GATE 2023 AG – Question 57
Two cylindrical reservoirs A(diameter 8 m) and B(diameter 10 m) connect through a 30 m pipe of 250 mm internal diameter and Darcy friction factor.025. A initially contains 10 m water above its14 m base elevation;B is initially empty with base elevation6.6 m. Neglect entrance/exit losses. Find hours to empty A. Use π=3.14,g=9.81 m/s²;see source figure.
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Correct answer: 3.30 to 3.40
Explanation
The official accepted answer is **3.30–3.40 hours**. A simple communicating-reservoir calculation does not reproduce it from the printed dimensions. Let transferred volume v lower A by $v/A_A$ and raise B by $v/A_B$,with $A_A=50.24,A_B=78.5$ m². Surface-head difference is $H=17.4-v(1/A_A+1/A_B)$. Darcy pipe flow is $Q=a\sqrt{2gDH/(fL)}$,where a=.0490625 m². Integrating from v=0 to 502.4 m³ gives approximately **.429 hour**. If B is treated as an atmospheric free-outlet condition rather than a rising connected reservoir, the boundary and outlet elevation must be specified. The diagram/printed data therefore do not establish the keyed3.35-hour result under this standard model; official grading is retained without inventing a changed diameter or length.