LECTURE NOTES - I 
                          
                          
                          
                          
                          
                          
           « FLUID MECHANICS » 
       
       
       
       
       
       
                Prof. Dr. Atıl BULU 
                          
                          
                          
                          
                          
                          
                 Istanbul Technical University 
                 College of Civil Engineering 
                 Civil Engineering Department 
                   Hydraulics Division 
                                                
                                                
                                        CHAPTER 1 
                                                
                                                
                                     FUNDAMENTALS 
                                                   
                                                
                 1.1. INTRODUCTION 
              
                 Man’s desire for knowledge of fluid phenomena began with his problems of water 
           supply, irrigation, navigation, and waterpower. 
                  
                 Matter exists in two states; the solid and the fluid, the fluid state being commonly 
           divided into the liquid and gaseous states. Solids differ from liquids and liquids from gases in 
           the spacing and latitude of motion of their molecules, these variables being large in a gas, 
           smaller in a liquid, and extremely small in a solid. Thus it follows that intermolecular 
           cohesive forces are large in a solid, smaller in a liquid, and extremely small in a gas. 
            
            
                 1.2. DIMENSIONS AND UNITS 
            
                 Dimension = A dimension is the measure by which a physical variable is expressed 
           quantitatively. 
            
                 Unit = A unit is a particular way of attaching a number to the quantitative dimension. 
            
                 Thus length is a dimension associated with such variables as distance, displacement, 
           width, deflection, and height, while centimeters or meters are both numerical units for 
           expressing length. 
            
                 In fluid mechanics, there are only four primary dimensions from which all the 
           dimensions can be derived: mass, length, time, and force. The brackets around a symbol like 
           [M] mean “the dimension” of mass. All other variables in fluid mechanics can be expressed in 
                                                                        -2
           terms of [M], [L], [T], and [F]. For example, acceleration has the dimensions [LT ]. Force [F] 
           is directly related to mass, length, and time by Newton’s second law, 
            
                 F = ma                                                                                           (1.1) 
                 Force= Mass×Acceleration
                                                
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           From this we see that, dimensionally, [F] = [MLT ]. 
            
                 1 kg-force = 9.81 Newton of force = 9.81 N 
                                                
                                                
                                                
                                                
                                                
                                              1                   Prof. Dr. Atıl BULU 
                                                          Primary Dimensions in SI and MKS Systems 
                                                                                            
                             Primary Dimension                                    MKS Units                                        SI Units
                                                                                            
                                     Force [F]                                  Kilogram (kg)                             Newton (N=kg.m/s2) 
                                                                                            
                                                                                                   2                              Kilogram 
                                     Mass [M] M=G/g = (kgsec/m) 
                                                                                            
                                    Length [L]                                     Meter (m)                                      Meter (m) 
                                               
                                     Time [T]                                    Second (sec)                                   Second (sec) 
                                           
                                                                                            
                                                           Secondary Dimensions in Fluid Mechanics 
                                                                                            
                            Secondary Dimension                                   MKS Units                                        SI Units
                                                                                            
                                                2                                          2                                              2
                                     Area [L ]                                           m                                             m
                                                                                            
                                                   3                                       3                                              3
                                  Volume [L ]                                            m                                             m
                                                                                            
                                                    -1
                                 Velocity [LT ] m/sec  m/sec 
                                                                                            
                                                       -2                                     2                                              2
                              Acceleration [LT ]                                      m/sec                                          m/sec
                                                                                            
                               Pressure or stress                                             2                                          2
                                    -2            -1  -2                              kg/m                                  Pa= N/m (Pascal) 
                              [FL ] = [ML T ] 
                                                                                            
                                                         -1                                 -1                                             -1
                           Angular Velocity [T ]                                       sec                                            sec
                                                                                            
                                  Energy, work                                         kg.m                                   J = Nm (Joule) 
                                                 2 -2
                                [FL] = [ML T ] 
                                                                                            
                                       Power                                        kg.m/sec                                 W = J/sec (Watt) 
                                     -1            2 -3
                              [FLT ] = [ML T ] 
                                                                                            
                               Specific mass (ρ)                                            2    4                                          3
                                     -3           2 -4                             kg.sec /m                                         kg/m
                               [ML ] = [FT L ] 
                                                                                            
                              Specific weight (γ)                                             3                                             3
                                    -3            -2  -2                              Kg/m                                            N/m
                              [FL ] = [ML T ] 
                                                                                            
                                  
                                 Specific mass = ρ = The mass, the amount of matter, contained in a volume. This will 
                      be expressed in mass-length-time dimensions, and will have the dimensions of mass [M] per 
                                            3
                      unit volume [L ]. Thus, 
                       
                                 SpecificMass = Mass  
                                                        Volume
                                                                                          2                                      Prof. Dr. Atıl BULU 
                                                          ⎡M⎤ ⎡FT2⎤
                                                                                                     2       4
                                                []                                      ()
                                                 ρ =⎢ 3⎥=⎢ 4 ⎥, kgsec m  
                                                          ⎣L ⎦           ⎣ L ⎦
                                                                                                                         
                                           Specific weight= γ = will be expressed in force-length-time dimensions and will have 
                                                                                                                3
                             dimensions of force [F] per unit volume [L ]. 
                              
                                            Specificweight = Weight
                                                                              Volume
                                                                                                      
                                                       ⎡ F ⎤         ⎡ M ⎤                       3
                                                                                     ()
                                            []γ   = ⎢ 3⎥ = ⎢ 2 2⎥, kg m
                                                       ⎣L ⎦          ⎣LT ⎦
                                                                                                                         
                             Because the weight (a force), W, related to its mass, M, by Newton’s second law of motion in 
                             the form 
                              
                                            W=Mg 
                                                                                                                         
                             In which g is the acceleration due to the local force of gravity, specific weight and specific 
                             mass will be related by a similar equation, 
                              
                                            γ = ρg                                                                                                              (1.2) 
                                                                                                                         
                                                                                                                                               o                                                                3
                                           EXAMPLE 1.1: Specific weight of the water at 4 C temperature is γ = 1000 kg/m . 
                             What is its the specific mass? 
                              
                                           SOLUTION:  
                                            
                                                                       (           3)
                                            γ = ρg =1000 kg m
                                                    1000                                     2       4  
                                                                                ()
                                            ρ = 9.81 =101.94 kgsec                               m
                                            
                                           EXAMPLE 1.2: A body weighs 1000 kg when exposed to a standard earth gravity     
                                                          2
                             g = 9.81 m/sec .  a) What is its mass? b) What will be the weight of the body be in Newton if 
                             it is exposed to the Moon’s standard acceleration g                                                           = 1.62 m/sec2? c) How fast will the 
                                                                                                                                   moon
                             body accelerate if a net force of 100 kg is applied to it on the Moon or on the Earth?  
                              
                                           SOLUTION: 
                              
                                           a)  Since,                    (      )
                                            W=mg=1000kg
                                                                                                                     
                                                      W 1000                                            2       4
                                                                                           ()
                                            M= g = 9.81 =101.94kgsec m
                                                                                                                                       2
                                           b)  The mass of the body remains 101.94 kgsec /m regardless of its location. Then, 
                                                                                                                       3                                                   Prof. Dr. Atıl BULU