GATE 2020 CE (CE1) – Question 59

Fluid Mechanics · Flow in pipes and pipe networks · 2 marks · Numerical answer

Reservoirs P, Q and R connect through pipes at junction S as shown. Piezometric head at S is 100 m; pipe S–R length is 180 m. Take g = 9.81 m/s² and water density 1000 kg/m³. Considering only frictional loss with f = 0.03 in all pipes, find lowermost reservoir R level above datum (m), to one decimal.

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Correct answer: 97.2 to 97.8

Explanation

Continuity gives outlet speed $V_R=(0.30/0.45)^2(2.56+1.98)=2.01778$ m/s. Friction loss is $f(L/D)V_R^2/(2g)=2.490$ m. With only frictional loss specified, R level is $100-2.490=\mathbf{97.5}$ m.