GATE 2025 ES – Question 55
Pipeline O–P–Q–R divides into parallel branches X, Y, Z between P and Q. Dimensions are shown. All pipes have friction factor .02;use g=10 m/s². The P–Q head difference is 10 m. Find Q–R head loss in m, to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 5.05 to 5.40
Explanation
Using Darcy–Weisbach,$v_j=\sqrt{2ghD_j/(fL_j)}$. Branch data (D, L) in metres are (.100,1000),(.125,800),(.150,960). The resulting flows are .00785398,.01533981,.02208932 m³/s, total .04528311. Downstream Q–R has D=.200 m, L=500 m, so $v=Q/(\pi D^2/4)=1.4414$ m/s. Its loss is $h_f=.02(500/.2)v^2/(2\cdot10)=\mathbf{5.19}$ m. The O–P section does not enter the given P–Q head balance.