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Material Type: Notes; Professor: Brandes; Class: Fluid Mechanics; Subject: Civil Engineering; University: Lafayette College; Term: Spring 2004;
Typology: Study notes
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DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING; LAFAYETTE COLLEGE
Abbreviations and Symbols CE 251, Spring 2004
= fluid shear stress (shear force over a shear area) [F/L^2 ] p = fluid pressure (compressive force over an area: pounds per square inch (psi), Pascal (Pa) = N/ m^2 ) [F/L^2 ] u = internal energy per unit mass (J/kg) [FL/M] W = work (Joules) [FL]
= density [M/L^3 ] ( w = 1000 kg/m^3 = 1 g/cm^3 = 1.94 slugs/ft^3 ) g = acceleration of gravity = 9.81 m/s^2 = 32.2 ft/s^2 = specific weight [F/L^3 ] = g ( w = 9.8 kN/m^3 = 62.4 lbs/ft^3 ) SG = specific gravity [] = x / w = x / w = dynamic viscosity (also called absolute viscosity) [Ft/L^2 ] ( w = 1 x 10-3^ N-s/m^2 = 2.1 x 10-5^ lb-s/ft^2 @ 20C or 70F) = kinematic viscosity [L^2 /t] = ( w = 1 x 10-6^ m^2 /s = 1.1 x 10-5^ ft^2 /s @ 20C or 70F) Ev = bulk modulus of elasticity [F/L^2 ] ( Evw = 2,170,500 kN/m^2 = 318,000 psi) = surface tension [F/L] ( aw = 0.073 N/m = 0.005 lb/ft)
R = specific gas constant = R/mw ( Rair = 287 J/kg˚K) [FL/MT = L^2 /t^2 T] c = specific heat: heat required to raise the temp of a unit mass by one degree (J/kg˚K) k = adiabatic constant = ratio of c at const pressure to c at constant volume ( cp/cv ) ( kair = 1.4)
r = radial distance from a pipe centerline [L] y = perpendicular distance from a flow boundary [L] h = fluid “head” [L], a vertical depth of fluid; pressure is often converted to an equivalent height of fluid using h = p / z = vertical height above some datum [L] hL = head loss due to friction and turbulence [L]
V = average velocity through a cross-section of flow [L/t] A = area [L^2 ] Q = volumetric flow rate = VA [L^3 /t] v = velocity at a specific point in the flow [L/t] v* = “friction velocity", an important parameter in boundary layer flow (not a true velocity) [L/t]
Re = Reynolds number, a dimensionless force ratio important in pipe flow (inertial/viscous) Fr = Froude number, another dimensionless force ratio important in gravity flow (inertial/gravity)
Note: dimensions are in brackets, F = force, M = mass, L = length, t = time, T = temp