Difficulty: Easy
Correct Answer: Volumetric discharge (flow rate)
Explanation:
Introduction / Context:
Differential head meters such as orifice meters, venturimeters, and flow nozzles are ubiquitous in industry. They create a known relationship between pressure drop and flow rate, enabling robust discharge measurements with appropriate coefficients and calibration.
Given Data / Assumptions:
Concept / Approach:
Bernoulli plus continuity across the orifice section relates pressure drop to velocity through the throat area. The volumetric discharge Q is then Q = Cd * A2 * sqrt[2 * Δp / (rho * (1 − beta^4))], where A2 is the orifice area and beta is diameter ratio. With Cd known, Q follows from measured Δp.
Step-by-Step Solution:
Measure pressure differential Δp using taps and a manometer/transducer.Compute throat velocity and multiply by throat area.Apply discharge coefficient Cd to correct for losses and non-idealities.
Verification / Alternative check:
Comparison against volumetric tank tests confirms the orifice meter’s Q accuracy within prescribed ranges of Reynolds number and beta ratio when standards are followed.
Why Other Options Are Wrong:
Static pressure: a pressure gauge alone does this; orifice meter depends on Δp.Average speed independent of area: discharge requires area * velocity.Local vena-contracta velocity: not directly measured by the pressure taps.Density: not directly measured; it must be known or inferred.
Common Pitfalls:
Final Answer:
Volumetric discharge (flow rate)
Discussion & Comments