{
"document_id": 11428,
"page": 97,
"width_pt": 612,
"height_pt": 792,
"rotation": 0,
"pipeline_version": "paddleocr-vl-1.6+paul-48",
"engine": "paddleocr_vl",
"source_run_id": 11539,
"item_count": 19,
"counts_by_type": {
"footer": 1,
"formula": 7,
"header": 1,
"heading": 1,
"text": 9
},
"build_ms": 1,
"items": [
{
"id": "p97.1",
"order": 1,
"type": "header",
"bbox": {
"l": 242.16,
"t": 792,
"r": 343.92,
"b": 786.24
},
"text": "",
"attrs": {
"block_label": "header"
},
"level": 2
},
{
"id": "p97.2",
"order": 2,
"type": "text",
"bbox": {
"l": 122.64,
"t": 655.68,
"r": 277.2,
"b": 638.16
},
"text": "The wetted area is given by:"
},
{
"id": "p97.3",
"order": 3,
"type": "formula",
"bbox": {
"l": 158.4,
"t": 624.48,
"r": 343.92,
"b": 591.6
},
"text": "\\mathrm{A}_{\\mathrm{w}}=\\frac{2\\mathrm{h}^{\\prime}\\left(\\mathrm{L}_{2}+\\mathrm{W}_{2}+2\\mathrm{h}^{\\prime}\\right)}{\\sin\\beta}+\\mathrm{A}_{2}",
"attrs": {
"block_label": "display_formula",
"latex": "\\mathrm{A}_{\\mathrm{w}}=\\frac{2\\mathrm{h}^{\\prime}\\left(\\mathrm{L}_{2}+\\mathrm{W}_{2}+2\\mathrm{h}^{\\prime}\\right)}{\\sin\\beta}+\\mathrm{A}_{2}",
"notation": "latex",
"alt": "A sub w equals frac 2 h to the power of prime of L sub 2 plus W sub 2 plus 2 h to the power of prime sin beta plus A sub 2",
"mathml": ""
}
},
{
"id": "p97.4",
"order": 4,
"type": "text",
"bbox": {
"l": 462.48,
"t": 621.84,
"r": 479.52,
"b": 606.48
},
"text": "(5)",
"attrs": {
"raw_type": "FORMULA_NUMBER",
"block_label": "formula_number"
}
},
{
"id": "p97.5",
"order": 5,
"type": "text",
"bbox": {
"l": 81.36,
"t": 575.76,
"r": 372,
"b": 558
},
"text": "The time required for the basin to empty is given by:"
},
{
"id": "p97.6",
"order": 6,
"type": "formula",
"bbox": {
"l": 159.36,
"t": 544.56,
"r": 237.36,
"b": 510.24
},
"text": "\\mathrm{T}=\\frac{\\mathrm{V}}{\\mathrm{R}\\times\\mathrm{A}_{\\mathrm{w}}}",
"attrs": {
"block_label": "display_formula",
"latex": "\\mathrm{T}=\\frac{\\mathrm{V}}{\\mathrm{R}\\times\\mathrm{A}_{\\mathrm{w}}}",
"notation": "latex",
"alt": "T equals frac V R times A sub w",
"mathml": ""
}
},
{
"id": "p97.7",
"order": 7,
"type": "text",
"bbox": {
"l": 460.08,
"t": 542.4,
"r": 476.64,
"b": 526.56
},
"text": "(6)",
"attrs": {
"raw_type": "FORMULA_NUMBER",
"block_label": "formula_number"
}
},
{
"id": "p97.8",
"order": 8,
"type": "text",
"bbox": {
"l": 81.36,
"t": 484.08,
"r": 307.68,
"b": 466.32
},
"text": "where R = percolation rate in gal/ft [p97.8.1]/day.",
"children": [
{
"id": "p97.8.1",
"order": 9,
"type": "text",
"bbox": {
"l": 81.36,
"t": 484.08,
"r": 307.68,
"b": 466.32
},
"text": "²",
"attrs": {
"inline": true,
"text_offset": 37,
"text_span": 9,
"bbox_estimated": true
}
}
]
},
{
"id": "p97.9",
"order": 10,
"type": "text",
"bbox": {
"l": 81.6,
"t": 460.32,
"r": 257.04,
"b": 441.84
},
"text": "The factor of safety is given by:"
},
{
"id": "p97.10",
"order": 11,
"type": "formula",
"bbox": {
"l": 159.36,
"t": 420.96,
"r": 212.4,
"b": 390
},
"text": "FS = 7/T",
"attrs": {
"block_label": "display_formula",
"latex": "\\mathrm{FS}=\\frac{7}{\\mathrm{T}}",
"alt": "FS equals frac 7 T",
"mathml": ""
}
},
{
"id": "p97.11",
"order": 12,
"type": "text",
"bbox": {
"l": 459.12,
"t": 418.56,
"r": 476.16,
"b": 402
},
"text": "(7)",
"attrs": {
"raw_type": "FORMULA_NUMBER",
"block_label": "formula_number"
}
},
{
"id": "p97.12",
"order": 13,
"type": "heading",
"bbox": {
"l": 80.64,
"t": 352.56,
"r": 307.44,
"b": 333.12
},
"text": "Example Retention Basin Problem",
"attrs": {
"block_label": "paragraph_title"
},
"level": 3
},
{
"id": "p97.13",
"order": 14,
"type": "text",
"bbox": {
"l": 116.16,
"t": 317.04,
"r": 562.56,
"b": 281.28
},
"text": "50' x 80' basin (bottom dimensions), 10' deep with 2:1 side slopes( = 26.6°), and an absorption rate of 20 gal/ft²/day."
},
{
"id": "p97.14",
"order": 15,
"type": "formula",
"bbox": {
"l": 116.64,
"t": 265.2,
"r": 265.92,
"b": 247.68
},
"text": "A2 = (50)(80) = 4,000 ft²",
"attrs": {
"block_label": "display_formula",
"latex": "\\mathrm{A2}=(50)(80)=4,000\\ \\mathrm{ft}^{2}",
"alt": "A2 equals 50 times 80 equals 4, 000 ft squared",
"mathml": ""
}
},
{
"id": "p97.15",
"order": 16,
"type": "formula",
"bbox": {
"l": 115.92,
"t": 239.04,
"r": 378.72,
"b": 201.84
},
"text": "\\mathrm{\\begin{array}{rl}{\\mathrm{L}_{1}=\\mathrm{L}_{2}}&{+\\underbrace{2\\mathrm{h}}_{\\mathrm{\\displaystyle~\\tan~\\beta~}}=80+\\underbrace{2(10)}_{\\mathrm{\\mathrm{~\\tan~26.6^\\circ~}}}=120}\\end{array}}",
"attrs": {
"block_label": "display_formula",
"latex": "\\mathrm{\\begin{array}{r l}{\\mathrm{L}_{1}=\\mathrm{L}_{2}}&{+\\underbrace{2\\mathrm{h}}_{\\mathrm{\\displaystyle~\\tan~\\beta~}}=80+\\underbrace{2(10)}_{\\mathrm{\\mathrm{~\\tan~26.6^\\circ~}}}=120}\\end{array}}",
"notation": "latex",
"alt": "begin array rl L sub 1 equals L sub 2 & plus underbrace 2 h sub displaystyle tan beta equals 80 plus underbrace 2 times 10 sub tan 26.6 to the power of circ equals 120 end array",
"mathml": ""
}
},
{
"id": "p97.16",
"order": 17,
"type": "formula",
"bbox": {
"l": 113.28,
"t": 185.52,
"r": 345.6,
"b": 150.48
},
"text": "\\mathrm{W}_{1}=\\mathrm{W}_{2}+\\frac{2\\mathrm{h}}{\\tan\\beta}\\ \\frac{50+\\underline{2(10)}}{\\tan26.6^{\\circ}}=90^{\\prime}",
"attrs": {
"block_label": "display_formula",
"latex": "\\mathrm{W}_{1}=\\mathrm{W}_{2}+\\frac{2\\mathrm{h}}{\\tan\\beta}\\ \\frac{50+\\underline{2(10)}}{\\tan26.6^{\\circ}}=90^{\\prime}",
"notation": "latex",
"alt": "W sub 1 equals W sub 2 plus frac 2 h tan beta frac 50 plus underline 2 times 10 tan 26.6 to the power of circ equals 90 to the power of prime",
"mathml": ""
}
},
{
"id": "p97.17",
"order": 18,
"type": "formula",
"bbox": {
"l": 116.64,
"t": 133.68,
"r": 295.92,
"b": 114.24
},
"text": "A_{1}\\quad=(90)(120)=10,800\\mathrm{ft}^{2}",
"attrs": {
"block_label": "display_formula",
"latex": "A_{1}\\quad=(90)(120)=10,800\\mathrm{f t}^{2}",
"notation": "latex",
"alt": "A sub 1 equals 90 times 120 equals 10, 800 ft squared",
"mathml": ""
}
},
{
"id": "p97.18",
"order": 19,
"type": "footer",
"bbox": {
"l": 306.96,
"t": 60,
"r": 345.84,
"b": 44.64
},
"text": "V - 18",
"attrs": {
"block_label": "footer"
}
}
],
"excluded_furniture": {
"first": [],
"last": []
}
}