<p>P09454 – The Volute</p><p>From Centrifugal Pump Design (pp 146 Tuzson 2000), the driving equations for the volute shape are Q 360 A  Ct and</p><p>Ct 2 D2 Ct  D2  D3  D2  360</p><p>Where Q = flow rate</p><p>Ct2=Tangential Velocity at diffuser exit</p><p>D2=Diffuser O.D.</p><p>D3=Volute Throat centerline diameter Θ=Angle</p><p>Based on industry design practices, this area is sized up 25% to account for friction and slip losses in the housing (Tuzson pp146). Additionally, a clearance with the diffuser needs to be accounted for, which amounts to 5% of the diffuser ring’s</p><p>O.D.</p><p>For the sake of a more simple design, a constant volute depth “t” is assumed. Because of this, the equation for volute cross-sectional area can be solved directly for the radius of the volute wall. Combining all design factors and terms yields the following governing equation for the volute radius in terms of the angle θ:</p><p>  2  Q D   D  D    2 3 2 360  1.05D R  1.25*    2 720Ct2 D2t 2</p><p>This design gives a volute throat height of .88”. A pump discharge of 1 inch is desired, so after the volute throat a gradual diffuser is incorporated into the design to bring the width to 1 inch. Volute Cross-Sectional Area</p><p>D2 Diffuser OD 6.25 in D3 Volute Diameter at throat Increase 25% to account for losses 7.32 in 5% of Diffuser OD clearance@neck Ct2 Tangential Velocity Exiting Diffuser 93.73 in/s (1 gal = 0.13368 ft3) A=t*R Q Flow Rate 88.2805 in3/s 22.93 gpm R Varying volute wall radius t volute depth θ (deg) R (in) X coord Y coord 0.79 in 0 3.28125 0.0000 3.2813 1 3.283321 0.0573 3.2828 2 3.285394 0.1147 3.2834 3 3.287468 0.1721 3.2830 4 3.289545 0.2295 3.2815 5 3.291624 0.2869 3.2791 =1.25*($G$11*($E$6*A16+($E$8-$E$6)*(A16^2)/360)/(360*$E$10*$E$6*$E$15))/2+$E$6/2*1.05 6 3.293704 0.3443 3.2757 7 3.295787 0.4017 3.2712 8 3.297872 0.4590 3.2658 9 3.299958 0.5162 3.2593 10 3.302047 0.5734 3.2519 11 3.304137 0.6305 3.2434 12 3.30623 0.6874 3.2340 13 3.308324 0.7442 3.2235 14 3.310421 0.8009 3.2121</p><p>Table 1: Sample of Excel Calculations used Figure 1: Plot of Volute Points. Figure 2: Solid model of final volute design.</p>