Internal mouthpiece (orifice) – pressure head at vena contracta In an internal mouthpiece, the absolute pressure head at the vena contracta is __________ the atmospheric pressure head by an amount equal to the height of liquid above the vena contracta:

Introduction:
Flow through mouthpieces involves contraction and acceleration, creating a vena contracta where velocity is maximum and pressure is minimum. Understanding pressure at this section is key for cavitation checks and discharge estimation.

Given Data / Assumptions:

• Steady incompressible flow.
• Internal mouthpiece with well-formed vena contracta.
• Negligible elevation change between reservoir free surface and jet centerline compared to head terms.

Concept / Approach:
Applying Bernoulli between the free surface and the vena contracta gives a pressure drop equal to the elevation (head) difference that accelerates the fluid. At the vena contracta, pressure may fall below atmospheric by approximately the liquid head above that section.

Step-by-Step Solution:
1) Take points: (1) free surface (p ≈ p_atm, V ≈ 0), (2) vena contracta (p_vc, V_vc).2) Bernoulli: p_atm/gamma + H = p_vc/gamma + V_vc^2/(2g) + losses.3) The acceleration head H primarily converts to velocity head; thus p_vc/gamma ≈ p_atm/gamma − (H − losses).4) Therefore the absolute pressure head at vena contracta is less than atmospheric by roughly the height of liquid above it (allowing for small losses).

Verification / Alternative check:
Observed cavitation or air entrainment near sharp-edged orifices is consistent with low absolute pressure at the vena contracta.

Why Other Options Are Wrong:

• More than: contradicts acceleration-induced pressure drop.
• Equal to: ignores conversion of head to kinetic energy.
• Indeterminate: while exact value needs losses, the trend (less than atmospheric) is well established.

Common Pitfalls:
Confusing gauge and absolute pressure; neglecting contraction coefficient effects on velocity head.

Final Answer:
less than