{"id":162,"date":"2024-04-08T20:55:20","date_gmt":"2024-04-08T11:55:20","guid":{"rendered":"https:\/\/www.flumen-jp.com\/wordpress\/?p=162"},"modified":"2024-07-04T17:34:17","modified_gmt":"2024-07-04T08:34:17","slug":"manning","status":"publish","type":"post","link":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/2024\/04\/08\/manning\/","title":{"rendered":"\u30de\u30cb\u30f3\u30b0\u5c0f\u567a"},"content":{"rendered":"\n<p>\u2003\u5143\u306e\u8077\u5834\u3067\u8a71\u984c\u63d0\u4f9b\u306e\u305f\u3081\u306b\u4f5c\u3063\u305f\u30b3\u30f3\u30c6\u30f3\u30c4\u3067\u3059\u3002\u5143\u30cd\u30bf\u306f<a href=\"http:\/\/ponce.sdsu.edu\/manning_history.html\">\u3053\u3061\u3089<\/a>\u306b\u306a\u308a\u307e\u3059\u3002<br>\u3000130 \u5e74\u524d\u306b\u30a2\u30a4\u30eb\u30e9\u30f3\u30c9\u306e\u5e02\u4e95\u306e\u571f\u6728\u6280\u8853\u8005\u304c\u6669\u5e74\u306b\u66f8\u3044\u305f\u4e00\u904d\u306e\u8ad6\u6587\u3067\u8a18\u8f09\u3057\u305f\u8fd1\u4f3c\u5f0f\u304c\u5168\u4e16\u754c\u7684\u306b\u4f7f\u308f\u308c\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u3001\u3068\u3044\u3046\u8a71\u3067\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"695\" height=\"1024\" src=\"https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/manning-695x1024.png\" alt=\"\" class=\"wp-image-163\" style=\"width:400px\" srcset=\"https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/manning-695x1024.png 695w, https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/manning-204x300.png 204w, https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/manning-768x1132.png 768w, https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/manning.png 1018w\" sizes=\"auto, (max-width: 695px) 100vw, 695px\" \/><\/figure>\n\n\n\n<div style=\"height:46px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u5e74 \u8b5c<\/h3>\n\n\n\n<p>\u2003\u5148\u305a\u306f Manning \u3055\u3093\u306e\u751f\u6daf\u306e\u4e3b\u306a\u51fa\u6765\u4e8b\u3067\u3059\u3002<br>\u3000\u307b\u307c\u3001\u52dd\u6d77\u821f\uff081823-1899\uff09\u3068\u540c\u3058\u6642\u4ee3\u306e\u4eba\u3001\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>\u5e74<\/th><th class=\"has-text-align-center\" data-align=\"center\">\u6b73<\/th><th>\u51fa\u6765\u4e8b<\/th><\/tr><\/thead><tbody><tr><td>1816.10.22<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td>\u7236\u89aa\u306e\u4efb\u5730\u3001\u30ce\u30eb\u30de\u30f3\u30c7\u30a3\u30fc (\u4ecf) \u306b\u3066\u8a95\u751f<\/td><\/tr><tr><td>1826<\/td><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><td>\u30a6\u30a9\u30fc\u30bf\u30fc\u30d5\u30a9\u30fc\u30c9 (\u30a2\u30a4\u30eb\u30e9\u30f3\u30c9) \u306b\u79fb\u4f4f<\/td><\/tr><tr><td>\uff1f<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td>\u4f1a\u8a08\u58eb\u3068\u3057\u3066\u5c31\u8077<\/td><\/tr><tr><td>1846<\/td><td class=\"has-text-align-center\" data-align=\"center\">30<\/td><td>\u30a2\u30a4\u30eb\u30e9\u30f3\u30c9\u516c\u5171\u4e8b\u696d\u5c40\u5e79\u7dda\u6392\u6c34\u8ab2\u306b\u88fd\u56f3\u5de5\u3068\u3057\u3066\u8ee2\u8077<\/td><\/tr><tr><td><\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td>\u305d\u306e\u5f8c\u3001\u540c\u5c40\u306e\u30b5\u30df\u30e5\u30a8\u30eb\uff65\u30ed\u30d0\u30fc\u30c8\u306e\u30a2\u30b7\u30b9\u30bf\u30f3\u30c8\u306b\u5c31\u304f<\/td><\/tr><tr><td>1848-55<\/td><td class=\"has-text-align-center\" data-align=\"center\">32-39<\/td><td>\u540c\u8ab2\u306b\u3066\u5730\u533a\u306e\u6280\u5e2b\u306b\u6607\u683c<\/td><\/tr><tr><td><\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td>\u3053\u306e\u9593\u306b\u30c0\u30d3\u30e5\u30a4\u30bd\u30f3\u306e\u8457\u66f8\u3068\u51fa\u4f1a\u3044\u6c34\u7406\u5b66\u306b\u76ee\u899a\u3081\u308b<\/td><\/tr><tr><td>1855-69<\/td><td class=\"has-text-align-center\" data-align=\"center\">39-50<\/td><td>\u30c0\u30a6\u30f3\u30b7\u30e3\u30fc\u516c\u7235\u306b\u96c7\u308f\u308c\u3066\u30c0\u30a6\u30f3\u30c9\u30e9\u30e0\u7bc9\u6e2f\u306e\u73fe\u5834\u76e3\u7763\u306b\u5c31\u304f<\/td><\/tr><tr><td><\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td>\u30d9\u30eb\u30d5\u30a1\u30b9\u30c8\u306e\u914d\u6c34\u4e8b\u696d\u306b\u3082\u5f93\u4e8b<\/td><\/tr><tr><td>1869 (\u660e\u6cbb\uff12\u5e74)<\/td><td class=\"has-text-align-center\" data-align=\"center\">50<\/td><td>\u6280\u5e2b\u9577\u88dc\u4f50\u3068\u3057\u3066\u30a2\u30a4\u30eb\u30e9\u30f3\u30c9\u516c\u5171\u4e8b\u696d\u5c40\u306b\u5fa9\u8077 <\/td><\/tr><tr><td>1874<\/td><td class=\"has-text-align-center\" data-align=\"center\">58<\/td><td>\u6280\u5e2b\u9577\u306b\u6607\u683c<\/td><\/tr><tr><td>1889.12.4<\/td><td class=\"has-text-align-center\" data-align=\"center\">73<\/td><td>\u30a2\u30a4\u30eb\u30e9\u30f3\u30c9\u571f\u6728\u5b66\u4f1a\u306b\u8ad6\u6587\u3092\u63d0\u51fa<\/td><\/tr><tr><td>1891<\/td><td class=\"has-text-align-center\" data-align=\"center\">75<\/td><td>\u30a2\u30a4\u30eb\u30e9\u30f3\u30c9\u516c\u5171\u4e8b\u696d\u5c40\u9000\u8077\u3002\u8ad6\u6587\u304c\u5b66\u4f1a\u8a8c\u306b\u63b2\u8f09\u3055\u308c\u308b<\/td><\/tr><tr><td>1897.12.9<\/td><td class=\"has-text-align-center\" data-align=\"center\">81<\/td><td>\u30c0\u30d6\u30ea\u30f3\u306b\u3066\u6c38\u7720<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div style=\"height:35px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u30aa\u30ea\u30b8\u30ca\u30eb\u306e\u30de\u30cb\u30f3\u30b0\u5f0f<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6d41\u4f53\u529b\u5b66\uff65\u6c34\u7406\u5b66\u306b\u95a2\u3059\u308b\u6559\u80b2\u3082\u6b63\u898f\u306e\u8a13\u7df4\u3082\u53d7\u3051\u3066\u3044\u306a\u3044\u5f7c\u306b\u3068\u3063\u3066\u5b9f\u52d9\u3092\u3053\u306a\u3059\u305f\u3081\u306e\u7c21\u6613\u5f0f\u304c\u5fc5\u8981\u3067\u3042\u3063\u305f<\/li>\n\n\n\n<li>\u305d\u3053\u3067\u3001\u5f53\u6642\u8457\u540d\u3067\u3042\u3063\u305f 7 \u7a2e\u985e\u306e\u6d41\u901f\u516c\u5f0f (Du Buat, Eyelwein, Weisbach, St. Venant, Neville, Darcy and Bazin, Ganguillet and Kutter) \u3092\u7528\u3044\u3066\u3001\u52fe\u914d\u3068\u5f84\u6df1\u3092\u5909\u3048\u305f\u6642\u306e\u6d41\u901f\u3092\u8a08\u7b97\u3057\u3066\u6bd4\u8f03<\/li>\n\n\n\n<li>\u5148\u305a 7 \u5f0f\u306e\u5e73\u5747\u5024\u306e\u8fd1\u4f3c\u5f0f\u3068\u3057\u3066 \\(V=32\\bigl[ RS(1+R^{1\/3})\\bigr]^{1\/2}\\)<\/li>\n\n\n\n<li>\u3053\u308c\u3092\u7c21\u5358\u5316\u3057\u3066 \\(V=CR^x S^{1\/2}\\)<\/li>\n\n\n\n<li>\u305d\u3057\u3066\u30011885\u5e74\u306b\u306f \\(C\\) \u306f Ganguillet and Kutter \u306e \\(n\\) \u306e\u9006\u6570\u3068\u307b\u307c\u7b49\u4fa1\u3001\u3068\u3057\u3066<br> $$V=CR^{2\/3} S^{1\/2}$$<\/li>\n\n\n\n<li>\u3064\u307e\u308a\u3001\u4eca\u65e5\u3001\u6211\u3005\u304c\u300c\u30de\u30cb\u30f3\u30b0\u306e\u7956\u5ea6\u4fc2\u6570\u300d\u3068\u3057\u3066\u3044\u308b\u4fc2\u6570\u306f\u6b21\u306e Ganguillet and Kutter \u5f0f\u4e2d\u306e\u5b9a\u6570\u3002<\/li>\n<\/ul>\n\n\n\n<p>$$<br>V = \\frac{\\displaystyle{23+\\frac{1}{n}+\\frac{0.00155}{S}}\\vphantom{\\int}}<br>{\\displaystyle{1 + \\left( 23 + \\frac{0.00155}{S}\\right)\\frac{n}{\\sqrt{R}}}\\vphantom{\\int}}<br>\\sqrt{RS}<br>$$<\/p>\n\n\n\n<div style=\"height:36px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u305d\u306e\u5f8c<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5f53\u6642\u3001\u7acb\u65b9\u6839\u306e\u8a08\u7b97\u304c\u9762\u5012\u3067\u3042\u3063\u305f\u3053\u3068\u3001\\(n\\) \u304c\u7121\u6b21\u5143\u3067\u306a\u3044\u3053\u3068\u304c\u4e0d\u6e80\u3060\u3063\u305f\u306e\u3067\u3001\u5f7c\u306e\u63d0\u6848\u3057\u305f\u6700\u7d42\u5f62\u306f\u4e0b\u5f0f\u3067\u3042\u3063\u305f<\/li>\n<\/ul>\n\n\n\n<p>$$<br>V = C&#8217;\\sqrt{gS}\\left[\\sqrt{R}+\\frac{0.22(R &#8211; 0.15 m)}{\\sqrt{m}}\\right]<br>$$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1918 \u5e74\u306b\u30ad\u30f3\u30b0\u535a\u58eb (\u30df\u30b7\u30ac\u30f3\u5927) \u304c\u76e3\u4fee\u3057\u305f\u300c\u6c34\u5de5\u5b66\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u300d\u306b\u4eca\u65e5\u77e5\u3089\u308c\u3066\u3044\u308b\u6b21\u5f0f\u304c\u7d39\u4ecb\u3055\u308c\u305f\u3053\u3068\u3067\u666e\u53ca\u3057\u3001\u4e00\u90e8\u306e\u6559\u79d1\u66f8\u306b\u3082\u63b2\u8f09\u3055\u308c\u305f<\/li>\n<\/ul>\n\n\n\n<p>$$<br>V=\\frac{1}{n}R^{2\/3} \\sqrt{S}<br>$$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u3061\u306a\u307f\u306b <a href=\"https:\/\/en.wikipedia.org\/wiki\/Manning_formula\">Wikipedia<\/a> \u306b\u3088\u308c\u3070\u3001\u30de\u30cb\u30f3\u30b0\u306b\u5148\u3093\u3058\u308b\u3053\u3068 23 \u5e74\u524d\u306e 1867\u5e74 \u306b\u30b4\u30af\u30ec\u30fc\u30eb (\u4ecf) \u304c\u540c\u69d8\u306e\u5f0f\u3092\u767a\u8868\u3057\u3066\u3044\u305f\u6a21\u69d8\u3067\u3001\u30e8\u30fc\u30ed\u30c3\u30d1\u3067\u306f\u300c\u30b4\u30af\u30ec\u30fc\u30eb\uff65\u30de\u30cb\u30f3\u30b0\uff65\u30b9\u30c8\u30ea\u30af\u30e9\u30fc\u5f0f\u300d\u3068\u547c\u3070\u308c\u3066\u3044\u308b\u7531<\/li>\n<\/ul>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f59 \u8a71<\/h3>\n\n\n\n<p>\u2003\u300c\u5e74\u8b5c\u300d\u3067\u8a18\u3057\u305f\u3088\u3046\u306b Manning \u3055\u3093\u306f\u30c0\u30d3\u30e5\u30a4\u30bd\u30f3\uff08d\u2018Aubisson des Voissons \u4ecf 1769-1841\uff09\u306e\u8457\u66f8\u306b\u3075\u308c\u3066\u6c34\u7406\u5b66\u306b\u76ee\u899a\u3081\u305f\u3002<br>\u2003\u30c0\u30d3\u30e5\u30a4\u30bd\u30f3\u304c\u63d0\u6848\u3057\u305f\u6b21\u306e\u6a4b\u811a\u306b\u3088\u308b\u5830\u4e0a\u3052\u306e\u63a8\u5b9a\u5f0f\u306f<strong>\u672a\u3060\u306b<\/strong>\u672c\u90a6\u306e\u6280\u8853\u30de\u30cb\u30e5\u30a2\u30eb\u306b\u63b2\u8f09\u3055\u308c\u3066\u3044\u308b<\/p>\n\n\n\n<p>$$<br>h= \\frac{\\alpha Q^2}{2g}\\left[<br>\\left\\{\\frac{1}{\\mu(B &#8211; a)H_3} \\right\\}^{2}-<br>\\left\\{\\frac{1}{B(H_3 + h)} \\right\\}^{2}<br>\\right]$$<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"809\" src=\"https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/Aubisson-1024x809.png\" alt=\"\" class=\"wp-image-164\" style=\"width:400px\" srcset=\"https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/Aubisson-1024x809.png 1024w, https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/Aubisson-300x237.png 300w, https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/Aubisson-768x607.png 768w, https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/Aubisson-1536x1214.png 1536w, https:\/\/www.flumen-jp.com\/wordpress\/wp-content\/uploads\/2024\/04\/Aubisson.png 1683w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u304c\u30fb\u30fb\u30fb\u3002\u3053\u306e\u5f0f\u306f<\/p>\n\n\n\n<blockquote class=\"wp-block-quote has-medium-font-size is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u6469\u64e6\u640d\u5931\u306a\u3057\u3001\u4e0a\u56f3\u3067 \\(H_2 =H_3\\)\u3001\u6a4b\u811a\u306e\u5f62\u72b6\u5225\u306e\u7e2e\u6d41\u3092\u4eee\u5b9a\u3057\u3066\u3001\\(\\mbox{I &#8211; II -III}\\) \u306e\u904b\u52d5\u91cf\u306e\u4fdd\u5b58\u3092\u8003\u3048\u305f (\u3060\u3051)<\/p>\n<\/blockquote>\n\n\n\n<p>\u306e\u3082\u306e\u3067\u3001\u660e\u3089\u304b\u306b\u77e9\u5f62\u306e\u5c0f\u6c34\u8def\u9650\u5b9a\u3002\u305d\u3046\u3067\u306a\u3044\u3068\u3001\u5265\u96e2\u6e26\u306e\u30b5\u30a4\u30ba\u304c\u6a4b\u811a\u306e\u9593\u9694\u306b\u4f9d\u5b58\u3059\u308b\u3082\u306e\u306b\u306a\u3063\u3066\u4f4e\u6c34\u8def\u5185\u306e\u6a4b\u811a\u3082\u5824\u9632\u969b\u306e\u9ad8\u6c34\u6577\u306e\u6a4b\u811a\u3082\u540c\u3058\u62b5\u6297\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u3002\u3080\u3084\u307f\u306b\u4f7f\u3063\u3061\u3083\u30c0\u30e1\u3063\u3057\u3087\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u2003\u5143\u306e\u8077\u5834\u3067\u8a71\u984c\u63d0\u4f9b\u306e\u305f\u3081\u306b\u4f5c\u3063\u305f\u30b3\u30f3\u30c6\u30f3\u30c4\u3067\u3059\u3002\u5143\u30cd\u30bf\u306f\u3053\u3061\u3089\u306b\u306a\u308a\u307e\u3059\u3002\u3000130 \u5e74\u524d\u306b\u30a2\u30a4\u30eb\u30e9\u30f3\u30c9\u306e\u5e02\u4e95\u306e\u571f\u6728\u6280\u8853\u8005\u304c\u6669\u5e74\u306b\u66f8\u3044\u305f\u4e00\u904d\u306e\u8ad6\u6587\u3067\u8a18\u8f09\u3057\u305f\u8fd1\u4f3c\u5f0f\u304c\u5168\u4e16\u754c\u7684\u306b\u4f7f\u308f\u308c\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u3001\u3068\u3044\u3046\u8a71\u3067\u3059\u3002 \u5e74 \u8b5c  [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[16,15],"class_list":["post-162","post","type-post","status-publish","format-standard","hentry","category-misc","tag-kutter","tag-manning"],"_links":{"self":[{"href":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/wp-json\/wp\/v2\/posts\/162","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/wp-json\/wp\/v2\/comments?post=162"}],"version-history":[{"count":21,"href":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/wp-json\/wp\/v2\/posts\/162\/revisions"}],"predecessor-version":[{"id":351,"href":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/wp-json\/wp\/v2\/posts\/162\/revisions\/351"}],"wp:attachment":[{"href":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/wp-json\/wp\/v2\/media?parent=162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/wp-json\/wp\/v2\/categories?post=162"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.flumen-jp.com\/wordpress\/index.php\/wp-json\/wp\/v2\/tags?post=162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}