Introduction to Fluid Mechanics

Fluids: Statics vs Dynamics

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

Fluid Statics Basic Principles: Fluid is at rest : no shear forces Pressure is the only force acting What are the forces acting on the block? Air pressure on the surface - neglect Weight of the water above the block Pressure only a function of depth

Units SI - International System Length Meter Time Sec Mass Kg Temp 0K = 0C + 273.15 Force Newton = Nt = 1 kg m / s2 Gravity 9.81 m/s2 Work = Fxd Joule = N-m Power = F/t Watt = Joule/sec

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

Properties of Fluids Density = r (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 = g (Heaviness of fluid) weight per unit volume g = rg 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 = rf / rw SG of Hg = 13.55

Ideal Gas Law relates pressure to Temp for a gas P = rRT 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 m = 1.12 x 10-3 N-s/m2 Surface tension - forces between 2 liquids or gas and liquid - droplets on a windshield.

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

Manometers - measure DP 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

Manometers P = g x h + PO Simple Example: Find the pressure at point A in this open u-tube monometer with an atmospheric pressure Po PD = g W x hE-D + Po Pc = PD PB = PC - g Hg x hC-B PA = PB

Archimedes Principle: Will it Float? Section 3: Buoyancy Archimedes Principle: Will it Float? The upward vertical force felt by a submerged, or partially submerged, body is known as the buoyancy force. It is equal to the weight of the fluid displaced by the submerged portion of the body. The buoyancy force acts through the centroid of the displaced volume, known as the   center of buoyancy. A body will sink until the buoyancy force is equal to the weight of the body. FB = g x Vdisplaced FB = gW x Vdisp = Vdisp FB W = FB FB