{"id":2974,"date":"2020-02-08T15:21:17","date_gmt":"2020-02-08T14:21:17","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=2974"},"modified":"2024-03-29T09:08:36","modified_gmt":"2024-03-29T08:08:36","slug":"how-to-calculate-and-solve-for-discharge-chezys-equation-water-budget","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2020\/02\/08\/how-to-calculate-and-solve-for-discharge-chezys-equation-water-budget\/","title":{"rendered":"How to Calculate and Solve for Discharge | Chezy’s Equation | Water Budget"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents discharge | Chezy’s Equation. To calculate discharge, four essential parameters are needed and these parameters are Area (A), Chezy’s Constant (C), Hydraulic Radius (R)<\/strong> and Slope (S).<\/strong><\/p>\n

The formula for calculating discharge:<\/p>\n

Q = AC\u221a(RS)<\/p>\n

Where;<\/p>\n

Q = Discharge
\nA = Area
\nC = Chezy’s Constant
\nR = Hydraulic Radius
\nS = Slope<\/p>\n

Let’s solve an example;
\nFind the discharge when the area is 25, the chezy’s constant is 16, the hydraulic radius is 9 and the slope is 21.<\/p>\n

This implies that;<\/p>\n

A = Area = 25
\nC = Chezy’s Constant = 16
\nR = Hydraulic Radius = 9
\nS = Slope = 21<\/p>\n

Q = AC\u221a(RS)
\nQ = (25)(16)\u221a((9)(21))
\nThen, Q = (25)(16)\u221a(189)
\nQ = (25)(16)(13.74)
\nQ = 5499.09<\/p>\n

Therefore, the discharge<\/strong> according to Chezy’s equation<\/strong> is\u00a05499.09<\/b>.<\/p>\n

Read more:\u00a0How to Calculate and Solve for Discharge Current | Unconfined Aquifer | Water Budget<\/a><\/p>\n

Calculating the Area when the Discharge, the Chezy’s Constant, the Hydraulic Radius and the Slope are Given<\/strong><\/h3>\n

A = Q<\/sup> \/ C \u221aRS<\/sub><\/p>\n

Where;<\/p>\n

A = Area
\nQ = Discharge
\nC = Chezy’s Constant
\nR = Hydraulic Radius
\nS = Slope<\/p>\n

Let’s solve an example;
\nFind the area when the discharge is 40, the chezy’s constant is 10, the hydraulic radius is 5 and the slope is 9.<\/p>\n

This implies that;<\/p>\n

Q = Discharge = 40
\nC = Chezy’s Constant = 10
\nR = Hydraulic Radius = 5
\nS = Slope = 9<\/p>\n

A = Q<\/sup> \/ C \u221aRS<\/sub>
\nSo, A = 40<\/sup> \/ 10 \u221a(5)(9)<\/sub>
\nA = 40<\/sup> \/ 10 \u221a45<\/sub>
\nA = 40<\/sup> \/ 10 (6.708)<\/sub>
\nThen, A = 40<\/sup> \/ 67.08<\/sub>
\nA = 0.596<\/p>\n

Therefore, the\u00a0area\u00a0<\/strong>is\u00a00.596.<\/strong><\/p>\n

Calculating the Chezy’s Constant when the Discharge, the Area, the Hydraulic Radius and the Slope are Given<\/strong><\/h3>\n

C = Q<\/sup> \/ A \u221aRS<\/sub><\/p>\n

Where;<\/p>\n

C = Chezy’s Constant
\nQ = Discharge
\nA = Area
\nR = Hydraulic Radius
\nS = Slope<\/p>\n

Let’s solve an example;
\nGiven that the discharge is 38, the area is 24, the hydraulic radius is 12 and the slope is 7. Find the Chezy’s Constant?<\/p>\n

This implies that;<\/p>\n

Q = Discharge = 38
\nA = Area = 24
\nR = Hydraulic Radius = 12
\nS = Slope = 7<\/p>\n

C = Q<\/sup> \/ A \u221aRS<\/sub>
\nSo, C = 38<\/sup> \/ 24 \u221a(12)(7)<\/sub>
\nC = 38<\/sup> \/ 24 \u221a84<\/sub>
\nThen, C = 38<\/sup> \/ 24 (9.16)<\/sub>
\nC = 38<\/sup> \/ 219.84<\/sub>
\nC = 0.172<\/p>\n

Therefore, the\u00a0chezy’s constant\u00a0<\/strong>is\u00a00.172.<\/strong><\/p>\n

Calculating the Hydraulic Radius when the Discharge, the Area, the Chezy’s Constant and the Slope are Given<\/strong><\/h3>\n

R = (Q<\/sup> \/ AC<\/sub>)2<\/sup><\/sup> \/ S<\/sub><\/p>\n

Where;<\/p>\n

R = Hydraulic Radius
\nC = Chezy’s Constant
\nQ = Discharge
\nA = Area
\nS = Slope<\/p>\n

Let’s solve an example;
\nFind the hydraulic radius when the chezy’s constant is 5, the discharge is 50, the area is 7 and the slope is 2.<\/p>\n

This implies that;<\/p>\n

C = Chezy’s Constant = 5
\nQ = Discharge = 50
\nA = Area = 7
\nS = Slope = 2<\/p>\n

R = (Q<\/sup> \/ AC<\/sub>)2<\/sup><\/sup> \/ S<\/sub>
\nSo, R = (50<\/sup> \/ 7 x 5<\/sub>)2<\/sup><\/sup> \/ 2<\/sub>
\nR = (50<\/sup> \/ 35<\/sub>)2<\/sup><\/sup> \/ 2<\/sub>
\nR = (1.428)2<\/sup><\/sup> \/ 2<\/sub>
\nThen, R = 2.04<\/sup> \/ 2<\/sub>
\nR = 1.02<\/p>\n

Therefore, the\u00a0hydraulic radius\u00a0<\/strong>is\u00a01.02.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Hydrostatic Pressure of a Dam | Water Budget<\/a><\/p>\n

Calculating the Slope when the Discharge, the Area, the Chezy’s Constant and the Hydraulic Radius are Given<\/strong><\/h3>\n

S = (Q<\/sup> \/ AC<\/sub>)2<\/sup><\/sup> \/ R<\/sub><\/p>\n

Where;<\/p>\n

S = Slope
\nQ = Discharge
\nA = Area
\nC = Chezy’s Constant
\nR = Hydraulic Radius<\/p>\n

Let’s solve an example;
\nFind the slope when the discharge is 80, the area is 10, the chezy’s constant is 4 and the hydraulic radius is 8.<\/p>\n

This implies that;<\/p>\n

Q = Discharge = 80
\nA = Area\u00a0 = 10
\nC = Chezy’s Constant = 4
\nR = Hydraulic Radius = 8<\/p>\n

S = (Q<\/sup> \/ AC<\/sub>)2<\/sup><\/sup> \/ R<\/sub>
\nThen, S = (80<\/sup> \/ 10 x 4<\/sub>)2<\/sup><\/sup> \/ 8<\/sub>
\nS = (80<\/sup> \/ 40<\/sub>)2<\/sup><\/sup> \/ 8<\/sub>
\nS = (2)2<\/sup><\/sup> \/ 8<\/sub>
\nThat is, S = 4<\/sup> \/ 8<\/sub>
\nS = 0.5<\/p>\n

Therefore, the\u00a0slope\u00a0<\/strong>is\u00a00.5.<\/strong><\/p>\n

How to Calculate and Solve for Discharge | Chezy’s Equation Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the discharge | chezy’s equation.<\/p>\n

To get the answer and workings of the discharge | chezy’s equation using the Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe\u00a0<\/strong>for\u00a0NGN 1,500\u00a0<\/strong>per\u00a0annum<\/strong>\u00a0to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a>
\nApple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a>
\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on\u00a0Agricultural\u00a0<\/b>under\u00a0Engineering<\/strong>.<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Water Budget\u00a0<\/strong>under\u00a0Agricultural<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Discharge| Chezy’s Equation<\/strong>\u00a0<\/strong>under\u00a0Water Budget<\/strong><\/p>\n

\"How<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the discharge | chezy’s equation according to the respective parameters which are the Area (A), Chezy’s Constant (C), Hydraulic Radius (R)<\/strong> and Slope (S).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Area (A)<\/strong> is 25<\/strong>, Chezy’s Constant (C)<\/strong> is 16<\/strong>, Hydraulic Radius (R)<\/strong> is 9 <\/strong>and Slope (S)<\/strong> is 21<\/strong>.<\/p>\n

\"How<\/p>\n

Finally, Click on Calculate<\/p>\n

\"\"
\n\"\"<\/p>\n

As you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the discharge | chezy’s equation and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents discharge | Chezy’s Equation. To calculate discharge, four essential parameters are needed and these…","protected":false},"author":5,"featured_media":13500,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":"","_members_access_role":[],"_members_access_error":""},"categories":[47],"tags":[828,246,84,839,838,60,298,87,837,827],"class_list":["post-2974","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-agricultural","tag-area","tag-calculator-encyclopedia","tag-chezys-constant","tag-discharge","tag-engineering","tag-hydraulic-radius","tag-nickzom-calculator","tag-slope","tag-water-budget","cs-entry"],"yoast_head":"\nHow 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