Quantitative Models for the Effects of Differential-pressure Manometer Scale Resolution and Hot-wire Voltage Measurement Bit Depth on Gaussian Fluctuation Characteristics

A rigorous analytical framework quantifies the influence of instrument resolution on flow-velocity statistics. Differential-pressure fluctuations recorded by a Pitot tube are assumed Gaussian, whereas pressure-transducer graduations are treated as a uniform error of width Δ. The dimensionless parameter Δ/۴s, where σ denotes the Gaussian standard deviation, is varied systematically from ۰.۱ to ۱۰. For Δ/۴s £ ۰.۱ the composite probability-density function preserves the peak, variance, and kurtosis of the underlying Gaussian distribution. At the empirical two-sigma setting (Δ/۴s = ۱), graduation error depresses the peak and inflates variance and tail probability; for larger ratios the uniform component dominates entirely. These transitions are derived analytically and verified numerically, yielding explicit criteria for acceptable scale width. The framework is extended to hot-wire anemometry by modelling A/D-converter quantisation as an equivalent uniform error. Finite bit depth thickens velocity-fluctuation tails and exaggerates turbulence intensity, mirroring the pressure case. Consequently, fine graduation intervals and adequate bit resolution are essential for high-precision diagnostics. The derived guidelines facilitate rational instrument selection and provide a self-consistent basis for uncertainty analysis in advanced fluid-mechanics experiments. Broader implementation of the method promises improved reliability in atmospheric monitoring, aeroacoustic testing, and other applications where subtle fluctuations require uncompromised fidelity and accuracy.

کلیدواژه ها:

Wind tunnel experiment ، Pitot tube ، Differential manometer ، Bit depth ، Gaussian distribution