Orifices and Mouthpieces – Vena Contracta Location In a short cylindrical external mouthpiece running free, the vena contracta forms at a distance from the outlet equal to what fraction of the orifice diameter?

Introduction:
The vena contracta is the section where a jet from an orifice or mouthpiece attains minimum cross-section and maximum velocity just downstream of the opening. Its location depends on the geometry.

Given Data / Assumptions:

• Short cylindrical external mouthpiece.
• Running free (not drowned or submerged at the outlet).
• Diameter of the orifice is the reference scale.

Concept / Approach:

For a short external cylindrical mouthpiece discharging freely, experiments show that vena contracta typically occurs at about half a diameter downstream from the outlet plane of the orifice.

Step-by-Step Solution:

Verification / Alternative check:

Classic hydraulics texts present diagrams placing the contracted jet minimum at about 0.5 d downstream for this geometry.

Why Other Options Are Wrong:

Equal to diameter / one-fourth / one-third / three-fourths: Do not match the standard empirical placement for short cylindrical mouthpieces running free.

Common Pitfalls:

Confusing mouthpieces with thin orifices or long pipes where contraction behavior differs. The fraction changes with geometry and whether the jet is submerged.

Final Answer:

one-half of the diameter