Venturimeter Design — Throat/Pipe Diameter Ratio to Avoid Separation To avoid flow separation at the throat in a Venturimeter, a commonly recommended ratio of throat diameter (d_t) to pipe diameter (D) is approximately:

Introduction:A Venturimeter measures discharge in closed conduits using a smooth converging section, a short throat, and a long diffuser. The throat/pipe diameter ratio (beta = d_t/D) influences pressure recovery, head loss, and the risk of separation. Picking a suitable beta ensures accurate differential readings while avoiding excessive losses or cavitation.

Given Data / Assumptions:

• Incompressible liquid; Reynolds number high enough for fully turbulent core.
• Smooth, gradual contraction and diffuser angles within standard practice.
• No cavitation; adequate upstream straight length.

Concept / Approach:Too small a throat (beta very low) yields very high velocities and large pressure drops, risking cavitation and unnecessary losses; too large a throat (beta too high) reduces measurable differential and can exacerbate sensitivity to installation effects. A widely adopted compromise is beta ≈ 0.5, which balances measurement differential and recovery while keeping diffuser angles gentle enough to prevent separation.

Step-by-Step Solution:Define beta = d_t / D.Choose beta that ensures moderate acceleration and manageable diffuser expansion.Select the commonly recommended value beta ≈ 0.50 to avoid separation at the throat and allow good pressure recovery.

Verification / Alternative check:Design handbooks list typical Venturimeter betas in the 0.4–0.6 range, with 0.5 a frequent default for water services to balance accuracy and losses.

Why Other Options Are Wrong:0.25 and 0.33 produce very high velocities and risk cavitation; 0.80 yields too small a differential and can reduce accuracy and stability.

Common Pitfalls:Ignoring diffuser angle limits (~5–7° half-angle typical) which are critical for preventing separation; neglecting upstream disturbances.

Final Answer:0.50