Venturimeter principle – pressure comparison between inlet and throat For an incompressible flow through a properly installed venturimeter, the static pressure at the throat is __________ than the static pressure at the inlet (upstream section).

Introduction / Context:
Venturimeters infer flow rate from the pressure drop produced as fluid accelerates from a larger upstream area to a smaller throat area. Recognizing the qualitative pressure change across these sections is foundational.

Given Data / Assumptions:

• Steady incompressible flow (e.g., water) in a horizontal meter for simplicity.
• Negligible energy losses between the pressure taps compared to the main acceleration effect.
• No cavitation at the throat (pressure remains above vapor pressure).

Concept / Approach:
Bernoulli’s equation states that along a streamline, p/γ + V^2/(2g) + z is approximately constant (minus losses). At the throat, area is smaller, velocity is higher, so velocity head increases. To conserve energy, static pressure head must decrease, hence p_throat < p_inlet.

Step-by-Step Solution:
Step 1: Note A_inlet > A_throat → V_throat > V_inlet.Step 2: Apply Bernoulli: increase in V^2/(2g) must be balanced by a drop in p/γ (for equal elevations and small losses).Step 3: Conclude p_throat < p_inlet, producing a measurable differential head.Step 4: Use the differential head with calibration to compute discharge.

Verification / Alternative check:
Manometer connections on a venturimeter always show a lower head at the throat limb relative to the upstream limb at any nonzero flow.

Why Other Options Are Wrong:

• Higher or same: violate Bernoulli for accelerating flow.
• Zero at design discharge: pressure is not zero; cavitation would be a concern long before that.
• Roughness: affects loss but not the fundamental trend that throat pressure is lower.

Common Pitfalls:
Neglecting elevation differences in inclined installations; always include z terms when necessary.

Final Answer:
lower