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                                                        Fundamentals of Engineering Review 
                       
                      Fluid Mechanics (Prof. Hayley Shen)     Spring 2010 
                       
                          Fluid Properties 
                          Fluid Statics 
                          Fluid Dynamics 
                          Dimensional Analysis 
                          Applications 
                       
                      Fluid Properties (Table) 
                      Density 
                      Specific weight, specific gravity 
                      Viscosity (absolute or dynamics, kinematic) 
                      Bulk modulus 
                      Speed of sound 
                      Surface tension 
                      Vapor pressure 
                       
                      Fluid Statics 
                      Pressure vs. elevation 
                      Manometers 
                      Force over submerged plane and curved surfaces 
                      Buoyancy 
                       
                      Fluid Dynamics 
                      Continuity equation 
                      Linear momentum equation 
                      Angular momentum equation 
                      Energy equation 
                      Bernoulli equation 
                      EGL and HGL 
                       
                      Dimensional Analysis 
                      Buckingham Pi Theorem 
                      Common dimensionless parameters 
                      Dynamic similitude 
                       
                      Applications 
                      Pipe flow- 
                                Reynolds number, Laminar and Turbulent flows, Entrance length, Darcy-Weisbach 
                                equation, Moody chart, hydraulic radius, pump and turbine head. 
                      Open channel flow- 
                       Chezy-Manning equation 
                                EGL (Energy Grade Line)  and HGL (Hydraulic Grade Line) 
                       
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                         Fluid Properties (Table) 
                         Density 
                         Specific weight, specific gravity 
                         Viscosity (absolute or dynamic, kinematic) 
                         Bulk modulus 
                         Speed of sound 
                         Surface tension 
                         Vapor pressure 
                          
                              SG fluid                     fluid      
                                        H O@4oC           H O@4oC
                                            2                  2
                                 u  F  
                                        z      A
                              E  dp    c Ev  
                                  v       d/                  
                               p  p  2                                 h  2 cos          
                                  i      o     R         pi           po                   R
                          
                         Example 
                         Find the terminal velocity of the object. 
                                                                                        
                          
                          
                          
                          
                          
                          
                          
                          
                          
                          
                          
                          
                          
                          
                          
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                      Fluid Statics 
                      Pressure vs. elevation 
                      Manometers 
                      Force over submerged plane and curved surfaces 
                      Buoyancy 
                       
                           p  p  0,   x, y : horinzontal axes    p   ,  z: vertical axis 
                            x     y                                         z
                          When used in manometers, the above says that you h when you go up from some 
                           point and h when you go down. Inclined manometers are used to amplify the 
                           menisci difference and increase accuracy.  
                            pabs  pgage  patm   Absolute pressures are often indicated as psia, and gage pressure 
                           as psig. 
                          For plane surfaces, use 
                            F   y sinA for the total pressure force, where  
                             R       c
                            c: centroid of the submerged surface; y : the distance between the centroid and the top 
                                                                              c
                           of the fluid   along the orientation of the surface A; A is the 
                           submerged area;   is the angle of incline of surface A. This force 
                           is not applied at the centroid. It is below the centroid. The point 
                           of application is along the incline of surface at a distance  yR 
                           below the surface 
                             y   y  Ixc  
                              R      c    y A
                                            c
                          For curved surface, separate the pressure force into horizontal and vertical part. The 
                          horizontal part becomes plane surface and the vertical force becomes weight. 
                                                       
                          F F F  on the vertical projection,  F  weight of fluid above  W  F  
                            h      R       2                                     v                                           1
                           F                              .  If an object is submerged in several different fluids, must 
                              buoyancy      fluid  submerged
                          calculate the buoyancy in each of them, then add together. When using buoyancy in 
                          problems, FBD is often needed. 
                       
                      Example  
                      Find the tension in the cable if the system is 
                      neutrally buoyant.  
                       
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                      Fluid Dynamics 
                      Continuity equation 
                      Linear momentum equation 
                      Angular momentum equation (Moment of momentum equation) 
                      Energy equation 
                      Bernoulli equation 
                      EGL and HGL 
                       
                                                                       ˆ
                                                          d           V ndA
                      Continuity equation :                              0
                                                   t CV           CS
                                                 
                                            :    (    )     (     )     or              incompressible: 
                               steady state      Av      Av             m m                               Q Q
                                                       in          out        in     out                        in     out
                      Linear momentum equation :                                ˆ               
                                                               Vd VVndAFs
                                                          t CV              CS
                                                               
                               steady state :                        where          
                                               M M F                         M mv
                                                  out      in     total           i       i
                      Moment-of -momentum equation:                                             ˆ          
                                                                          r Vd rVV ndA0
                                                                    t CV                 CS
                                                                              
                               steady state :    (r vm)           (r vm) 
                                             
                                                           out                 in    o(total)
                      Steady state energy equation with one inlet and one outlet :
                       ~     p    v2                 ~     p    v2
                      (                    )       (                                     
                       u           gz       m u              gz) m Q            W
                                 2         out                2         in       net in    shaft in
                       ~ v2                     ~ v2                                      ~    ~     p
                                                                              
                      (h       gz) m(h              gz) mQ             W         ,  h  u       enthalpy
                                      out                      in        net in   shaft in
                             2                       2                                               
                                                         p     v2
                      H H h h,  H                            z,  h  0  always.
                         out     in      L     s             2g          L
                                
                      W         mgh        Qh
                        shaft       s       s                                                                           
                                                p    v2
                      Bernoulli equation :   2g  z  constant along a streamline
                      Bernoulli equation is a conservation of energy equation. It is never 100% applicable. 
                                                  p     v2
                      EGL: line connecting    2g  z  (total head line) 
                      HGL: line connecting  p  z  (piezometric head line) 
                                                   
                      Example (Venturi meter) 
                      Which is true? 
                      1.  the pressure at B is increased 
                      2.  the velocity at B is decreased 
                      3.  the potential energy at C is decreased 
                      4.  the flow energy at B is decreased 
                      5.  the kinetic energy at B is reduced