Flow of the Bingham-Papanastasiou Regularized Material in a Channel in the Presence of Obstacles: Correlation between Hydrodynamic Forces and Spacing of Obstacles

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2"><span style="width: 14.8838ptpx;"><svg height="8.8423pt" id="M67" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 14.8838 8.8423" width="14.8838pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.205,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 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class="align_left">5</td><td class="align_center">5.137276</td><td class="align_center">5.454255</td><td class="align_center">5.596619</td><td class="align_center">3.805926</td><td class="align_center">4.819291</td><td class="align_center">5.431213</td></tr><tr><td class="align_left">10</td><td class="align_center">7.678170</td><td class="align_center">8.310039</td><td class="align_center">8.614542</td><td class="align_center">6.367975</td><td class="align_center">7.945050</td><td class="align_center">8.746971</td></tr><tr><td class="align_left">15</td><td class="align_center">10.25628</td><td class="align_center">11.21117</td><td class="align_center">11.67250</td><td class="align_center">8.858097</td><td class="align_center">11.01676</td><td class="align_center">11.97415</td></tr><tr><td class="align_left">20</td><td class="align_center">12.82765</td><td class="align_center">14.13960</td><td class="align_center">14.74656</td><td class="align_center">11.31237</td><td class="align_center">14.05077</td><td class="align_center">15.16758</td></tr><tr><td class="align_left">25</td><td class="align_center">15.37404</td><td class="align_center">17.06890</td><td class="align_center">17.82168</td><td class="align_center">13.75576</td><td class="align_center">17.05546</td><td class="align_center">18.34279</td></tr><tr><td class="align_left">30</td><td class="align_center">17.88776</td><td class="align_center">19.99205</td><td class="align_center">20.89772</td><td class="align_center">16.19818</td><td class="align_center">20.03657</td><td class="align_center">21.51033</td></tr><tr><td class="align_left">35</td><td class="align_center">20.37520</td><td class="align_center">22.90187</td><td class="align_center">23.96913</td><td class="align_center">18.63270</td><td class="align_center">22.99907</td><td class="align_center">24.66939</td></tr><tr><td class="align_left">40</td><td class="align_center">22.84084</td><td class="align_center">25.79407</td><td class="align_center">27.03447</td><td class="align_center">21.06723</td><td class="align_center">25.94571</td><td class="align_center">27.81974</td></tr><tr><td class="align_left">45</td><td class="align_center">25.28895</td><td class="align_center">28.67168</td><td class="align_center">30.09469</td><td class="align_center">23.49771</td><td class="align_center">28.87985</td><td class="align_center">30.96336</td></tr><tr><td class="align_left">50</td><td class="align_center">27.72366</td><td class="align_center">31.53868</td><td class="align_center">33.14860</td><td class="align_center">25.92784</td><td class="align_center">31.80647</td><td class="align_center">34.10000</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Influence of <svg height="8.8423pt" id="M65" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 17.0591 8.8423" width="17.0591pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.205,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"></path></g></svg>and separation distance on drag coefficient<span class="nowrap"><svg height="11.927pt" id="M66" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 14.4007 11.927" width="14.4007pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><path d="M538 684C542 703 539 710 529 710C512 710 455 682 363 674L361 644H396C444 644 448 642 438 594L405 438C373 450 347 451 336 451C288 451 200 416 147 374C69 312 24 207 24 113C24 29 60 -12 94 -12C126 -12 156 4 196 30C231 53 296 100 346 166H348L328 81C311 10 325 -12 348 -12C380 -12 450 24 512 98L495 125C466 97 431 70 417 70C408 70 408 80 411 98L538 684ZM390 373L361 240C336 196 210 56 145 56C132 56 113 73 113 131C113 216 156 338 220 379C243 394 266 402 303 402C331 402 375 388 390 373Z"></path></g></svg>.</span></div>

Modelling and Simulation in Engineering

tab2

Table 2

Table 2: Flow of the Bingham-Papanastasiou Regularized Material in a Channel in the Presence of Obstacles: Correlation between Hydrodynamic Forces and Spacing of Obstacles 

Table 2 | Flow of the Bingham-Papanastasiou Regularized Material in a Channel in the Presence of Obstacles: Correlation between Hydrodynamic Forces and Spacing of Obstacles 