 35 kg/cm2 Alumina (Al2O3) 20 - 30 Types of Refractory Bricks and its composition- Lime (CaO) 2-5 Bricks Composition Silica- 95-97%, Iron Oxide (Fe2O3) 3-5 Acid Refractory Lime- 1-2% Magnesia (MgO) 125 D.P.C Name Name Multistorey Class-B 7 75 Rounded Cant building ended 15-25 Sundry bricks - - ≃ 21 Double Compass Type of Lime Obtained After Calcination- cant Pure lime stone Pure lime Bull Perforated Dolomite Magnesia lime nosed Kankar Hydraulic lime Hollow Coping Chalk Pure lime Gypsum Pure lime Queen King Calcined lime stone Quick lime closer Closer Non-hydraulic Bat Calcined dolomite stone 3 lime Brick 4 Shale Pure lime General Data about bricks- Chemical Formula Name of lime Water Compressive Types of absorp- Strength Use Calcium carbonate Lime Stone bricks [CaCO3] tion (%) (Kg/cm2) Facing work Quick lime, Lump 1st Class ≤ 20 >105 Calcium oxide [CaO] lime, white lime, Rich R.B.Slab lime, Pure lime Hidden 2nd Class ≤ 22 >70 Calcium Hydroxide Slaked lime, Fat lime Structure [Ca (OH)2] Temporary 3rd Class > 25 >35 brick Calcium Sulphate Plaster of Paris masonry 1 [CaSO 4. H 2 O] 2 Bricks 4th Class Calcium Sulphate Gypsum ballast, lime (Jhamma or [CaSO4. 2H2O] 10 -12 350 concrete over burnt foundation, Chemical Reaction of Lime bricks) road metals 816ºC 1. CaCO3  Calcination → CaO + CO2 ↑ Perforated Pure lime Partition Bricks 15 70 2. CaO + H2O → Ca (OH)2 Wall (IS 2222) 3. Ca (OH)2 + CO2 → CaCO3 + H2O + Heat For making heat proof, Feedly Moderate Eminently Hollow Bricks Item 20 35 sound proof, Hydraulic Hydraulic Hydraulic (IS 3952) description damp proof lime lime Lime walls % 11 to 20% 21 to 30% 05 to 10% Paving impurities Road Slacking Few 1 or 2 1 day or Bricks 50 m3 4+1 for each 50m3 work Medium Sand 2.6 - 2.9 Note - 1 Sample = 6 cube Coarse Sand 2.9 - 3.2 Standard deviation of concrete- Workability, Slump and Compacting Factor of Grade of concrete Standard Concrete with 20 mm and 40 mm Size of deviation (σ) Aggregate (N/mm2) Degree of Slump Compa- Use for which M-10 to M-15 3.5 Worka- in mm cting Conc.is Suitable bility Factor M-20 to M-25 4 Used in road M-30 to M-55 5 making-roads Very Low 0-25 0.78 For Maximum 20 mm Nominal Size Aggregate- vibrated by power operated machines Exposer Min. Cement Min. Grade of Max. Water Min. Conc. Cement Concrete For foundations Condition Content (Kg/m3) Ratio Cover with light (mm) reinforcement, Low 25-50 0.85 P.C. RCC P.C. RCC P.C. RCC Roads vibrated by hand Mild 220 300 - M-20 0.60 0.55 20 operated Machines Moderate 240 300 M-15 M-25 0.60 0.50 30 manually compact- flat Severe 250 320 M-20 M-30 0.50 0.45 45 slabs using crushed agg. Normal rein - Very 260 340 M-20 M-35 0.45 0.45 50 forced concrete servere Medium 50-100 0.92 manually Extreme 280 360 M-25 M-40 0.40 0.40 75 compacted and heavily rein- forced Note: P.C. = Plain Concrete, RCC= Reinforced sections with Cement Concrete vibrations for sections with Max. Water Content Per Cum of Conc. For congested Nominal Max. Size of Aggregate- 100- High 0.95 Reinforcement. Not 175 Nominal Max. Max. Water normally suitable for vibration. Size of Agg.(mm) Content (Kg) General Features of the Main Types of Portland 10 208 Cement- 20 186 ASTM Type Classification Type-I Ordinary Portland cement 40 165 Type-II Moderate Sulphate Resistance Compressive Strength of Concrete at Various Age- (Modified cement) Age Strength% Type III Rapid Hardening cement 1 day 16 Type IV Low Heat cement 3 days 40 Type V Sulphate Resisting cement 7 days 65 Type IP Portland Pozzolana cement 14 days 90 28 days Type IS Portland slag cement 99 Civil Engineering Capsule 11 YCT  Permissible limit for solids in concrete water as Min. Grade of Conc. Required for Various Types per IS 456-2000 of Construction- Material Permissible Limit Minimum Types of Construction Organic 200 mg/l Grade Inorganic 3000 mg/l M-5, M-7.5 Lean concrete base Sulphate 400 mg/l Chlorides M-15 Plain cement concrete (i) RCC 500 mg/l M-20 RCC (General construction) (ii) PCC 2000 mg/l M-30 Water tank, Domes Suspended 2000 mg/l M-30 RCC in sea water and Post- Effect of sugar in cement conc. tensioned Quantity Effect M-40 Pre-tensioned 0.05% No effect 0.15% Retarder 0.20% Accelerator 0.25% Set more Rapidly but loose strength PERT (Programme Evaluation and Review Note - Sugar is consider as retarder Technique)- Strength of conc. Increase with age- Three time estimates are made Month Age Factor Follows β distribution 1 1 Probabilistic Approach 3 1.1 For Research and Development work 6 1.15 Some Useful Formula 12 1.2 t O + 4t m + t p Consistency and Degree of Workability for Vee- tE = 6 Bee Degree- Vee-Bee Consistency Degree of tp − tO Degree Vorkability σ= 6 20-40 Very Low Very very low 2 workable concrete  tp − tO  σ2 =   = variance 10-20 Low Very low  6  Workable concrete Where, 5-10 Medium Low workable σ = Standard deviation concrete tO = Optimistic time 3-5 High Medium workable tp = Pessimistic time concrete tm = Most likely time 1-3 Very High High workable tE = Expected completion time of an activity concrete Event Time- 1000 m 33.33% " " " ±2 97.72% ±3 99.87% Types of Bond- CPM (Critical Path Method)– Stretcher All bricks are laid as stretchers on the One time estimate bond faces of the wall generally used for Deterministic approach partition wall (10 cm) Minimum cost is found corresponding to Header All the bricks are laid as header on optimum time bond the face of wall. Use staining of well, For repetitive type of work corbels footing.....etc. Normal distribution is followed English Alternate course of header & Activity Times- bond stretcher. Mostely used in EST = TEi or EFT = TEi + t ij government work. It is costly and LFT = TLi or LST = LFT − t ij stronger than flemish bond Flemish Each course has alternate header & Float Flot denotes the range within which bond stretchers. Flemish bond give better activity time or its finish time may appearance then english bond fluctuates without effecting the Facing Bricks of different thickness are to be completion of the project. bond used in the facing or backing of the wall Total float FT = LST– EST or FT = LFT – EFT Classification of wall- Free float FF = TEj − TEi − Teij or FF = FT − S j Load bearing wall Non-load bearing Independent F1 = TEi − TLi − Teij or FID = FF − Si wall float Solid wall with piers Partition wall Tail Event Slack- (pilasters) FT = 0 For critical path Vineered wall Panel wall FT> 0 For sub critical path FT < 0 For super critical path Cavity wall Free standing wall Interfering float F(IN) Sj = FT - FF Solid wall Curtain wall Crash cost − Normal cost Frieze : A coarse of stone provided immediately Cost slope = Normal time − Crash time below cornice is called frieze Bull nose/cow nose : Use for making corner or curve shape in brick masonry. Perpend : It is that vertical joint on face of the wall, which lie directly above the vertical joints in the Classification of Building According to NBC- alternate course. Door and window- S.N. Class Types of Buildings 1. Group A Residential Building 1. Doors for residential building: 2. Group B Educational Building External door (1×2) to (1.1×2)m Internal door (0.9×2) to (1×2)m 3. Group C Institutional Building Doors for bathrooms & water closet- 4. Group D Assembly Building (0.7×2) to (0.8×2) m 5. Group E Business Building 2. Public building (School, Hospital, 6. Group F Mercantile Building Library): 7. Group G Industrial Building (a) (1.2×2) m, 8. Group H Storage Building (b) (1.2×2.1) m, 9. Group I Hazardous Building (c) (1.2×2.25) m Civil Engineering Capsule 13 YCT  Use of Door- Maximum pitch/slope for public building - 33º Sliding door For AC building Minimum width of stair in commercial building -1 m Swinging door For residential Head room must be 2.05 m Folding door For covering large Relation b/w Riser and Tread covering opening 2R + T = 60 Revolving door Public building Rolling steel shutter Garrage, Godowns R + T = 40 to 45 Designations of door Length ×type of door R × T = 400 to 450 × height Where, R = Rise in cm Size of Timber Chaukhat- T = Tread in cm (i) For door- 8×10cm-10×12cm In public building the maximum riser is limited to (ii) For window- 8×8 cm - 8×10 cm 15 cm (iii) Ventilator- 8 cm ×8 cm In Case of straight staircase Window- No. of tread = No. of riser –1 Located on Northen side (maximum day light available) In case of one landing and two flight Minimum window area = 1/8 of total floor area No. of tread = No. of riser –2 of room Types of Roof Trusses and Their Span- Total area of window - (10-20)% of floor area Types of Roof Max. Span of room Public building : Minimum area of window = 20% Lean to roof (Verandah) 2.5 m of total floor area Couple roof 3.5 m Coupl close roof 4.5 m Particulate Arch Lintel Shape Curved Horizontal Collar beam roof 4.8 m & straight King-Post truss 5 to 8 m Bed joint Joints are radial Joints are Queen-Post truss 8 to 12 m exception horizontal Bel-Fast truss (Lattice roof) up to 30 m monolithic construction North-Light roof truss 20 to 30 m Leteral Exert on vertical Do not Minimum Slope for the Main Roof Covering- thrust support exert Roof Covering Materials Slope Rise Provided Not G.I. Sheet 1 º provided 26 Appearance Good architectural Simple 2 appearance appearance Asbestos Sheet 30º Strength Quite strong Equally Roof Tiles 40º vertical uniform strong for loading but weak uniform & under point loading point loading Property of Staircase Width of stair in domestic building- 90 cm Width of stair in public building- (1.5-1.8) m Number of total step in a flight 12 Number of steps in a flight 3 Angle of inclinations 25-40 º Arch Components Civil Engineering Capsule 14 YCT  Temperature Dynamic Viscosity For liquid T↑ µ↓ For gases T↑ µ↑ Kinematic Viscosity– Properties of Fluid Dynamic Viscosity µ Properties Formula Unit Dimension υ= = Mass Density ρ Density or M Mass ρ= kg/m3 ML−3 Unit- SI – m2/sec V Density CGS – cm2/sec or stoke Specific w= W = mg = ρg N/m3 or 1 stoke = 10-4 m2/sec or 1 cm2/sec Weight or Weight V V kg ML−2 T −2 1 m2/sec = 104 stoke Density wwater = 9.81 × 1000 m 2s 2 Note- υair > υwater Density or wt. density of liquid SLiquid = For liquid- surface tension ↓(decrease) with ↑ Density or wt. density of water (increase) in temperature. Specific Wt. density of liquid Dimension Unitless Excess Pressure- Gravity = S×1000×9.81 N/m3 less Density of liquid Pressure inside drop 4σ = S×1000 kg/m3 p= (solid like sphere) d V 1 Specific v= = 3 −1 3 Pressure inside bubble, 8σ Volume m ρ m /kg M L p= d (soap bubble) K= 2σ Bulk Pressure inside liquid jet p= Modulus − dp =− dp.V N/m2 ML−1T −2 d dV / V dV σ = Surface tension Compressi 1 d = diameter of bubble β= M −1LT 2 bility K m2/N Rise or depression of liquid in capillary tube SI - N/m Surface F 4σ cos θ σ= CGS - MT −2 h= Tension l dyne/cm ρgd SI - θ = 00 for pure water and glass tube Vapour Force  F N/m2  pv =  −1 ML T −2 θ = 1280 for mercury and glass tube Pressure Area  A CGS - dyne/cm2 Note- Capillary action occurs due to adhesion and cohesion both Newton’s Law of Viscosity– Types of Fluid– du dθ τ=µ =µ Ideal Fluid It is incompressible and have no dy dt viscosity du Real Fluid It possess viscosity and = velocity gradient Compressibility dy Ideal plastic In this shear stress is more than yield dθ Fluid du dθ ⇒ Rate of shear strain or shear deformation. value and shear stress (τ) ∝ or dt dy dt Dynamic Viscosity (µ)– Newtonian In this type of fluid, shear stress is τ Fluid directly proportional to rate of shear µ= strain or du / dy Newtonian fluid does not change Unit of Viscosity- with viscosity or with the rate of SI – N-s/m2 or Pa–s deformation or shear strain. Ex. Water, Kerosene, Petrol, CGS – dyne–s/cm2 Benzene, Ethanol M.K.S– kgf–s/m2 Non- In this shear stress is not proportional 1 Newtonian to the rate of shear strain. This fluid 1 poise = N–s/m2 10 Fluid does not obey Newton's law of 1 Centipoises = 10-2 Poise viscosity. Civil Engineering Capsule 15 YCT  Inverted Triangle h h x= h= 3 2 Circle d 5d x= h= 2 8 Trapezium Non-Newtonian Fluid–  a + 3b h   a + 2b  h h =   2 x=  a + 2b  a + b  3 A. Time Independent- (i) Dilatent Quick sand, Sugar Solution, butter (ii) Bingham Plastic Creams, Toothpaste, Half circle Drilling Muds 3πr 3πD 4r 2D or (iii) Pseudo Plastic Polymer solutions, or 16 32 3π 3π milk, blood, syrup B. Time Dependent Metacentric height, (i) Thixotropic Lipstick, Printer inks, G.M. = B.M. – B.G. Enamels Paint, Jelly Imin (ii) Rheopectic Gypsum pastes and = − B.G. Vimmersed Bentonite slurry Imin = M.O.I. Geometric properties of some important shapes- Time period of Oscillation– Plane Surface Center of Depth of k2 Gravity center of T = 2π G.M × g (C.G.) pressure (C.P.) k = Least Radius of gyration Metacentric height for rolling condition will be less Rectangle than Metacentric height for pitching condition. Floating body rotation axis in different condition– d x= 2d Pitching Transverse axis 2 h= 3 Rolling Longitudinal axis Yawing Transverse axis (Perpendicular to the plane) Equilibrium condition for Submerged and floating Triangle body– Equilibrium Submerged Floating body condition body 2h 3h x= h= Stable B is above G M is above G 3 4 Unstable B is below G M is below G Neutral B and G coincide M and G coincide Civil Engineering Capsule 16 YCT  Metacentric Height for various ships- dp Types of ship Metacentric height For h, measured upward = −ρg = − w dh Merchant ship < 1.0 m sailing ship < 1.50 m Pressure Head- Battle ship < 2.0 m  p p River boat < 3.50 m  h = ρg or w    G.MCargo ship > G.MPassenger ship, So cargo ship is less comfortable. Hydrostatic force of curved surfaces- Pascal's Law– [ FH = ρgAx ] Pressure at a point in a fluid system is equally distributed in all direction. It applied to fluid at rest. A - Projected Area Pascal's law is avoid if shear stress = 0 x - Vertical distance of C.O.G. of body from free px = py = pz surface. Unit of Pressure– Resultant Force 'F' = (FH ) 2 + (Fv ) 2 1Pa = 1N/m2 1Bar = 105Pa Fv– Weight of liquid block above curved kgf surface. 1atm = 101325Pa 1 2 = 9.81×104N/m2 cm Total pressure and center of pressure for 1Psi = 6894.76 Pa submerged plane at different surface position- 1 Torr = 133.3 Pa =1 mm Hg Surface Total Pressure Center of Position Pressure (hcp) Horizontal F = ρgAX hcp = X Position = wAX Vertical F = ρgAX IG h cp = X + Position AX = wAX Pabs = Patm + Pgauge Inclined F = ρgAX IG Position h cp = X + Sin 2 θ Pvaccum = Patm – P'abs AX = wAX Hydrostatic Law- The rate of increase of pressure in vertical Curved FH = ρg ∫ h.dA sin θ direction is equal to weight density of the fluid Surface at that point. Fv = ρg ∫ h.dA cos θ  dp   dh = w = ρg    dp FR = FH2 + Fv2 For h, measured downward = ρg = w dh = wAx Civil Engineering Capsule 17 YCT  Types of Fluid Flow– Type of Local or Convective Total or Steady Flow Fluid property like density, pressure, Flow Temporal or Advective Max. Acceleration Acceleration Acceleration velocity does not change with time. Steady + 0 0 0 ∂v ∂p ∂ρ Uniform = 0, = 0, =0 ∂t ∂t ∂t Flow Unsteady Flow Fluid property changes with time Unsteady + 0 Local Uniform ∂v ∂p ∂ρ Flow ≠ 0, ≠ 0, ≠0 ∂t ∂t ∂t Unsteady + Local + Uniform Flow At a given time, fluid property does Non- Convective Uniform not change with respect to the space. Flow  ∂v  Steady and 0 Convective   =0  ∂s  t = Constant Non-Uni- form Flow Non-Uniform At a given time, velocity changes with Forced Vortex Flow– Flow respect to space- r = Radius of fluid particle [ v = ω× r ] ω = Angular velocity  ∂v    ≠0 Free Vortex Flow–  ∂s  t = Constant  v = c  c = constant Laminar Flow Fluid particles move along well-  r  defined path or stream line and all the Forced Vortex Flow Free Vortex Flow stream lines are straight and parallel. For this some external There is no external Adjacent layer does not cross each force/torque required to torque required to other. rotate fluid mass. rotate fluid mass. It is also known as stream line Ex. Ex. 1. Flow of water through the 1. Flow through kitchen flow or viscous flow. runner of a turbine. sink. Turbulent Fluid particle moves in a zig-zag or in 2. Flow of Liquid passing 2. Liquid flow through a Flow random order. through impeller of hole at the bottom of centrifugal pumps. container. Compressible Density of fluid changes from point to 3. Rotation of Water in a 3. A whirelpool in a Flow point or density is not constant in washing machine. river. fluid flow i.e. ρ ≠ constant. v 2 r 2 ω2 R 2 ω2 4. Flow fields due to z= = = tornado. Incompressible Density remains constant i.e. ρ = 2g 2g 2g 5. Liquid flow around a Flow constant. z = height of parabolid circular bend in a formed) pipe. Rotational During flow along streamline, fluid Flow particles rotate about their own axis in both the circular as well as straight line motion. Irrotational Fluid particle does not rotate about its own axis in both circular as well as Kinetic Energy correction factor- straight line motion. Actual K.E. α= Local or It is the rate of increase of velocity K.E. Calculated from average velocity Temporal with respect to the time at a given Momentum Correction factor- Acceleration point in a flow field Actual linear momentum/sec. β= ∂u ∂v ∂w Linear momentum/sec. calculated from Vavg. , or Local acceleration ∂t ∂t ∂t Flow Condition α β Convective It is the rate of change of velocity due Laminar flow in pipe 2 1.33 to the change of position of fluid in a Laminar flow b/w 1.543 1.2 Acceleration parallel plates fluid flow. Turbulent flow in pipe 4/3 or 1.33 1.2 Civil Engineering Capsule 18 YCT  Continuity equation is based on conservation of Equation of motion– mass principle 1. Newton's Equation of Motion Euler's equation is based on- Conservation of Fx = F g + Fp + F v + Ft + Fc Momentum principle 2. Reynold's Equation of Motion p v2 Fx = F g + Fp + F v + Ft Bernoulli's equation = + +z =c 3. Navier-Stokes Equation ρg 2g Fx = F g + Fp + F v Bernoulli's equation is based on- Conservation of 4. Euler's Equation of Motion Energy Principle Fx = F g + Fp Each term of Bernoulli's equation represents Euler's Equation– Energy per unit weight  dp  Rate of Flow or Discharge  ∫ p + ∫ gdz + ∫ vdv = Constant  [Q = A × V] Bernoulli's Equation– where, A = Cross-sectional area of pipe  p v2  V = Average velocity of Fluid.  ρg + 2g + z = constant    Unit = m3/sec. Where, Continuity Equation– [ρ1 A1V1 = ρ2A2V2]– Compressible Fluid p = Pressure head ρg [A1V1 = A2V2]– Incompressible Fluid. ρ = density, A = Area of Pipe, V = Average Velocity v2 = Velocity head. Continuity Equation in 3-D– 2g ∂ ∂ ∂ z = Potential head. (ρu) + (ρv) + (ρw) = 0 for Incompressible Fluid. p ∂x ∂y ∂z Piezometric Head = +z ρg Velocity Potential Function–  −∂φ −∂φ −∂φ  p V2 Stagnation Head = +  u = ∂x v = ∂y w = ∂z  ρg 2g   Stream Function– Bernoulli's equation for real fluid  +∂ψ +∂ψ  p1 v12 p v2 + + z1 = 2 + 2 + z 2 + h L  ∂x = v ∂y = −u  ρg 2g ρg 2g   Relation between Stream Function and Velocity Venturimeter– Potential Function–  a1a 2  Q actual = C d × 2gh   ∂φ ∂ψ   ∂φ −∂ψ   a12 − a 22   ∂x = ∂y   ∂y = ∂x        Cd = Co-efficient of venturimeter 0.97 - 0.99 Angular Deformation– S  1 h = x  h – 1 – Liquid heavier then flowing liquid = [ ∆θ1 + ∆θ2 ] S  o  2 Shear Strain Rate– in pipe 1  ∂v ∂u   S  = + h = x 1 − l  – For Liquid lighter than flowing 2  ∂x ∂y   S0  Rotation– liquid in pipe) Sh = Specific gravity of heavier liquid. 1  ∂v ∂u  wz =  −  So = Specific gravity of liquid flowing in pipe 2  ∂x ∂y  Sl = Specific gravity of lighter liquid. 1  ∂w ∂v  Orificemeter or orifice plate- wx =  −  2  ∂y ∂z   C a a 2gh  Q = d 0 1  1  ∂u ∂w   a12 − a 02  wy =  −   2  ∂z ∂x  a0 = Area of orifice → Vorticity is twice the rotation '2w'. Cd = 0.65 – 0.70 Civil Engineering Capsule 19 YCT  Pitot Tube– Value of Hydraulic Co-efficient-  p − p2  Coefficient of velocity 0.95-0.99 ≃ 0.98  Vth = 2gh  , Vth = 2g  1  ( Cv )    ρg  Coefficient of 0.61-0.69 ≃ 0.64 P1/ρg – stagnation head P2/ρg – Static head contraction, Cc Important point- Coefficient of Discharge 0.61-0.64 ≃ 0.62 Type of flow meter Cost Accuracy Head loss Cd Venturimeter High High Low Coefficient of - ≃ 0.063 Resistance, Cr Orifice meter Low Low High Coefficient of Discharge (Cd) for mouthpiece- Flow Nozzle Medium Medium Medium Types of Mouthpiece Cd Instruments & Their Measuring Parameter- External Mouthpiece 0.855 Instrument Measuring parameter Internal mouthpiece Venturimeter Discharge or flow rate (i) Running full 0.707 (ii) Running free 0.50 Orificemeter Discharge or flow rate Convergent or convergent 1.00 Flow nozzle Discharge or flow rate divergent mouthpiece Elbow meter Discharge in vertical segment or Discharge Over a Notch or Weir– flow rate 1. Rectangular Notch or Weir Nozzle meter Discharge or flow rate 2 Q = Cd.L 2g.H 3/ 2 Pitot tube Velocity of fluid flow 3 L = Width of weir Prandtl tube Velocity of fluid flow If velocity of approach = Va (Boundary layer theory)  V2  Then, H = H+Ha or  H + a  Current meter Velocity in open channel  2g  Weirs Discharge in open channel 2 ∴ Q = Cd.L 2g  (H + H a )3/ 2 − H 3/a 2  Rotameter Flow rate or discharge in vertical 3 2. According to Francis Formula- segment 2 Hot-wire For measuring the gas or air Q = Cd 2g [ L − 0.1nH ] H 3/ 2 3 Anemometer velocity = 1.84 [L–0.1 nH).H3/2 Anemometer Velocity with high accuracy Contraction value is taken 0.1H for each ends of Pyrometer High temperature measurement Weir According to Benzin's– Hydrometer Specific gravity Q = mL 2g.H 3/ 2 Hygrometer Humidity 2 0.003 Orifice- m = Cd = 0.405 + Hydraulic Co-efficient– 3 H 3. Triangular Notch or Weir– Co-efficient of velocity, Cv 8 Actual velocity of jet at vena-contracta Vact Q = Cd 2g tan θ / 2.H 5/ 2 = = 15 Theoretical velocity Vth If θ = 90° then tan θ/2 = 1 Cv = 0.98 for sharp edged orifices 8 Co-efficient of Contraction, Cc Q= Cd 2gH 5 / 2 15 Area of jet at vena-contracta (a c ) oR Cc = = Area of orifice (a) Q = 1.417H 5 / 2 (If θ = 900) Co-efficient of Discharge, Cd 4. Trapezoidal Notch or Weir- Actual Discharge Q Qact Q = Q Rectangular + QTriangular Cd = = act = Theoretical Discharge Qth a 2gh 2  4 θ Q = Cd 2g.H 3 / 2  L +.H tan  Cd = Cv × Cc 3  5 2 Civil Engineering Capsule 20 YCT  Effect on Discharge due to error in the Where, measurement of head for– Area m= (i) Rectangular Weir or Notch Wetted Perimeter dQ 3 dH hf = = 1.5%. Error i= = Hydraulic gradient Q 2 H L (ii) Triangular Weir or Notch– 8g C= dQ 5 dH f = = 2.5%. Error B. Minor Losses– Q 2 H It is due to- For Cipolletti Weir or notch 1. Sudden Enlargement of Pipe- Side slope = 1 : 4 (H:V) ( V1 − V2 ) 2 2 2 or θ/2 = 14°2' V12  A1  V22  A 2  h EL = = 1 −  =  − 1 Broad Crested Weir- 2g 2g  A 2  2g  A1  H = 0.1 − 0.4 2. Sudden Contraction- L or 2L > H 0.5V 2 hc = Narrow Crested Weir 2g H 3. Inlet Loss- > 1.6 L 0.5V 2 or 2L < H hi = 2g H = Height of Water above crest L = Length of crest 4. Exit Loss- Discharge Over a Broad Crested Weir- V2 h ex = Q = 1.705.Cd.L.H 3/ 2 2g Flow Through Pipe 5. Due to pipe Bend and pipe Fitting- V2 Loss of Energy in Pipes- hb/F = k A. Major Losses (mainly due to friction)– 2g (a) Darcy - Weisbach Formula– k depends upon f LV 2 1. Angle of bend hf = 2gD 2. Pipe dia 3. Type of pipe fitting 4f ' LV 2 and h f = (Fanning equation) 4. Radius of curvature of bend. 2gD Maximum Efficiency of Transmission of Power- Where, f = Darcy friction factor H − hf f ' = Co-efficient of friction η= H Note- 64 (For max. Transmission power) f= (For Laminar flow, Re < 2000) H Re H = 3hf or hf = 3 0.3164 f= (For Turbulent flow 4000 < Re < 105) ∴ η = 2/3 or 66.7% R e1/ 4 Hydraulic Grade Line (H.G.L.)- 16 f '= (For Laminar Flow) p Re = +z ρg 0.079 f ' = 1/ 4 (For Turbulent flow Re Total Energy Line (T.E.L)- Note- f = 4f ' p V2 = +z+ (b) Chezy's Formula- ρg 2g Mean Velocity, ∴ T.E.L. always > H.G.L.  8g  V = C mi C =  T.E.L. always drop in the direction of flow due to  f  loss of head. Civil Engineering Capsule 21 YCT  Water Hammer- Froude Inertia force Fi V Case of Water hammer Pressure head = Number Gravity force Fg Lg Gradual closure of valve p L.V = w gt Weber Inertia force Fi V = Sudden closure of valve in rigid p VC V k Number Surface tension Fs σ / ρL pipe = = w g g ρ Euler's Inertia force Fi V Sudden closure of valve in p V = elastic pipe = Number Pressure force Fp P/ρ w 1 D  t = time of closing valve in sec. ρg 2  +  x = thickness of pipe  K xE  Cauchy Inertia force V2 Closure of valve will be gradual 2L Number Elastic force C2 if t> C Classification of flow based on mach number- Closure of valve will be 2L Instantaneous if t< Mach C Types of flow Important Dimensionless Number: Number Number Definition Equation 1 Super sonic flow Inertia force Fi V V Number = = >6 Hyper sonic flow Elastic force Fe C K/ρ Laminar flow through plate- Laminar flow through pipe- 1. Shear stress distribution- 1. Shear stress distribution- ∂p  t  r ∂p τ = −  − y τ=− ∂x  2  2 ∂x at y = 0, τ = τmax at, r = 0, τ = 0 2. Velocity distribution- r = R, τ = max 1  ∂p    ( ty − y ) 2. Velocity distribution- u=− 2 1  ∂p   r2  2µ  ∂x  u = −   R 2 1 − 2  4µ  ∂x   R  1  ∂p  2 1  ∂p  u max = −  t u max = −   R 2 8µ  ∂x  4µ  ∂x  r' = 0.707R (Average velocity = Local velocity) 3 u max = u avg 3. Discharge- 2 π  ∂p  4 Q= − D 3. Discharge- 128µ  ∂x  D = Diameter of pipe 1  ∂p  3 Q= − t 4. Head Loss- 12µ  ∂x  32µu avg.L hf = (Hagen-Poiseulle formula) 4. Head Loss- ρgD 2 12µu avg.L 2 fLu avg  64  hf = = f =  ρgt 2 2gD  Re  Civil Engineering Capsule 22 YCT  Model laws and its application- Laminar Sub-layer 11.6 υ Models Applications thickness δ= Vx Reynolds model law Submarines completely under υ = Kinematic viscosity water Vx = Friction velocity Motion of air-planes Displacement thickness δ  u Flow through venturimeter, δ* = ∫ 1 −  dy 0 U orifice meter Momentum thickness δ Flow through small sized u u θ=∫ 1 −  dy pipes. 0 U U δ Mach model law Aerodynamic testing Energy thickness u u2  δ = ∫ 1 − 2  dy ** Under water testing of 0 U U  torpedoes Shape factor δ* Water-hammer problem. H= θ Froude model law Open channels. Von-Karman's dθ τ Free surface flow such as flow Momentum Integral = o dx ρU 2 over spillways, weirs, sluices. Equation Flow of jet from an orifice or It is used for- τo = shear stress at surface nozzle. Laminar, Transition and Flow of different density Turbulent boundary layer fluids one above the other. δ > δ* > δ** > θ Weber model law Flow over weir for small Drag and lift force- heads 1 Capillary flows Drag force, FD = Cd ρAV 2 2 Flow of very thin sheet of 1 liquid over a surface. Lift force, FL = C L ρAV 2 2 Euler's model law Turbulent flow in pipeline Drag force on sphere, FD = 3πµ.V.D where viscous force and Where, surface tensile forces are A = Projected area of body entirely absent. V = Relative wind velocity Where the phenomenon of Cd & CL = Coefficient of drag and lift cavitations occurs. Important Relations (Blasius Results) : Characteristics Laminar Boundary layer Turbulent boundary layer Boundary layer thickness (δx) δx = 5x Re x ( δ x ∝ x1/ 2 ) δx = 0.377x (Re x )1/ 5 (δ x ∝ x 4 / 5 ) Local skin friction coefficient (Cfx) 0.664 0.059 Cfx = Cfx = ( Rex ) 1/ 5 Re x Average skin friction coefficient or drag 1.328 5 0.073 Cfa = Cfa = Cfx = ( Rex ) 1/ 5 coefficient (Cfa or Cd) Re x 4 Displacement thickness (δ) 1.72x 0.048x δ= δ= ( Re x ) 1/ 5 Re x Momentum Thickness (θ) 0.669x 0.037x θ= θ= ( Re x ) 1/ 5 Re x Civil Engineering Capsule 23 YCT  On the basis of Nikuradse's experiment the boundary layer is classified as- k Smooth boundary layer V* K < 0.25 6.0 Where, > 70 δ * υ V* = average shear velocity υ = kinematic viscosity K = Avg. roughness Open channel flow - Nature of flow according to Reynolds number for pipe, and open channel flow– Nature of flow Reynolds No, RN = ρVD/µ b/w parallel plates Flow through Pipe Flow Open channel flow Soil Laminar flow RN < 2000 RN < 500 RN < 1000 RN < 1 Transitional flow 2000 < RN < 4000 500 < RN < 1000 1000 < RN < 2000 1< RN < 2 Turbulent flow RN > 4000 RN > 1000 RN > 2000 RN > 2 Lower critical flow point RN = 2000 RN = 500 RN = 1000 RN = 1 Higher critical flow point RN = 4000 RN = 1000 RN = 2000 RN = 2 For most Economical channel section- Re