Plug flow

<h2 id="determination">Determination</h2>
<p>For flows in pipes, if flow is turbulent then the <a href="/facts/Laminar_sublayer/vpoCFnJn">laminar sublayer</a> caused by the pipe wall is so thin that it is negligible. Plug flow will be achieved if the sublayer thickness is much less than the pipe diameter (
  
    
      
        
          δ
          
            s
          
        
      
    
    {\displaystyle \delta _{s}}
  
<<<i>D</i>).
</p>

δ
          
            s
          
        
        =
        
          
            
              5
              ν
            
            
              u
              
                ∗
              
            
          
        
      
    
    {\displaystyle \delta _{s}={\frac {5\nu }{u^{*}}}}

u
          
            ∗
          
        
        =
        
          
            (
            
              
                
                  τ
                  
                    w
                  
                
                ρ
              
            
            )
          
          
            1
            
              /
            
            2
          
        
      
    
    {\displaystyle u^{*}=\left({\frac {\tau _{w}}{\rho }}\right)^{1/2}}

τ
          
            w
          
        
        =
        
          
            
              D
              Δ
              P
            
            
              4
              L
            
          
        
      
    
    {\displaystyle \tau _{w}={\frac {D\Delta P}{4L}}}
  
<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>

Δ
              P
            
            L
          
        
        =
        
          
            
              f
              ρ
              
                V
                
                  2
                
              
            
            
              2
              D
            
          
        
      
    
    {\displaystyle {\frac {\Delta P}{L}}={\frac {f\rho V^{2}}{2D}}}
  
<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>

1
            
              
                
                  f
                
              
            
          
        
        =
        −
        2.0
        
          log
          
            10
          
        
        ⁡
        
          (
          
            
              
                
                  ϵ
                  
                    /
                  
                  D
                
                3.7
              
            
            +
            
              
                2.51
                
                  
                    Re
                  
                  
                    
                      
                        f
                      
                    
                  
                
              
            
          
          )
        
        ,
        
          (turbulent flow)
        
      
    
    {\displaystyle {1 \over {\sqrt {\mathit {f}}}}=-2.0\log _{10}\left({\frac {\epsilon /D}{3.7}}+{\frac {2.51}{{\text{Re}}{\sqrt {\mathit {f}}}}}\right),{\text{(turbulent flow)}}}

<p>where 
  
    
      
        f
      
    
    {\displaystyle f}
  
 is the <a href="/facts/Darcy_friction_factor/WLXgEHpP">Darcy friction factor</a> (from the above equation or the <a href="/facts/Moody_Chart/tUbSjCQW">Moody Chart</a>), 
  
    
      
        
          δ
          
            s
          
        
      
    
    {\displaystyle \delta _{s}}
  
 is the sublayer thickness, 
  
    
      
        D
      
    
    {\displaystyle D}
  
 is the pipe diameter, 
  
    
      
        ρ
      
    
    {\displaystyle \rho }
  
 is the <a href="/facts/Density/92p6hh9I">density</a>, 
  
    
      
        
          u
          
            ∗
          
        
      
    
    {\displaystyle u^{*}}
  
 is the <a href="/facts/Friction_velocity/rPdMpcd2">friction velocity</a> (not an actual velocity of the fluid), 
  
    
      
        V
      
    
    {\displaystyle V}
  
 is the average velocity of the plug (in the pipe), 
  
    
      
        
          τ
          
            w
          
        
      
    
    {\displaystyle \tau _{w}}
  
 is the shear on the wall, and 
  
    
      
        Δ
        P
      
    
    {\displaystyle \Delta P}
  
 is the pressure loss down the length 
  
    
      
        L
      
    
    {\displaystyle L}
  
 of the pipe. 
  
    
      
        ϵ
      
    
    {\displaystyle \epsilon }
  
 is the relative roughness of the pipe.
In this regime the pressure drop is a result of inertia-dominated turbulent <a href="/facts/Shear_stress/aWWnzIhE">shear stress</a> rather than viscosity-dominated laminar shear stress.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Hagen-Poiseuille_flow/eJkIJ2SV">Hagen-Poiseuille flow</a></li>
<li><a href="/facts/Plug_flow_reactor_model/kCMMrS1M">Plug flow reactor model</a></li></ul>
<h2 id="notes">Notes</h2>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Massey, Bernard; Ward-Smith, John (1999). "6.2 Steady laminar flow in circular pipes: The Hagen-Poiseuille law". Mechanics of fluids (7th ed.). Cheltenham: Thornes. ISBN 9780748740437. <a href="9780748740437" target="_blank">9780748740437</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Munson, Bruce R.; Young, Donald F.; Okiishi, Theodore H. (2006). "Section 8.4". Fundamentals of fluid mechanics (5th ed.). Hoboken, NJ: Wiley. ISBN 9780471675822. <a href="9780471675822" target="_blank">9780471675822</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Engineers Edge. "Pressure Drop Along Pipe Length". Engineers Edge, LLC. Retrieved 17 April 2018. <a href="http://www.engineersedge.com/fluid_flow/pressure_drop/pressure_drop.htm" target="_blank">http://www.engineersedge.com/fluid_flow/pressure_drop/pressure_drop.htm</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Plug flow open-in-new

Plug flow