Venturimeter design — relative lengths of cones In a standard venturimeter, the length of the divergent (diffuser) cone is typically how much compared to the convergent cone?

Introduction / Context:
A venturimeter measures discharge using pressure difference between an upstream section and a throat. The geometry of the convergent and divergent cones is chosen to minimize head loss: a short, steep convergent (to accelerate flow) and a longer, gentle divergent (to recover pressure without separation).

Given Data / Assumptions:

• Steady, incompressible flow through a classical venturimeter.
• Goal is good pressure recovery with minimal separation in diffuser.

Concept / Approach:
Adverse pressure gradients in diffusers cause boundary layer separation if the divergence angle is too large. To avoid this, the diffuser is made longer with a small half-angle (often around 3°–7°). Empirically, the diffuser length is about three to four times the length of the convergent cone for good performance and low permanent head loss.

Step-by-Step Solution:
Recognize that the diffuser must be longer to allow gradual area expansion.Typical design guidance: L_diffuser ≈ 3 to 4 * L_convergent.Select option “three to four times.”

Verification / Alternative check:
Handbooks and standard fluid machinery texts consistently recommend longer diffusers than convergents to avoid flow separation; field designs often fall within this 3–4× range.

Why Other Options Are Wrong:

• Equal to or double: too short for reliable pressure recovery.
• Five to six times: unnecessarily long, increases size and cost without proportional benefit.

Common Pitfalls:

• Confusing diffuser length with area ratios; the key is gentle expansion angle, which implies longer length for a given area change.

Final Answer:
three to four times