Experiment 2 - Part 2

Q1: Why are pressure differences normalized with dynamic pressure in the pitch and yaw equations?

Normalizing the differential pressures by the average dynamic pressure allows for:

• Dimensionless calibration curves (∆P/𝑝_dyn), which generalize the relationship across varying flow speeds.

• Reduced sensitivity to fluctuations in flow conditions.

• Better polynomial fitting across different Mach numbers.

Q2: What could be the impact of incorrect alignment between the probe and flow in determining pitch/yaw angles?

Incorrect alignment introduces systematic error:

• Skews the pressure distribution, which leads to wrong ∆P_pitch/∆P_yaw.

• Causes incorrect estimation of local flow direction, leading to flawed calibration.

• Errors propagate into mass flow estimation when velocity vectors are reconstructed later.

Q3: Why is a 5th-degree polynomial used to relate pressures to α, β, and velocity?

• Captures the nonlinear and coupled effects of flow angle and speed on pressure distribution.

• 5th-degree is a compromise: flexible enough for good accuracy, but not overly prone to overfitting.

• Also aligns with literature and previous calibration practices (e.g., Wörrlein).

Q4: What is the significance of the β parameter in ISO 5167-2, and how does it affect flow rate calculation?

• β = d/D is the orifice diameter to pipe diameter ratio.

• Affects the discharge coefficient C and expansion factor ε, which are critical in the mass flow equation.

• Extreme β values (too small or too large) can lead to:

  • Flow separation,

  • Increased uncertainty,

  • Breakdown of the ISO 5167 assumptions.

Q5: Why must barometric pressure and temperature be recorded for the orifice method?

• Needed to compute fluid density from ideal gas law:

  ρ=p/RT

• Accurate density is essential to convert volumetric flow to mass flow.

• Pressure deviations or uncorrected temperature drifts would cause systematic mass flow error.

Q6: Why do we need to compute the Reynolds number and viscosity, and how are they used?

• Reynolds number affects the discharge coefficient C, which is Re-dependent.

• Viscosity (μ) is used in Re = ρVD/μ.

• Accurate Re → accurate C → correct mass flow estimate.

Q7: Why is ring-wise integration used, and what assumptions does it rely on?

• Assumes axisymmetric jet → simplifies 2D integral into 1D over radius:

  Q˙=2π∑uiriΔri

• Efficient and accurate for symmetric flows, reducing computational complexity.

• If jet is asymmetric, ring-wise integration may underestimate localized features.

Q8: What are possible sources of error in this numerical integration method?

• Insufficient spatial resolution (too large ∆r).

• Interpolation errors between grid points.

• Non-ideal jet alignment or turbulence.

• Probe misalignment or drift during scan.

Q9: Why is dynamic pressure computed locally for each node in Measurement C?

• Each node may have different flow speed and direction.

• Using a single global dynamic pressure would misrepresent local conditions.

• Local P_dyn → accurate local velocity → accurate volume integration.

Q10: How would you increase the accuracy of Measurement C results?

• Use finer grid resolution (smaller ∆r).

• Repeat measurements at each grid point and average.

• Cross-check with Pitot or orifice-based results.

• Ensure precise probe alignment and calibration.