{"id":7819,"date":"2024-04-15T02:50:55","date_gmt":"2024-04-15T02:50:55","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=7819"},"modified":"2024-04-15T02:50:55","modified_gmt":"2024-04-15T02:50:55","slug":"if-q-is-the-average-sewage-flow-from-a-city-of-population-p-the-maximum-sewage-flow-a-textq-left-frac4-sqrt-textp-18-sqrt-textp-righttextq-b","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-q-is-the-average-sewage-flow-from-a-city-of-population-p-the-maximum-sewage-flow-a-textq-left-frac4-sqrt-textp-18-sqrt-textp-righttextq-b\/","title":{"rendered":"If q is the average sewage flow from a city of population P, the maximum sewage flow A. $${\\text{Q}} = \\left( {\\frac{{4 + \\sqrt {\\text{P}} }}{{18 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ B. $${\\text{Q}} = \\left( {\\frac{{18 + {\\text{P}}}}{{4 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ C. $${\\text{Q}} = \\left( {\\frac{{18 + \\sqrt {\\text{P}} }}{{4 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ D. $${\\text{Q}} = \\left( {\\frac{{5 + \\sqrt {\\text{P}} }}{{15 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$"},"content":{"rendered":"

[amp_mcq option1=”$${\\text{Q}} = \\left( {\\frac{{4 + \\sqrt {\\text{P}} }}{{18 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$” option2=”$${\\text{Q}} = \\left( {\\frac{{18 + {\\text{P}}}}{{4 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$” option3=”$${\\text{Q}} = \\left( {\\frac{{18 + \\sqrt {\\text{P}} }}{{4 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$” option4=”$${\\text{Q}} = \\left( {\\frac{{5 + \\sqrt {\\text{P}} }}{{15 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$” correct=”option3″]<\/p>\n

The correct answer is $\\boxed{\\text{Q} = \\left( {\\frac{{4 + \\sqrt {\\text{P}} }}{{18 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}}$.<\/p>\n

The average sewage flow from a city of population $P$ is $q$. The maximum sewage flow is the average flow plus a factor that accounts for the fact that sewage flow is not constant throughout the day. This factor is called the peak factor, and it is typically between 1.5 and 2.<\/p>\n

The maximum sewage flow is therefore given by<\/p>\n

$$\\text{Q} = q(1 + \\text{peak factor})$$<\/p>\n

The peak factor is a function of the city’s population, and it can be estimated using the following equation:<\/p>\n

$$\\text{peak factor} = \\frac{18 + \\sqrt{P}}{4 + \\sqrt{P}}$$<\/p>\n

Substituting this into the equation for the maximum sewage flow, we get<\/p>\n

$$\\text{Q} = q\\left(1 + \\frac{18 + \\sqrt{P}}{4 + \\sqrt{P}}\\right) = \\left( {\\frac{{4 + \\sqrt {\\text{P}} }}{{18 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$<\/p>\n

This is the equation for the maximum sewage flow, and it is the correct answer to the question.<\/p>\n

The other options are incorrect because they do not account for the peak factor. Option A does not include the peak factor at all, while options B and C include the peak factor but use the wrong formula for it.<\/p>\n","protected":false},"excerpt":{"rendered":"

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\\sqrt {\\text{P}} }}{{18 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ B. $${\\text{Q}} = \\left( {\\frac{{18 + {\\text{P}}}}{{4 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ C. $${\\text{Q}} = \\left( {\\frac{{18 + \\sqrt {\\text{P}} }}{{4 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ D. $${\\text{Q}} = \\left( {\\frac{{5 + \\sqrt {\\text{P}} }}{{15 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/if-q-is-the-average-sewage-flow-from-a-city-of-population-p-the-maximum-sewage-flow-a-textq-left-frac4-sqrt-textp-18-sqrt-textp-righttextq-b\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If q is the average sewage flow from a city of population P, the maximum sewage flow A. $${\\text{Q}} = \\left( {\\frac{{4 + \\sqrt {\\text{P}} }}{{18 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ B. $${\\text{Q}} = \\left( {\\frac{{18 + {\\text{P}}}}{{4 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ C. $${\\text{Q}} = \\left( {\\frac{{18 + \\sqrt {\\text{P}} }}{{4 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ D. $${\\text{Q}} = \\left( {\\frac{{5 + \\sqrt {\\text{P}} }}{{15 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=”$${text{Q}} = left( {frac{{4 + sqrt {text{P}} }}{{18 + sqrt {text{P}} }}} right){text{q}}$$” option2=”$${text{Q}} = left( {frac{{18 + {text{P}}}}{{4 + sqrt {text{P}} }}} right){text{q}}$$” option3=”$${text{Q}} = left( {frac{{18 + sqrt {text{P}} }}{{4 + sqrt {text{P}} }}} right){text{q}}$$” option4=”$${text{Q}} = left( {frac{{5 + sqrt {text{P}} }}{{15 + sqrt {text{P}} }}} right){text{q}}$$” correct=”option3″]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-q-is-the-average-sewage-flow-from-a-city-of-population-p-the-maximum-sewage-flow-a-textq-left-frac4-sqrt-textp-18-sqrt-textp-righttextq-b\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T02:50:55+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"If q is the average sewage flow from a city of population P, the maximum sewage flow A. $${\\text{Q}} = \\left( {\\frac{{4 + \\sqrt {\\text{P}} }}{{18 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ B. $${\\text{Q}} = \\left( 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\\right){\\text{q}}$$ C. $${\\text{Q}} = \\left( {\\frac{{18 + \\sqrt {\\text{P}} }}{{4 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$ D. $${\\text{Q}} = \\left( {\\frac{{5 + \\sqrt {\\text{P}} }}{{15 + \\sqrt {\\text{P}} }}} \\right){\\text{q}}$$","og_description":"[amp_mcq option1=”$${text{Q}} = left( {frac{{4 + sqrt {text{P}} }}{{18 + sqrt {text{P}} }}} right){text{q}}$$” option2=”$${text{Q}} = left( {frac{{18 + {text{P}}}}{{4 + sqrt {text{P}} }}} right){text{q}}$$” option3=”$${text{Q}} = left( {frac{{18 + sqrt {text{P}} }}{{4 + sqrt {text{P}} }}} right){text{q}}$$” option4=”$${text{Q}} = left( {frac{{5 + sqrt {text{P}} }}{{15 + sqrt {text{P}} }}} right){text{q}}$$” correct=”option3″]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-q-is-the-average-sewage-flow-from-a-city-of-population-p-the-maximum-sewage-flow-a-textq-left-frac4-sqrt-textp-18-sqrt-textp-righttextq-b\/","og_site_name":"MCQ and Quiz for 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