A wind-tunnel experiment used to determine the drag force acting on a cylinder by measuring the velocity deficit in its downstream wake.
Instead of measuring drag directly with a force sensor, the experiment used conservation of momentum to relate the loss of fluid momentum in the wake to the aerodynamic force acting on the cylinder.
Pitot-static pressure measurements were collected at multiple vertical locations downstream of the cylinder and converted into local velocity values using Bernoulli’s equation.
Determine aerodynamic drag indirectly from measured wake behavior.
- Process pitot-static pressure measurements collected downstream of the cylinder.
- Convert pressure differences into local flow velocity using Bernoulli’s equation.
- Construct velocity profiles across the cylinder wake.
- Calculate the momentum deficit produced by the cylinder.
- Numerically integrate the wake profile using the trapezoidal rule.
- Determine drag force for multiple wind-tunnel operating speeds.
- Compare the measured relationship between velocity and aerodynamic drag.
Three wind-tunnel runs were performed at different flow speeds. For each run, pressure measurements were collected at multiple vertical positions within the wake.
Pitot-static measurements were collected across the downstream wake.
Pressure differences were converted into local velocity using Bernoulli’s equation.
Local velocity values were plotted against vertical measurement position.
Wake momentum deficit was numerically integrated to determine drag.
Experimental data was processed in Excel. Position measurements were converted from inches to meters, while pressure data was converted into velocity values.
Used to determine air density.
Used in the drag calculation.
Implemented manually in Excel.
The upstream velocity for each run was estimated using the maximum measured velocity in the corresponding dataset.
The momentum-deficit integrand u(y)[U₁ − u(y)] was calculated at each measurement location before applying numerical integration across the wake.
The cylinder removes momentum from the incoming airflow, creating a lower-velocity wake downstream.
Air approaches the cylinder with approximately uniform velocity.
Flow interacts with the body and loses momentum.
Downstream velocity becomes lower near the centerline.
The measured momentum deficit is related to aerodynamic drag.
The calculated drag increased across all three runs as the upstream velocity increased.
Drag = 0.0819 N
Drag = 0.1473 N
Drag = 0.2209 N
Higher wind-tunnel speeds produced a stronger velocity deficit in the wake and a larger corresponding momentum loss.
Drag increased nonlinearly with upstream velocity.
The experimental trend indicated that drag increased more rapidly than a linear relationship as wind-tunnel speed increased.
The fitted trend was consistent with drag being approximately proportional to the square of velocity.
Approximate experimental trend based on the three test conditions.
Several experimental limitations could affect the calculated velocity profiles and resulting drag estimates.
Misalignment between the probe and local flow direction could alter pressure measurements.
Small pressure variations affect calculated velocity because of the square-root relationship.
A finite number of wake measurements reduces numerical integration resolution.
Upstream velocity was estimated from wake data rather than measured independently.
The experiment demonstrated how aerodynamic forces can be determined indirectly from changes in the surrounding flow field.
Rather than relying on a direct force measurement, conservation of momentum connected the measured wake velocity deficit to the drag acting on the cylinder.
The project strengthened my experience with wind-tunnel data, fluid mechanics, experimental uncertainty, numerical integration, and interpretation of aerodynamic wake behavior.
Fluid Mechanics Lab Report
The complete report contains the experiment theory, methodology, velocity-profile processing, numerical integration, drag results, wake plots, discussion, and experimental error analysis.