--- title: "Population in survey year from design demand 800 m3" subject: "Water Supply Engineering" chapter: 3 key: "semester_5/water_supply_engineering:pop-s73" source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pop-s73 site: BCT Engineering --- # Population in survey year from design demand 800 m3 Water Supply Engineering · Chapter 3: Quantity of Water - Asked in: 2073 Shrawan, 8 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pop-s73 - Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-3 ## Question Data obtained from a baseline survey of a newly formed municipality in year 2016 A.D are as follows. No. of day students in school = 2500, No. of big animals = 4000, No. of small animals = 6400. There are twenty offices, one hospital with 50 beds. The total water demand of municipality in design year with base period of 2 years and design period of 20 years is 800 $\mathrm{m^3}$. The population growth rate of that community is 1.9% per annum. Determine the population in survey year. ## Short answer Work backwards from 800 m3/d including 15% losses: net demand 695652 l/d; non-domestic demand 250500 l/d, so domestic demand 445152 l/d at 110 lpcd gives design population 4047 in 2038. Back to 2016 at 1.9% for 22 years gives 2675. ## Answer This is a reverse problem: the total design demand is known, so the design population is found first and then brought back to the survey year. Assumed rates: domestic 110 lpcd (municipality), day scholar 5 l/d, big animal 45 l/d, small animal 5 l/d, office staff 45 l/d (10 staff per office), hospital 340 l/bed/d, losses and wastage 15% of net demand. The total demand of 800 m$^3$ is taken per day, with losses included. #### Step 1: demand other than domestic | Demand | Quantity | Rate | l/day | |---|---|---|---| | Day students | 2,500 | 5 | 12,500 | | Big animals | 4,000 | 45 | 180,000 | | Small animals | 6,400 | 5 | 32,000 | | Offices (10 staff each) | 200 | 45 | 9,000 | | Hospital (50 beds) | 50 | 340 | 17,000 | | **Other demands** | | | **250,500** | #### Step 2: domestic demand in the design year Net demand $= \dfrac{800{,}000}{1.15} = 695{,}652$ l/day Domestic demand $= 695{,}652 - 250{,}500 = 445{,}152$ l/day $$ P_{2038} = \frac{445{,}152}{110} = 4{,}047 $$ #### Step 3: population in the survey year The design year is $2016+2+20 = 2038$, so $n = 22$ years. $$ P_{2038} = P_{2016}(1+r)^{n} \Rightarrow P_{2016} = \frac{4{,}047}{(1.019)^{22}} = 2{,}675 $$ **Answer: Population in the survey year (2016) = 2,675 (about 2,670); design year population = 4,047.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The 800 m^3 total demand includes losses. What is the first step? A. Subtract 15% of 250,500 B. Multiply by 1.15 C. Divide by 1.15 to get the net demand D. Divide by 110 Answer: C. Total = net x 1.15, so net = 800,000/1.15 = 695,652 l/day. (Key point: Remove losses first) 2. How is the design-year population obtained from the net demand? A. Subtract the non-domestic demands, then divide the domestic demand by 110 lpcd B. Divide the net demand by 110 directly C. Divide the other demands by 110 D. Multiply the domestic demand by 110 Answer: A. Domestic = 695,652 - 250,500 = 445,152 l/day; /110 = 4,047 persons. (Key point: Domestic demand and population) 3. How is the survey-year population found from 4,047? A. Multiply by (1.019)^22 B. Divide by (1.019)^20 C. Divide by 1.019 only D. Divide by (1.019)^22 Answer: D. Design year 2038 is 22 years after 2016, so P_2016 = P_2038/(1+r)^22. (Key point: Back to survey year) ## Close variants set in other exams - [Demand of new municipality 2016, 45,000 pop](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-a76) — Water Supply Engineering, chapter 3, asked 2× ## Related in Water Supply Engineering - [Demand of rural municipality 2018, 15,000 pop](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-c74) — Water Supply Engineering, chapter 3 - [Demand of rural municipality, base period 3 years](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-bk79) — Water Supply Engineering, chapter 3 - [Rural village demand, survey 2070 BS, base year 2073](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-as70) — Water Supply Engineering, chapter 3 - [Average demand, village survey 2013, design 25 years](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-c73) — Water Supply Engineering, chapter 3, asked 2× - [Demand of village 2070 BS, base period 5 years](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-c70) — Water Supply Engineering, chapter 3 - [Total demand, village survey 2013, design 15 years](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ademand-c69) — Water Supply Engineering, chapter 3, asked 2×