GATE CE 2023 Set 2 — Question 65
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumContinuity EquationFluid Kinematics & DynamicsWater Resources EngineeringWater QualityEnvironmental Engineering
Environmental Engineering → Fluid Kinematics & Dynamics → Continuity Equation
Last updated
Question
A system of seven river segments is shown in the schematic diagram. The ’s, ’s, and ’s ( to ) are the river segments, their corresponding flow rates, and concentrations of a conservative pollutant, respectively. Assume complete mixing at the intersections, no additional water loss or gain in the system, and steady state condition. Given: ; ; ; ; ; ; . What is the steady state concentration (in , rounded off to two decimal place) of the pollutant in the river segment 7 ?
Correct answer
10.58 to 10.78
Solution
To find the steady-state concentration in river segment 7 (), we perform mass and flow balances at each junction.Step 1: Junction 1 (Merging of and into )
Flow balance:
Mass balance:
Step 2: Junction 2 (Splitting of into and )
From the diagram, is an outflow from the junction. For a conservative pollutant, the concentration in the outflows ( and ) is the same as the inflow ().
Flow balance: Step 3: Junction 3 (Merging of and into )
Flow balance:
Mass balance:
Thus, the steady state concentration in segment 7 is .
Flow balance:
Mass balance:
Step 2: Junction 2 (Splitting of into and )
From the diagram, is an outflow from the junction. For a conservative pollutant, the concentration in the outflows ( and ) is the same as the inflow ().
Flow balance: Step 3: Junction 3 (Merging of and into )
Flow balance:
Mass balance:
Thus, the steady state concentration in segment 7 is .
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Fluid Kinematics & Dynamics
2026 Set 1 Q16Two reservoirs having different water levels are connected by two long parallel pipelines of same…2026 Set 1 Q17An irrigation canal is to be designed to deliver 10 cumec to meet the peak demand of 7500 hectare…2026 Set 2 Q19The Culturable Command Area (CCA) for a canal is 10000 hectares. The base period for a crop in the…2026 Set 2 Q20Following statements are made with respect to the mass curve of rainfall: (I) Slope at a point on…2026 Set 1 Q21A rapid sand filter bed of depth m has % porosity during service cycle. It is…