{"id":1131,"date":"2026-05-12T21:46:19","date_gmt":"2026-05-12T21:46:19","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/darcys-law\/"},"modified":"2026-05-13T03:10:33","modified_gmt":"2026-05-13T03:10:33","slug":"darcys-law","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/darcys-law\/","title":{"raw":"4.3 Darcy\u2019s Law","rendered":"4.3 Darcy\u2019s Law"},"content":{"raw":"<div id=\"darcys-law-1\" class=\"level1\">\r\n<div data-custom-style=\"First Paragraph\">\r\n\r\nAs previously described, Darcy\u2019s law is shown again in Equation\u00a0<a href=\"#Xad27bd134d25229585e45a28289f50d4d731144\"><span data-custom-style=\"Hyperlink\">(33)<\/span><\/a>.\r\n\r\n<\/div>\r\n<table style=\"width: 85%;\" data-custom-style=\"Table\"><colgroup> <col style=\"width: 8%;\" \/> <col style=\"width: 64%;\" \/> <col style=\"width: 11%;\" \/> <\/colgroup>\r\n<thead>\r\n<tr>\r\n<th><\/th>\r\n<th style=\"text-align: center;\">[latex]Q = - KA\\frac{dh}{dl}[\/latex]<\/th>\r\n<th style=\"text-align: right;\"><span id=\"Xad27bd134d25229585e45a28289f50d4d731144\" class=\"anchor\">(33)<\/span><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n<div data-custom-style=\"Body Text\">\r\n\r\nGo through the four steps and try to understand what the equation means.\r\n\r\n<\/div>\r\n<div data-custom-style=\"Body Text\">\r\n\r\n<em>Steps 1 and 2<\/em>. The variables and constants are as follows.\r\n\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]Q[\/latex]\u00a0=\u00a0volumetric discharge: variable with dimensions of L<sup>3<\/sup>T<sup>-1<\/sup><\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]K[\/latex]\u00a0=\u00a0hydraulic conductivity: constant with dimensions of LT<sup>-1<\/sup><\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]A[\/latex]\u00a0=\u00a0cross\u2011sectional area perpendicular to flow: variable with dimensions of L<sup>2<\/sup><\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]dh[\/latex]\u00a0=\u00a0change in head: variable with dimensions of L<\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote>[latex]dl[\/latex]\u00a0=\u00a0change in length along flow path: variable with dimensions of L<\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote><em>Step 3<\/em>. The numerator\u2011denominator relationships to discharge ([latex]Q[\/latex]) are:<\/blockquote>\r\n<\/div>\r\n<ul>\r\n \t<li>cross\u2011sectional area (<em>A<\/em>), directly proportional;<\/li>\r\n \t<li>change in head ([latex]dh[\/latex]), directly proportional;<\/li>\r\n \t<li>change in length ([latex]dl[\/latex]), inversely proportional;<\/li>\r\n \t<li>hydraulic gradient ([latex]dh\/dl[\/latex]), directly proportional; and<\/li>\r\n \t<li>hydraulic conductivity, directly proportional.<\/li>\r\n<\/ul>\r\n<div data-custom-style=\"Block Text\">\r\n<blockquote><em>Step 4<\/em>. There are no modifiers on the variables so the relationships are linear.<\/blockquote>\r\n<\/div>\r\n<div data-custom-style=\"First Paragraph\">\r\n\r\nUsing the above, we can express Darcy\u2019s law in a sentence as \u201cThe volumetric discharge is directly proportional to the cross\u2011sectional area and the hydraulic gradient, and the proportionality is regulated by a linear constant called the hydraulic conductivity\u201d <span id=\"extext06\" class=\"anchor\">(<a href=\"\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/exercise-6\/#exercise-6\"><span data-custom-style=\"Hyperlink\">Exercise 6<\/span><\/a>\u2ba7).<\/span>\r\n\r\n<\/div>\r\n<\/div>","rendered":"<div id=\"darcys-law-1\" class=\"level1\">\n<div data-custom-style=\"First Paragraph\">\n<p>As previously described, Darcy\u2019s law is shown again in Equation\u00a0<a href=\"#Xad27bd134d25229585e45a28289f50d4d731144\"><span data-custom-style=\"Hyperlink\">(33)<\/span><\/a>.<\/p>\n<\/div>\n<table style=\"width: 85%;\" data-custom-style=\"Table\">\n<colgroup>\n<col style=\"width: 8%;\" \/>\n<col style=\"width: 64%;\" \/>\n<col style=\"width: 11%;\" \/> <\/colgroup>\n<thead>\n<tr>\n<th><\/th>\n<th style=\"text-align: center;\">[latex]Q = - KA\\frac{dh}{dl}[\/latex]<\/th>\n<th style=\"text-align: right;\"><span id=\"Xad27bd134d25229585e45a28289f50d4d731144\" class=\"anchor\">(33)<\/span><\/th>\n<\/tr>\n<\/thead>\n<\/table>\n<div data-custom-style=\"Body Text\">\n<p>Go through the four steps and try to understand what the equation means.<\/p>\n<\/div>\n<div data-custom-style=\"Body Text\">\n<p><em>Steps 1 and 2<\/em>. The variables and constants are as follows.<\/p>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]Q[\/latex]\u00a0=\u00a0volumetric discharge: variable with dimensions of L<sup>3<\/sup>T<sup>-1<\/sup><\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]K[\/latex]\u00a0=\u00a0hydraulic conductivity: constant with dimensions of LT<sup>-1<\/sup><\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]A[\/latex]\u00a0=\u00a0cross\u2011sectional area perpendicular to flow: variable with dimensions of L<sup>2<\/sup><\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]dh[\/latex]\u00a0=\u00a0change in head: variable with dimensions of L<\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p>[latex]dl[\/latex]\u00a0=\u00a0change in length along flow path: variable with dimensions of L<\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"Block Text\">\n<blockquote><p><em>Step 3<\/em>. The numerator\u2011denominator relationships to discharge ([latex]Q[\/latex]) are:<\/p><\/blockquote>\n<\/div>\n<ul>\n<li>cross\u2011sectional area (<em>A<\/em>), directly proportional;<\/li>\n<li>change in head ([latex]dh[\/latex]), directly proportional;<\/li>\n<li>change in length ([latex]dl[\/latex]), inversely proportional;<\/li>\n<li>hydraulic gradient ([latex]dh\/dl[\/latex]), directly proportional; and<\/li>\n<li>hydraulic conductivity, directly proportional.<\/li>\n<\/ul>\n<div data-custom-style=\"Block Text\">\n<blockquote><p><em>Step 4<\/em>. There are no modifiers on the variables so the relationships are linear.<\/p><\/blockquote>\n<\/div>\n<div data-custom-style=\"First Paragraph\">\n<p>Using the above, we can express Darcy\u2019s law in a sentence as \u201cThe volumetric discharge is directly proportional to the cross\u2011sectional area and the hydraulic gradient, and the proportionality is regulated by a linear constant called the hydraulic conductivity\u201d <span id=\"extext06\" class=\"anchor\">(<a href=\"\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/exercise-6\/#exercise-6\"><span data-custom-style=\"Hyperlink\">Exercise 6<\/span><\/a>\u2ba7).<\/span><\/p>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":12,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1131","chapter","type-chapter","status-publish","hentry"],"part":1477,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1131","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":2,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1131\/revisions"}],"predecessor-version":[{"id":1717,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1131\/revisions\/1717"}],"part":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts\/1477"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1131\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/media?parent=1131"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapter-type?post=1131"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/contributor?post=1131"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/license?post=1131"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}