Problem 57765. Determine whether a hydrograph is a unit hydrograph

Created by ChrisR

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{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Q\"/></w:customXmlPr><w:r><w:t>Q</w:t></w:r></w:customXml><w:r><w:t> (or flow or discharge) as a function of time </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"t\"/></w:customXmlPr><w:r><w:t>t</w:t></w:r></w:customXml><w:r><w:t> resulting from a given excess rainfall (expressed as a depth </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"P\"/></w:customXmlPr><w:r><w:t>P</w:t></w:r></w:customXml><w:r><w:t>) for a storm of a specified duration. A </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>unit hydrograph </w:t></w:r><w:r><w:t>results from unit excess rainfall (e.g., </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>P</w:t></w:r></w:customXml><w:r><w:t> = 1 cm). </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"t\"/></w:customXmlPr><w:r><w:t>t</w:t></w:r></w:customXml><w:r><w:t> in minutes, the flow rate </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Q\"/></w:customXmlPr><w:r><w:t>Q</w:t></w:r></w:customXml><w:r><w:t> in </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"m^3/s\"/></w:customXmlPr><w:r><w:t>\\rm m^3/s</w:t></w:r></w:customXml><w:r><w:t>, and the catchment area </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"A\"/></w:customXmlPr><w:r><w:t>A</w:t></w:r></w:customXml><w:r><w:t> in </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"m^2\"/></w:customXmlPr><w:r><w:t>\\rm m^2</w:t></w:r></w:customXml><w:r><w:t>. Allow for a tolerance of 0.01 cm in the excess rainfall depth.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; 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: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; "><div 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: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 333.467px 8px; transform-origin: 333.467px 8px; unicode-bidi: normal; ">A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate Q<span 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: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; "> (or flow or discharge) as a function of time t<span 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: 188.267px 8px; transform-origin: 188.267px 8px; unicode-bidi: normal; "> resulting from a given excess rainfall (expressed as a depth P<span 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: 82.8333px 8px; transform-origin: 82.8333px 8px; unicode-bidi: normal; ">) for a storm of a specified duration. A <span 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: 50.575px 8px; transform-origin: 50.575px 8px; unicode-bidi: normal; ">unit hydrograph <span 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: 115.9px 8px; transform-origin: 115.9px 8px; unicode-bidi: normal; ">results from unit excess rainfall (e.g., P<span 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: 29.3583px 8px; transform-origin: 29.3583px 8px; unicode-bidi: normal; "> = 1 cm). </div><div style="block-size: 42px; 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 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 330.108px 8px; transform-origin: 330.108px 8px; unicode-bidi: normal; ">Write a function to determine whether a hydrograph is a unit hydrograph. Inputs to the function will be time t<span 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: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; "> in minutes, the flow rate Q<span 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: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; "> in <img src="data:image/png;base64,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" alt="m^3/s" style="width: 33px; height: 19.5px;" width="33" height="19.5"><span 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: 79.3417px 8px; transform-origin: 79.3417px 8px; unicode-bidi: normal; ">, and the catchment area A<span 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: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; "> in <img src="data:image/png;base64,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" alt="m^2" style="width: 19.5px; height: 19px;" width="19.5" height="19"><span 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: 188.642px 8px; transform-origin: 188.642px 8px; unicode-bidi: normal; ">. Allow for a tolerance of 0.01 cm in the excess rainfall depth.</div></div></div>

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Dyuman Joshi on 11 Mar 2023

Chris, the problem statement specifies that Area is in km2 but the test suite mention that Area is in m2.

ChrisR on 11 Mar 2023

Corrected. Thanks Dyuman.

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Problem 57765. Determine whether a hydrograph is a unit hydrograph

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Problem 57765. Determine whether a hydrograph is a unit hydrograph

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