Fluid Mechanics - Civil and Environmental Engineering - Lecture Slides, Slides of Civil Engineering

Download Fluid Mechanics - Civil and Environmental Engineering - Lecture Slides and more Slides Civil Engineering in PDF only on Docsity! Introduction to Fluid Mechanics CEVE 101 Docsity.com Atmospheric Pressure Pressure = Force per Unit Area Atmospheric Pressure is the weight of the column of air above a unit area. For example, the atmospheric pressure felt by a man is the weight of the column of air above his body divided by the area the air is resting on P = (Weight of column)/(Area of base) Standard Atmospheric Pressure: 1 atmosphere (atm) 14.7 lbs/in2 (psi) 760 Torr (mm Hg) 1013.25 millibars = 101.3 kPascals 1kPa = 1Nt/m2 Docsity.com Units English Length in Ft Time in Sec lbm (slug) - 1 slug = 32.2 lbm Force - lb Gravity - 32.2 ft/sec2 Work = slug-ft/s2 Docsity.com Properties of Fluids Density = ρ (decreases with rise in T)  mass per unit volume ( lbs/ft3 or kg/m3 ) for water density = 1.94 slugs/ft3 or 1000 kg/m3 Specific Weight = γ (Heaviness of fluid)  weight per unit volume γ = ρg for water spec wt = 62.4 lbs/ft3 or 9.81 kN/m3 Specific Gravity = SG  Ratio of the density of a fluid to the density of water SG = ρf / ρw SG of Hg = 13.55 Docsity.com Ideal Gas Law relates pressure to Temp for a gas P = ρRT T in 0K units R = 287 Joule / Kg-0K Pressure Force per unit area: lbs/in2 (psi), N/m2, mm Hg, mbar or atm 1 Nt/m2 = Pascal = Pa Std Atm P = 14.7 psi = 101.33 kPa = 1013 mb Viscosity fluid deforms when acted on by shear stress µ = 1.12 x 10-3 N-s/m2 Surface tension - forces between 2 liquids or gas and liquid - droplets on a windshield. Docsity.com Measurement of Pressure Barometer (Hg) - Toricelli 1644 Piezometer Tube U-Tube Manometer - between two points Aneroid barometer - based on spring deformation Pressure transducer - most advanced QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Docsity.com Manometers - measure ∆P Rules of thumb:  When evaluating, start from the known pressure end and work towards the unknown end  At equal elevations, pressure is constant in the SAME fluid  When moving down a monometer, pressure increases  When moving up a monometer, pressure decreases  Only include atmospheric pressure on open ends Docsity.com Manometers Find the pressure at point A in this open u- tube monometer with an atmospheric pressure Po PD = γ W x hE-D + Po Pc = PD PB = PC - γ Hg x hC-B PA = PB Simple Example: P = γ x h + PO Docsity.com Hydrostatic Force on a Plane Surface Basic Concepts and Naming C = Centroid or Center of Mass CP = Center of Pressure Fr = Resultant Force I = Moment of Inertia γh For a Rectangular Gate: Ixc = 1/12 bh3 Ixyc = 0 For a circle: Ixc = π r4 / 4 Ixyc = 0 Docsity.com Hydrostatic Force on a Plane Surface The Center of Pressure YR lies below the centroid - since pressure increases with depth FR = γ A YC sinθ or FR = γ A Hc YR = (Ixc / YcA) + Yc XR = (Ixyc / YcA) + Xc but for a rectangle or circle: XR = Xc For 90 degree walls: FR = γ A Hc Docsity.com Hydrostatics Example Problem # 1 What is the Magnitude and Location of the Resultant force of water on the door? γW = 62.4 lbs/ft3 Water Depth = 6 feet Door Height = 4 feet Door Width = 3 feet Docsity.com Buoyancy Example Problem # 1 A 500 lb buoy, with a 2 ft radius is tethered to the bed of a lake. What is the tensile force T in the cable? γW = 62.4 lbs/ft3 FB Docsity.com Buoyancy Example Problem # 1 Displaced Volume of Water: Vdisp-W = 4/3 x π x R3 Vdisp-W = 33.51 ft3 Buoyancy Force: FB = γW x Vdisp-w FB = 62.4 x 33.51 FB = 2091.024 lbs up Sum of the Forces: ΣFy = 0 = 500 - 2091.024 + T T = 1591.024 lbs down Docsity.com Assume Full Submersion: FB = Vol x γW FB = (100’ x 150’ x 800’) x 62.4 lbs/ft3 FB = 748,800,000 lbs Weight of Boat = 300,000,000 lbs The Force of Buoyancy is greater than the Weight of the Boat meaning the Boat will float! How much of the boat will be submerged? Assume weight = Displaced Volume WB = FB 300,000,000 = (100’ x H’ x 800’) x 62.4 lbs/ft3 H = Submersion depth = 60.1 feet Docsity.com