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And Robert L. Street, Elementary Fluid Mechanics, Copyright 1954, John Wiley & Sons, Inc. K. Vennard. Diagrams reprinted by permission of John Wiley & Sons, Inc 44 FLUID MECHANICS (continued) MOODY (STANTON) DIAGRAM Reprinted by permission of ASHRAE. 0015 FLUID MECHANICS (continued) DRAG COEFFICIENTS FOR SPHERES, DISKS, AND CYLINDERS ρV2A 24 , Re < 10 Re CD 2FD CD = 46 DV THERMODYNAMICS R is specific to each gas but can be found from PROPERTIES OF SINGLE-COMPONENT SYSTEMS R= Nomenclature 1. Intensive properties are independent of mass.

T TL dz = , where GJ GJ φ = total angle (radians) of twist, T = torque, and L = length of shaft. τφz = Gr [T/(GJ)] = Tr/J T GJ , where = L φ T/φ gives the twisting moment per radian of twist. This is called the torsional stiffness and is often denoted by the symbol k or c. For Hollow, Thin-Walled Shafts T τ= , where 2 Am t t = thickness of shaft wall and Am = the total mean area enclosed by the shaft measured to the midpoint of the wall. BEAMS Shearing Force and Bending Moment Sign Conventions 1.

Vennard. Diagrams reprinted by permission of John Wiley & Sons, Inc. 41 FLUID MECHANICS (continued) p = the internal pressure in the pipe line, A = the cross-sectional area of the pipe line, W = the weight of the fluid, V = the velocity of the fluid flow, α = the angle the pipe bend makes with the horizontal, ρ = the density of the fluid, and Q = the quantity of fluid flow. IMPULSE TURBINE • Jet Propulsion • W = Qρ (V1 – v)(1 – cos α) v, where W = power of the turbine. W max = Qρ (V12/4)(1 – cos α) When α = 180°, W max = (QρV 2)/2 = (QγV 2)/2g 1 1 F = Qρ(V2 – 0) MULTIPATH PIPELINE PROBLEMS • F = 2γhA2, where F γ h A2 Q V2 = = = = = = the propulsive force, the specific weight of the fluid, the height of the fluid above the outlet, the area of the nozzle tip, A2 2 gh , and 2 gh The same head loss occurs in each branch as in the combination of the two.

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