Slip factor

<h2 id="factors-accounting-for-slip-factor">Factors accounting for slip factor</h2>
<ul><li>Relative <a href="/facts/Eddy_(fluid_dynamics)/V0hTLblX">eddy</a>.</li>
<li>Back eddy.</li>
<li>Impeller design or geometry</li></ul>
<ol><li>Mean blade loading.</li>
<li>Thickness of blade.</li>
<li>Finite number of blades.</li></ol>
<ul><li>Fluid entry conditions.</li>
<li>Working fluid's <a href="/facts/Viscosity/QLVfrdCz">viscosity</a>.</li>
<li>Effect of <a href="/facts/Boundary_layer/go8gqWM1">boundary layer</a> growth.</li>
<li>Flow separation.</li>
<li>Friction forces on the walls of flow packages.</li>
<li>Boundary layer blockage.</li></ul>
<h2 id="mathematical-formulae-for-slip-factor">Mathematical Formulae for Slip factor</h2>

<p>Mathematically, the Slip factor denoted by 'σ' is defined as the ratio of the actual & ideal values of the whirl velocity components at the exit of the impeller. The ideal values can be calculated using an analytical approach while the actual values should be observed experimentally.
</p>

σ
        =
        
          
            
              V
              
                w
                2
              
              ′
            
            
              V
              
                w
                2
              
            
          
        
      
    
    {\displaystyle \sigma ={\frac {V'_{w2}}{V_{w2}}}}

<p>where, 
</p>
V'w2 : Actual Whirl Velocity Component ,
Vw2  : Ideal Whirl Velocity Component
<p>Usually,σ varies from 0-1 with an average ranging from 0.8-0.9.
</p><p>The Slip Velocity is given as:
</p><p>VS = Vw2 - V'w2 = Vw2(1-σ)
</p><p>The Whirl Velocity is given as:
</p><p>V'w2 = σ Vw2
</p>
<h2 id="slip-factor-correlations">Slip Factor correlations</h2>
<ul><li>Stodola's Equation: According to Stodola, it is the relative eddy that fills the entire exit session of the impeller passage. For a given flow geometry, the slip factor increases with the increase in the number of impeller blades, thus, accounts for one of the important parameter for losses.</li></ul>

σ
        =
        1
        −
        
          
            π
            z
          
        
        
          
            
              sin
              ⁡
              
                β
                
                  2
                
              
            
            
              (
              1
              −
              
                ϕ
                
                  2
                
              
              cot
              ⁡
              
                β
                
                  2
                
              
              )
            
          
        
      
    
    {\displaystyle \sigma =1-{\frac {\pi }{z}}{\frac {\sin \beta _{2}}{(1-\phi _{2}\cot \beta _{2})}}}

where, z = number of blades and 
  
    
      
        
          ϕ
          
            2
          
        
        =
        
          
            
              V
              
                r
                2
              
            
            
              U
              
                2
              
            
          
        
      
    
    {\displaystyle \phi _{2}={\frac {V_{r2}}{U_{2}}}}
  
 <a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a>
For Radial tip, β2 = 900 ∴ 
  
    
      
        σ
        =
        1
        −
        
          
            π
            z
          
        
      
    
    {\displaystyle \sigma =1-{\frac {\pi }{z}}}

Theoretically, In order to get the perfect ideal flow guidance, one can infinitesimally increase the number of thin vanes so that the flow should leave the impeller at an exact vane angle.
However, later experiments proved that beyond a particular value, a further increase in number of blades results in reduction of slip factor due to increase in blockage area.
<ul><li>Stanitz's Equation: Stanitz found the slip velocity does not depend upon the blade exit angle and hence, gave the following equation.</li></ul>

σ
        =
        1
        −
        
          
            1.98
            
              z
              (
              1
              −
              
                ϕ
                
                  2
                
              
              cot
              ⁡
              
                β
                
                  2
                
              
              )
            
          
        
      
    
    {\displaystyle \sigma =1-{\frac {1.98}{z(1-\phi _{2}\cot \beta _{2})}}}

where, z = number of blades,
β2 varies from 450 to 900.
For radial tip: β2 = 900  ∴ 
  
    
      
        σ
        =
        1
        −
        
          
            1.98
            z
          
        
        =
        1
        −
        
          
            
              0.63
              ∗
              p
              i
            
            z
          
        
      
    
    {\displaystyle \sigma =1-{\frac {1.98}{z}}=1-{\frac {0.63*pi}{z}}}

<ul><li>Balje's formula: An approximate formula given by Balje for radial-tipped (β2=900) blade impellers:</li></ul>

σ
        =
        [
        1
        +
        
          
            6.2
            
              z
              .
              
                n
                
                  2
                  
                    /
                  
                  3
                
              
            
          
        
        
          ]
          
            −
            1
          
        
      
    
    {\displaystyle \sigma =[1+{\frac {6.2}{z.n^{2/3}}}]^{-1}}

where, z = number of blades , n = 
  
    
      
        
          
            
              I
              m
              p
              e
              l
              l
              e
              r
               
              T
              i
              p
               
              D
              i
              a
              m
              e
              t
              e
              r
            
            
              E
              y
              e
               
              T
              i
              p
               
              D
              i
              a
              m
              e
              t
              e
              r
            
          
        
      
    
    {\displaystyle {\frac {Impeller\ Tip\ Diameter}{Eye\ Tip\ Diameter}}}

<p>The above explained models clearly states that the Slip factor is solely a function of geometry of Impeller. However, later studies proved that Slip factor depends on other factors as well namely 'mass flow rate',viscosity etc..
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Boundary_layer/go8gqWM1">Boundary layer</a> – Layer of fluid in the immediate vicinity of a bounding surface</li>
<li><a href="/facts/Fluid_mechanics/NIy4tRfE">Fluid mechanics</a> – Branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas)</li>
<li><a href="/facts/Flow_separation/Lnvdqo4p">Flow separation</a> – Detachment of a boundary layer from a surface into a wake</li></ul>
<h2 id="notes">Notes</h2>
<ul><li>It is found that the downfall in blade angle towards the impeller exit results in increment of slip factor with increasing flow rate and vice versa.</li>
<li><a href="http://pme.sagepub.com/content/188/1/415.abstract">Slip Factor being a function of mass flow rate because of back eddy</a>.</li></ul>

<ol><li>Flow simulation in radial pump impellers and evaluation of slip factor (July, 2015), <a href="http://pia.sagepub.com/content/early/2015/07/08/0957650915594953.full.pdf?ijkey=pW8QmRIKoDzyXzO&keytype=finite">http://pia.sagepub.com/content/early/2015/07/08/0957650915594953.full.pdf?ijkey=pW8QmRIKoDzyXzO&keytype=finite</a>.</li>
<li>Seppo A. Korpela (2011), Principles of Turbomachinery. John Wiley & Sons, Inc. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-470-53672-8.</li>
<li>S.L. Dixon (1998), Fluid Mechanics And Thermodynamics of Turbomachinery. Elsevier Butterworth-Heinemann, Inc. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-7506-7870-4.</li>
<li>Rama Gorla, Aijaz Khan, Turbomachinery:Design and Theory. Marcel Dekker, Inc. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-8247-0980-2.</li>
<li><a href="http://www.fkm.utm.my/~syahruls/3-teaching/2-fluid-II/fluid-II-enote/31-pump.pdf">Fluid Machine - FKM</a></li>
<li><a href="http://turbomachinery.asmedigitalcollection.asme.org/article.aspx?articleid=1468608">Analysis and Validation of a Unified Slip Factor Model for Impellers at Design and off-Design Conditions</a></li>
<li><a href="http://www.atlantis-press.com/publications/aisr/mems-12/index_mems-12.html?http%3A//www.atlantis-press.com/php/paper-details.php%3Fid%3D3802">Numerical Study of Slip Factor in Centrifugal Pumps and Study Factors Affecting its Performance</a></li>
<li><a href="http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/machine/ui/Course_home-8.htm">Fluid Machinery - NPTEL</a></li>
<li><a href="http://www.buet.ac.bd/me/icme/icme2003/Proceedings/PDF/ICME03-FL-12.pdf">Experimental and Analytical Investigations of Slip Factor In Radial Tipped Centrifugal Fan</a>.</li></ol>

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

<ol>
<li id="fn:1"><p>S.L. Dixon (1978), Fluid Mechanics, Thermodynamics of Turbomachinery. Pergamon Press, Third Edition. ISBN 0-08-022721-X <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Slip factor open-in-new

Slip factor