Question

Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end.
Which one of the following options correctly represents the velocity field in the converging section in cylindrical \( (r, \theta, z) \) coordinates?

• A. Two-dimensional function of \( r \) and \( z \)
• B. One-dimensional function of \( r \)
• C. Two-dimensional function of \( r \) and \( \theta \)
• D. One-dimensional function of \( z \)

Hint:

In axisymmetric flow problems, the velocity field generally depends on the radial and axial coordinates \( r \) and \( z \), while the angular coordinate \( \theta \) does not affect the flow.

Answer 1

The Correct Option is A

In this problem, we are dealing with a cylindrical pipe where the fluid flow is axisymmetric. This means that the flow properties at any point depend only on the radial coordinate \( r \) and the axial coordinate \( z \), but not on the angular coordinate \( \theta \).
Since the pipe is axisymmetric, the flow is not a function of \( \theta \), and therefore the velocity field will be a function of the radial distance \( r \) and the axial position \( z \) alone.
The governing equation for this type of flow is often reduced to a two-dimensional form that describes the variation of velocity in terms of \( r \) and \( z \). Hence, the velocity field in the converging section of the pipe will be described as a two-dimensional function of \( r \) and \( z \).
Thus, the correct answer is (A) Two-dimensional function of \( r \) and \( z \).