GATE XE (Engineering Sciences) 2025 - Question 35

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Section: Fluid Mechanics | Marks: 2

A liquid flows under steady and incompressible flow conditions from station 1 to station 4 through pipe sections P, Q, R, and S as shown in figure. Consider, 𝑑, 𝑉, and β„Ž represent the diameter, velocity, and head loss, respectively, in each pipe section with subscripts β€˜P’, β€˜Q’, β€˜R’, and β€˜S’. βˆ†β„Ž represents the head difference between the inlet (station 1) and outlet (station 4). All the pipe sections are placed on the same horizontal plane for which the figure shows the top view. Which one of the following options is correct for the given flow loop?

Figure for question 35, GATE XE (Engineering Sciences) 2025

  • A. βˆ†β„Ž= β„Žπ‘ƒ+ β„Žπ‘„+ β„Žπ‘…+ β„Žπ‘† and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 = 𝑉𝑆𝑑𝑆 2
  • B. βˆ†β„Ž= β„Žπ‘ƒ+ β„Žπ‘„+ β„Žπ‘… and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 = 𝑉𝑆𝑑𝑆 2
  • C. βˆ†β„Ž= β„Žπ‘ƒ+ β„Žπ‘„+ β„Žπ‘… and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 + 𝑉𝑆𝑑𝑆 2
  • D. βˆ†β„Ž= β„Žπ‘ƒ+ β„Žπ‘„+ β„Žπ‘…+ β„Žπ‘† and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 + 𝑉𝑆𝑑𝑆 2

Answer: C. βˆ†β„Ž= β„Žπ‘ƒ+ β„Žπ‘„+ β„Žπ‘… and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 + 𝑉𝑆𝑑𝑆 2

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