{
"document_id": 11428,
"page": 98,
"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": 8,
"counts_by_type": {
"formula": 7,
"text": 1
},
"build_ms": 1,
"items": [
{
"id": "p98.1",
"order": 1,
"type": "formula",
"bbox": {
"l": 212.4,
"t": 792,
"r": 366.72,
"b": 786.24
},
"text": "",
"attrs": {
"block_label": "display_formula"
}
},
{
"id": "p98.2",
"order": 2,
"type": "formula",
"bbox": {
"l": 137.76,
"t": 673.2,
"r": 470.88,
"b": 591.6
},
"text": "\\begin{aligned}\\mathrm{V}&=\\frac{\\mathrm{h}(\\mathrm{~A}_{1}+\\mathrm{~A}_{2}+\\sqrt{\\mathrm{~A}_{1}\\times\\mathrm{A}_{2}})}{3}\\\\&=\\frac{10(10,800+4,000+\\sqrt{(10,800)(4000)})}{3}=71,242\\mathrm{~ft}^{2}\\end{aligned}",
"attrs": {
"block_label": "display_formula",
"latex": "\\begin{aligned}\\mathrm{V}&=\\frac{\\mathrm{h}(\\mathrm{~A}_{1}+\\mathrm{~A}_{2}+\\sqrt{\\mathrm{~A}_{1}\\times\\mathrm{A}_{2}})}{3}\\\\&=\\frac{10(10,800+4,000+\\sqrt{(10,800)(4000)})}{3}=71,242\\mathrm{~ft}^{2}\\end{aligned}",
"notation": "latex",
"alt": "begin aligned V & equals frac h of A sub 1 plus A sub 2 plus sqrt A sub 1 times A sub 2 3 & equals 10 times 10, 800 plus 4, 000 plus the square root of of 10, 800 times 4000 over 3 equals 71, 242 ft squared end aligned",
"mathml": ""
}
},
{
"id": "p98.3",
"order": 3,
"type": "formula",
"bbox": {
"l": 137.76,
"t": 576.24,
"r": 400.56,
"b": 558.48
},
"text": "V = 71,242 ft² × 7.48 gal/ft³ = 532,892 gal",
"attrs": {
"block_label": "display_formula",
"latex": "\\mathrm{V}=71,242\\ \\mathrm{ft^2}\\ \\times\\ 7.48\\ \\mathrm{gal/ft^3}\\ =\\ 532,892\\ \\mathrm{gal}",
"alt": "V equals 71, 242 ft squared times 7.48 gal over ft cubed equals 532, 892 gal",
"mathml": ""
}
},
{
"id": "p98.4",
"order": 4,
"type": "formula",
"bbox": {
"l": 136.08,
"t": 529.68,
"r": 503.04,
"b": 427.68
},
"text": "\\begin{aligned}\\mathrm{h}^{\\prime}&=\\dfrac{\\mathrm{h}}{4}\\left[4-\\dfrac{(A_{1}+2\\sqrt{A_{1}\\times A_{2}}+3A_{2})}{(A_{1}+\\sqrt{A_{1}\\times A_{2}}+A_{2})}\\right]\\\\&=\\dfrac{10}{4}\\left[4-\\dfrac{[10,800+2\\sqrt{(10,800)(4000)}+3(4000)]}{[10,800+\\sqrt{(10,800)(4000)}+4000]}\\right]=5.8\\end{aligned}",
"attrs": {
"block_label": "display_formula",
"latex": "\\begin{aligned}\\mathrm{h}^{\\prime}&=\\dfrac{\\mathrm{h}}{4}\\left[4-\\dfrac{(A_{1}+2\\sqrt{A_{1}\\times A_{2}}+3A_{2})}{(A_{1}+\\sqrt{A_{1}\\times A_{2}}+A_{2})}\\right]\\\\&=\\dfrac{10}{4}\\left[4-\\dfrac{[10,800+2\\sqrt{(10,800)(4000)}+3(4000)]}{[10,800+\\sqrt{(10,800)(4000)}+4000]}\\right]=5.8\\end{aligned}",
"notation": "latex",
"alt": "begin aligned h to the power of prime & equals dfrac h 4 4 minus dfrac of A sub 1 plus 2 the square root of A sub 1 times A sub 2 plus 3 A sub 2 times A sub 1 plus the square root of A sub 1 times A sub 2 plus A sub 2 & equals dfrac 10 4 4 minus dfrac 10, 800 plus 2 the square root of of 10, 800 times 4000 plus 3 times 4000 10, 800 plus the square root of of 10, 800 times 4000 plus 4000 equals 5.8 end aligned",
"mathml": ""
}
},
{
"id": "p98.5",
"order": 5,
"type": "formula",
"bbox": {
"l": 132.48,
"t": 371.52,
"r": 428.4,
"b": 288.72
},
"text": "\\begin{array}{l} \\mathrm{Aw}~=~\\frac{2\\mathrm{h}^{\\prime}\\left[\\mathrm{~L}_{2}~+\\mathrm{~W}_{2}~+2\\mathrm{h}^{\\prime}\\right]}{\\sin\\beta}+\\mathrm{~A}_{2} \\\\ \\quad \\quad =~\\frac{2(5.8)\\left(80+50+2(5.8)\\right)}{\\sin26.6^{\\circ}}+4000~=~7,673~\\mathrm{ft}^{2} \\end{array}",
"attrs": {
"block_label": "display_formula",
"latex": "\\begin{array}{l} \\mathrm{A w}~=~\\frac{2\\mathrm{h}^{\\prime}\\left[\\mathrm{~L}_{2}~+\\mathrm{~W}_{2}~+2\\mathrm{h}^{\\prime}\\right]}{\\sin\\beta}+\\mathrm{~A}_{2} \\\\ \\quad \\quad =~\\frac{2(5.8)\\left(80+50+2(5.8)\\right)}{\\sin26.6^{\\circ}}+4000~=~7,673~\\mathrm{ft}^{2} \\end{array}",
"notation": "latex",
"alt": "begin array l Aw equals frac 2 h to the power of prime L sub 2 plus W sub 2 plus 2 h to the power of prime sin beta plus A sub 2 equals 2 times 5.8 times 80 plus 50 plus 2 times 5.8 over sin 26.6 to the power of circ plus 4000 equals 7, 673 ft squared end array",
"mathml": ""
}
},
{
"id": "p98.6",
"order": 6,
"type": "formula",
"bbox": {
"l": 137.28,
"t": 242.64,
"r": 373.92,
"b": 209.52
},
"text": "\\mathrm{T}=\\underbrace{\\mathrm{V}}_{\\mathrm{R}^{*}\\mathrm{A}_{\\mathrm{w}}}=\\underbrace{532,892}_{(20)(7,673)}=3.47\\mathrm{days}",
"attrs": {
"block_label": "display_formula",
"latex": "\\mathrm{T}=\\underbrace{\\mathrm{V}}_{\\mathrm{R}^{*}\\mathrm{A}_{\\mathrm{w}}}=\\underbrace{532,892}_{(20)(7,673)}=3.47\\mathrm{days}",
"notation": "latex",
"alt": "T equals underbrace V sub R to the power of * A sub w equals underbrace 532, 892 sub of 20 times 7, 673 equals 3.47 days",
"mathml": ""
}
},
{
"id": "p98.7",
"order": 7,
"type": "formula",
"bbox": {
"l": 137.76,
"t": 179.76,
"r": 242.16,
"b": 147.36
},
"text": "FS = 7/3.47 = 2.02",
"attrs": {
"block_label": "display_formula",
"latex": "FS = \\frac{7}{3.47} = 2.02",
"alt": "FS equals 7 over 3.47 equals 2.02",
"mathml": ""
}
},
{
"id": "p98.8",
"order": 8,
"type": "text",
"bbox": {
"l": 294.48,
"t": 82.32,
"r": 333.36,
"b": 67.2
},
"text": "V-19",
"attrs": {
"block_label": "number"
}
}
],
"excluded_furniture": {
"first": [],
"last": []
}
}