In a venturimeter, why is the divergent (diffuser) cone made longer than the convergent cone?

Introduction / Context:A venturimeter measures flow by accelerating fluid through a convergent to a throat and then decelerating it in a diffuser (divergent). The geometry of the diffuser is crucial for recovering pressure with minimal energy loss and avoiding separation.

Given Data / Assumptions:

• Incompressible flow through a standard venturimeter.
• Entrance (convergent) half-angle is typically steeper than the exit (diffuser) half-angle.
• Goal: minimize head loss while maintaining accurate pressure differential.

Concept / Approach:Rapid diffusion (sudden flow deceleration) can cause boundary-layer separation in the divergent section, producing large energy losses. A longer diffuser with a small half-angle (often about 5–7 degrees) decelerates the flow gradually, maintaining attached flow and enhancing pressure recovery.

Step-by-Step Solution:Flow accelerates in the convergent: velocity ↑, static pressure ↓.At the throat: maximum velocity, minimum static pressure.In the diffuser: velocity ↓, static pressure ↑; gradual expansion reduces adverse pressure gradient and separation.

Verification / Alternative check:Empirical data show lower permanent head loss for venturimeters with carefully designed long diffusers compared to short, steep diffusers or abrupt expansions.

Why Other Options Are Wrong:Shorter diffuser: increases separation risk and loss.Equal lengths purely for symmetry: not a performance criterion.“No reason” or “reduce throat area oscillations only”: do not address the fluid dynamic purpose of pressure recovery.

Common Pitfalls:

• Using too large a diffuser angle, leading to separation and high losses.
• Neglecting surface finish and Reynolds-number effects on diffuser performance.

Final Answer:To make the diffuser longer to achieve gradual pressure recovery and avoid flow separation