Venturimeter design detail:\nWhy is the divergent (diffuser) portion made longer than the convergent portion?

Introduction / Context:
A venturimeter incorporates a diffuser to recover pressure after the throat. Proper diffuser design is essential to convert kinetic energy back to static pressure while keeping losses small. The length and angle of the diffuser are selected to prevent boundary-layer separation and to minimize loss coefficients.

Given Data / Assumptions:

• Incompressible, subsonic internal flow.
• Adverse pressure gradient present in the diffuser.
• Goal: high pressure-recovery coefficient with low loss.

Concept / Approach:
Diffusers with too-steep divergence angles cause boundary-layer separation (“breaking away of the stream”), which dramatically increases form drag and losses. A longer, gentler diffuser maintains attached flow, improving pressure recovery and reducing friction/form losses. Hence both preventing separation and minimizing losses motivate a longer diffuser than the convergent section.

Step-by-Step Solution:

Verification / Alternative check:
Empirical design charts recommend small half-angles (≈3–7 degrees) for diffusers to balance length and losses, confirming the need for a longer diffuser.

Why Other Options Are Wrong:

• (a) alone or (b) alone: Both reasons are simultaneously valid.
• None of these: Contradicted by diffuser design practice.

Common Pitfalls:
Assuming symmetry between convergent and divergent sections; overlooking how adverse pressure gradients trigger separation if expansion is too rapid.

Final Answer:
both (a) and (b)