Convergent Mouthpiece — Pressure at Vena Contracta For a convergent mouthpiece discharging freely, is the absolute pressure head at the vena contracta equal to atmospheric pressure?

Introduction:
Short-tube discharges (mouthpieces) produce a contracted jet. Understanding static pressure at the section of minimum area (vena contracta) is essential for applying Bernoulli and selecting the proper coefficients for discharge predictions.

Given Data / Assumptions:

• Convergent mouthpiece discharging freely to the atmosphere (no submergence).
• Vena contracta forms at or just outside the mouthpiece exit.
• Steady, incompressible flow; negligible cavitation.

Concept / Approach:
At a free jet boundary exposed to the atmosphere, the static pressure equals atmospheric. For a convergent mouthpiece running free, the minimum jet section (vena contracta) is effectively at the free boundary; thus its static pressure equals atmospheric, even though velocity is maximum there. This is consistent with p_at_jet_surface = p_atm.

Step-by-Step Solution:
Apply Bernoulli from reservoir to jet: lossless ideal gives p/ gamma + V^2/(2g) + z = constant.At the free jet, static pressure equals p_atm; hence the pressure head term equals atmospheric head.The high speed at VC reflects conversion of pressure head to velocity head, not a sub-atmospheric static pressure at the free jet cross section.

Verification / Alternative check:
Experiments show pressure tapping at a free jet section reads atmospheric; sub-atmospheric readings occur inside sharp-edged orifices prior to the jet boundary, not at the exposed jet section.

Why Other Options Are Wrong:
False would imply sub- or super-atmospheric static pressure at a surface directly open to air; this contradicts boundary conditions.

Common Pitfalls:
Confusing interior throat pressure in enclosed nozzles (can be below atmospheric) with the static pressure of a free jet at the vena contracta.

Final Answer:
True