Venturimeter design—throat-to-pipe diameter ratio to avoid separation What range of throat diameter to pipe diameter is typically used in venturimeters to avoid flow separation and maintain reliable pressure recovery?

Introduction / Context:
Venturimeters measure discharge by creating a controlled constriction in a pipe. The choice of throat diameter greatly influences accuracy, head loss, and the risk of separation or cavitation. A practical ratio ensures a measurable differential without excessive losses or unstable flow.

Given Data / Assumptions:

• Axisymmetric venturi with smooth convergent and divergent sections.
• Incompressible liquid flow.
• Goal: avoid boundary-layer separation in diffuser and maintain good pressure recovery.

Concept / Approach:

Common design practice selects the throat-to-pipe diameter ratio (β = d_t / D) in the range of about 0.33 to 0.50. This offers a good compromise between measurable pressure drop and acceptable losses, while keeping velocities and adverse pressure gradients within limits.

Step-by-Step Solution:

Verification / Alternative check:

Standards and handbooks list typical β ranges for venturimeters; values near 0.4 are widely used in water systems to balance accuracy and loss.

Why Other Options Are Wrong:

(a) 1/4 to 1/8 is too small, causing very high throat velocities and risk of cavitation; (c) 1/2 to 3/4 is too large for many applications, giving very low differential heads and sensitivity issues; (d) is unnecessary.

Common Pitfalls:

Ignoring upstream disturbances; using too steep diffuser leading to separation; not accounting for temperature-dependent vapor pressure when checking cavitation.

Final Answer:

1/3 to 1/2