{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":60778,"title":"Complete hydraulic geometry relations","description":"Hydraulic geometry relations express the velocity , width , and depth  of a river as a function of the discharge (or flow) , which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\r\n\r\nwhere the coefficients have the appropriate dimensions. \r\nWrite a function that takes two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., ) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 200px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100px; transform-origin: 407px 100px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHydraulic geometry relations express the velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a river as a function of the discharge (or flow) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 26px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13px; text-align: left; transform-origin: 384px 13px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"203.5\" height=\"26\" alt=\"V = a1 Q^e1, B = a2 Q^e2, H = a3 Q^e3\" style=\"width: 203.5px; height: 26px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the coefficients have the appropriate dimensions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" alt=\"Q = VBH\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [anew,enew] = hydraulicGeometry(a,e)\r\n  anew = 1.1*a;\r\n  enew = 1.1*e;\r\nend","test_suite":"%\r\na = [NaN 7.2 0.27];\r\ne = [NaN 0.5 0.3];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.5144 7.2 0.27];\r\nenew_correct = [0.2 0.5 0.3];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.5 NaN 0.3];\r\ne = [0.25 NaN 0.3];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.5 6.6667 0.3];\r\nenew_correct = [0.25 0.45 0.3];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.45 7 NaN];\r\ne = [0.23 0.48 NaN];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.45 7 0.3175];\r\nenew_correct = [0.23 0.48 0.29];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.8 5 NaN];\r\ne = [NaN 0.3 0.4];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.8 5 0.25];\r\nenew_correct = [0.3 0.3 0.4];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.6 4 NaN];\r\ne = [0.1 NaN 0.4];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.6 4 0.4167];\r\nenew_correct = [0.1 0.5 0.4];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [NaN 4.6 0.8];\r\ne = [0.15 NaN 0.37];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.2717 4.6 0.8];\r\nenew_correct = [0.15 0.48 0.37];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-12-14T15:47:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-12-14T15:46:55.000Z","updated_at":"2026-03-11T11:38:03.000Z","published_at":"2024-12-14T15:47:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHydraulic geometry relations express the velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a river as a function of the discharge (or flow) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V = a1 Q^e1, B = a2 Q^e2, H = a3 Q^e3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV = a_1 Q^{e_1}, B = a_2 Q^{e_2}, H = a_3 Q^{e_3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the coefficients have the appropriate dimensions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = VBH\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = VBH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":60778,"title":"Complete hydraulic geometry relations","description":"Hydraulic geometry relations express the velocity , width , and depth  of a river as a function of the discharge (or flow) , which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\r\n\r\nwhere the coefficients have the appropriate dimensions. \r\nWrite a function that takes two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., ) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 200px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100px; transform-origin: 407px 100px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHydraulic geometry relations express the velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and depth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a river as a function of the discharge (or flow) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 26px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13px; text-align: left; transform-origin: 384px 13px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"203.5\" height=\"26\" alt=\"V = a1 Q^e1, B = a2 Q^e2, H = a3 Q^e3\" style=\"width: 203.5px; height: 26px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the coefficients have the appropriate dimensions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18\" alt=\"Q = VBH\" style=\"width: 63px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [anew,enew] = hydraulicGeometry(a,e)\r\n  anew = 1.1*a;\r\n  enew = 1.1*e;\r\nend","test_suite":"%\r\na = [NaN 7.2 0.27];\r\ne = [NaN 0.5 0.3];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.5144 7.2 0.27];\r\nenew_correct = [0.2 0.5 0.3];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.5 NaN 0.3];\r\ne = [0.25 NaN 0.3];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.5 6.6667 0.3];\r\nenew_correct = [0.25 0.45 0.3];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.45 7 NaN];\r\ne = [0.23 0.48 NaN];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.45 7 0.3175];\r\nenew_correct = [0.23 0.48 0.29];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.8 5 NaN];\r\ne = [NaN 0.3 0.4];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.8 5 0.25];\r\nenew_correct = [0.3 0.3 0.4];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [0.6 4 NaN];\r\ne = [0.1 NaN 0.4];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.6 4 0.4167];\r\nenew_correct = [0.1 0.5 0.4];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))\r\n\r\n%%\r\na = [NaN 4.6 0.8];\r\ne = [0.15 NaN 0.37];\r\n[anew,enew] = hydraulicGeometry(a,e);\r\nanew_correct = [0.2717 4.6 0.8];\r\nenew_correct = [0.15 0.48 0.37];\r\nassert(all(abs(anew-anew_correct)\u003c1e-4))\r\nassert(all(abs(enew-enew_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-12-14T15:47:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-12-14T15:46:55.000Z","updated_at":"2026-03-11T11:38:03.000Z","published_at":"2024-12-14T15:47:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHydraulic geometry relations express the velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and depth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of a river as a function of the discharge (or flow) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V = a1 Q^e1, B = a2 Q^e2, H = a3 Q^e3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV = a_1 Q^{e_1}, B = a_2 Q^{e_2}, H = a_3 Q^{e_3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the coefficients have the appropriate dimensions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = VBH\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = VBH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"rivers\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"rivers\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"rivers\"","","\"","rivers","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f0f4cc19078\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f0f4cc18fd8\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f0f4cc18498\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f0f4cc192f8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f0f4cc19258\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f0f4cc191b8\u003e":"map(difficulty_value,0,0,999) 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