Correct Option (A):
For a liquid undergoing streamline (laminar) flow in a cylindrical pipe, the velocity distribution across the pipe's cross-section is parabolic. Due to the viscosity of the fluid, the layer of liquid in direct contact with the pipe walls experiences a no-slip condition, resulting in zero velocity at the walls. The velocity progressively increases towards the central axis of the pipe, where it reaches its maximum value. This characteristic parabolic velocity profile is accurately represented by the diagram in option (1).
Incorrect Options:
- Option (2) illustrates a uniform velocity profile across the pipe's cross-section. Such a profile would only be observed in an ideal, non-viscous fluid, which is not representative of real liquids exhibiting streamline flow where viscous forces are significant.
- Option (3) depicts a linear velocity distribution. This does not correspond to the observed parabolic velocity profile for laminar flow of viscous fluids in cylindrical pipes.
- Option (4) shows a velocity profile where the velocity decreases towards the central axis and is maximum at the pipe walls. This contradicts the fundamental principle of laminar flow in pipes, where the velocity is zero at the walls and attains its maximum value at the central axis.