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GATE 2023 CH – Question 29

Fluid Mechanics and Mechanical Operations · Turbulent flow, boundary layer and flow past immersed bodies · 1 mark · Multiple select

For a fully developed turbulent flow of an incompressible Newtonian fluid through a pipe of constant diameter, which of the following statements is/are CORRECT?

  1. Reynolds stress, averaged over a sufficiently long time, is zero everywhere inside the pipe.
  2. Reynolds stress at the pipe wall is zero.
  3. Average velocity of the fluid is half of its center-line velocity.
  4. Average pressure gradient in the flow direction is constant.

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Show answer and explanation

Correct answer: (B) Reynolds stress at the pipe wall is zero.; (D) Average pressure gradient in the flow direction is constant.

Explanation

In turbulent flow the time-averaged Reynolds stress is not zero in the pipe (A is false), but all the velocity fluctuations vanish at the wall, so the Reynolds stress is zero at the wall (B is true). The mean velocity is half of the centre-line value in laminar flow, not in turbulent flow, where the profile is flatter (C is false). In fully developed flow in a pipe of constant diameter the average pressure gradient is constant (D is true).