Hydraulic Characteristics and Numerical Simulation of the Entrance Section of Ladder-Shaped Spillway

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left">Hydraulic parameters</td><td class="align_center">Conversion relation</td><td class="align_center">Similar scale</td><td class="align_center">Hydraulic parameters</td><td class="align_center">Conversion relation</td><td class="align_center">Similar scale</td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">Length <svg height="9.49473pt" id="M5" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 3.60972 9.49473" width="3.60972pt" 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="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z"></path></g></svg></td><td class="align_center"><span style="width: 10.8632ptpx;"><svg height="12.5794pt" id="M6" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 10.8632 12.5794" width="10.8632pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><path d="M238 675C244 702 241 710 231 710C220 710 155 682 74 673L70 643H101C147 643 151 635 142 594L39 111C18 11 36 -12 55 -12C89 -12 170 38 223 103L207 129C176 98 130 68 118 68C113 68 108 72 114 102L238 675Z"></path></g></svg></span></td><td class="align_center">25</td><td class="align_center">Flow <svg height="10.7866pt" id="M7" style="vertical-align:-2.150701pt" version="1.1" viewbox="-0.0498162 -8.6359 9.52083 10.7866" width="9.52083pt" 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="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z"></path></g></svg></td><td class="align_center"><span style="width: 54.0376ptpx;"><svg height="17.1922pt" id="M8" style="vertical-align:-4.6795pt" version="1.1" viewbox="-0.0498162 -12.5127 54.0376 17.1922" width="54.0376pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><path d="M750 355C750 552 603 667 428 667C199 667 24 497 24 286C24 118 146 -4 316 -16L336 -29C480 -122 544 -145 582 -154C606 -159 666 -170 714 -172L722 -146C652 -117 562 -75 472 -15L454 -3C623 38 750 176 750 355ZM646 353C646 210 556 50 414 25L385 41L304 27C193 50 128 152 128 282C128 474 254 626 418 626C571 626 646 519 646 353Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.541,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.804,0)"><path d="M529 97L508 118C475 75 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transform="matrix(.0091,0,0,-0.0091,44.999,-5.996)"><path d="M381 704H317L48 -163H112L381 704Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,48.906,-5.996)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g></svg></span></td><td class="align_center">3025</td></tr><tr><td class="align_left">Pressure <svg height="10.2124pt" id="M9" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt" 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="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 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213 -227 231 -213C231 -187 234 -77 240 -23C251 -6 277 30 309 69C424 208 493 299 493 373Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.985,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,37.248,0)"><path d="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,45.009,3.132)"><path d="M238 675C244 702 241 710 231 710C220 710 155 682 74 673L70 643H101C147 643 151 635 142 594L39 111C18 11 36 -12 55 -12C89 -12 170 38 223 103L207 129C176 98 130 68 118 68C113 68 108 72 114 102L238 675Z"></path></g></svg></span></td><td class="align_center">20</td><td class="align_center">Time <svg 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class="align_left">Flow velocity <svg height="6.04987pt" id="M13" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z"></path></g></svg></td><td class="align_center"><span style="width: 51.5075ptpx;"><svg height="15.822pt" id="M14" style="vertical-align:-3.309299pt" version="1.1" viewbox="-0.0498162 -12.5127 51.5075 15.822" width="51.5075pt" 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="M529 97L508 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<div>Hydraulic parameter similarity under the condition of gravity similarity.</div>

Geofluids

tab1

Table 1

Table 1: Hydraulic Characteristics and Numerical Simulation of the Entrance Section of Ladder-Shaped Spillway 