Calculation Formula Optimization and Effect of Ring Clearance on Axial Force of Multistage Pump

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="749375.fig.006a" src="https://static.hindawi.com/articles/mpe/volume-2013/749375/figures/749375.fig.006a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b> Axial force of first-stage impeller</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="749375.fig.006b" src="https://static.hindawi.com/articles/mpe/volume-2013/749375/figures/749375.fig.006b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Axial force of second-stage impeller</td></tr></table></td></tr></table>

<table><svg height="11.175" id="M66" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.7 11.175" width="10.7" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5
t29.5 81.5l72 387l7.5 40.5t1 26.5t-4 18t-15.5 10t-24 6t-37 4l8 28h461z" id="x1D439"></path></g>
</svg>-<svg height="14.3125" id="M67" style="vertical-align:-2.2932pt" version="1.1" viewbox="0 0 13.175 14.3125" width="13.175" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M745 361q0 -134 -83.5 -233t-214.5 -130l16 -11q97 -67 250 -132l-8 -23q-76 3 -131 16q-81 19 -242 125l-20 13q-129 8 -209 91t-80 208q0 160 116 271t289 111q136 0 226.5 -83t90.5 -223zM645 356q0 127 -57.5 201.5t-169.5 74.5q-126 0 -210.5 -104.5t-84.5 -248.5
q0 -97 46 -166.5t129 -87.5l84 15l29 -19q104 21 169 121.5t65 213.5z" id="x1D444"></path></g>
</svg> curve of primary and secondary impeller with different ring clearances.</table>

Mathematical Problems in Engineering

fig6

Figure 6

Figure 6: Calculation Formula Optimization and Effect of Ring Clearance on Axial Force of Multistage Pump 