[amp_mcq option1=”$$\\pi {{\\text{D}}^{\\frac{8}{3}}} = 4{{\\text{b}}^{\\frac{8}{3}}}$$” option2=”$$\\pi {{\\text{D}}^{\\frac{3}{8}}} = 4{{\\text{b}}^{\\frac{3}{8}}}$$” option3=”$$\\pi {{\\text{D}}^{\\frac{2}{3}}} = 4{{\\text{b}}^{\\frac{2}{3}}}$$” option4=”$$\\pi {{\\text{D}}^{\\frac{3}{2}}} = 4{{\\text{b}}^{\\frac{3}{3}}}$$” correct=”option3″]<\/p>\n
The correct answer is $\\pi D^{2\/3} = 4b^{2\/3}$.<\/p>\n
Hydraulically equivalent sewers have the same discharge capacity. The discharge capacity of a sewer is given by the Manning equation:<\/p>\n
$$Q = \\frac{1}{n} \\frac{A}{R^2} S$$<\/p>\n
where $Q$ is the discharge, $n$ is the Manning roughness coefficient, $A$ is the cross-sectional area, $R$ is the hydraulic radius, and $S$ is the slope of the sewer.<\/p>\n
For a circular sewer, the cross-sectional area is $A = \\pi D^2\/4$ and the hydraulic radius is $R = D\/2$. For a square sewer, the cross-sectional area is $A = b^2$ and the hydraulic radius is $R = b\/2$.<\/p>\n
Substituting these expressions into the Manning equation, we get:<\/p>\n
$$Q = \\frac{1}{n} \\frac{\\pi D^2\/4}{(D\/2)^2} S = \\frac{2}{n} \\pi D^2 S$$<\/p>\n
and<\/p>\n
$$Q = \\frac{1}{n} \\frac{b^2}{(b\/2)^2} S = 2n b^2 S$$<\/p>\n
Equating these two expressions, we get:<\/p>\n
$$\\frac{2}{n} \\pi D^2 S = 2n b^2 S$$<\/p>\n
or<\/p>\n
$$\\pi D^2 = 4nb^2$$<\/p>\n
or<\/p>\n
$$\\pi D^{2\/3} = 4b^{2\/3}$$<\/p>\n
Therefore, the relationship which holds good is $\\pi D^{2\/3} = 4b^{2\/3}$.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”$$\\pi {{\\text{D}}^{\\frac{8}{3}}} = 4{{\\text{b}}^{\\frac{8}{3}}}$$” option2=”$$\\pi {{\\text{D}}^{\\frac{3}{8}}} = 4{{\\text{b}}^{\\frac{3}{8}}}$$” option3=”$$\\pi {{\\text{D}}^{\\frac{2}{3}}} = 4{{\\text{b}}^{\\frac{2}{3}}}$$” option4=”$$\\pi {{\\text{D}}^{\\frac{3}{2}}} = 4{{\\text{b}}^{\\frac{3}{3}}}$$” correct=”option3″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[650],"tags":[],"class_list":["post-7618","post","type-post","status-publish","format-standard","hentry","category-waste-water-engineering","no-featured-image-padding"],"yoast_head":"\n