Aerospace engineers conducted a series of wind tunnel trials to evaluate passive boundary … — ACT

Aerospace engineers conducted a series of wind tunnel trials to evaluate passive boundary layer control on a swept-wing model using micro-vortex generators (VGs). In Experiment 1, the engineers intentionally varied the VG orientation angle relative to the freestream flow ( $\theta$ ) across five trials while maintaining a constant freestream velocity ( $v = 45\text{ m/s}$ ), wing angle of attack ( $\alpha = 12^\circ$ ), and ambient temperature ( $T = 20^\circ\text{C}$ ). For each trial, they recorded the normalized chordwise position of boundary layer separation ( $x_s/c$ ). Their data are shown in the table below:

Trial	VG Angle ( $\theta$ )	Freestream Velocity ( $v$ )	Separation Position ( $x_s/c$ )
1	$0^\circ$	$45\text{ m/s}$	$0.62$
2	$5^\circ$	$45\text{ m/s}$	$0.71$
3	$10^\circ$	$45\text{ m/s}$	$0.80$
4	$15^\circ$	$45\text{ m/s}$	$0.86$
5	$20^\circ$	$45\text{ m/s}$	$0.83$

Based on Experiment 1, which of the following correctly identifies the independent variable, the dependent variable, and one controlled variable?

Independent variable: VG orientation angle ( $\theta$ ); Dependent variable: boundary layer separation position ( $x_s/c$ ); Controlled variable: freestream velocity ( $v$ )Answer
B
Independent variable: boundary layer separation position ( $x_s/c$ ); Dependent variable: VG orientation angle ( $\theta$ ); Controlled variable: freestream velocity ( $v$ )
C
Independent variable: freestream velocity ( $v$ ); Dependent variable: boundary layer separation position ( $x_s/c$ ); Controlled variable: VG orientation angle ( $\theta$ )
D
Independent variable: VG orientation angle ( $\theta$ ); Dependent variable: freestream velocity ( $v$ ); Controlled variable: boundary layer separation position ( $x_s/c$ )

Answer

The independent variable is the VG orientation angle (

\theta

), the dependent variable is the boundary layer separation position (

x_s/c

), and a controlled variable is the freestream velocity (

v

The option identifying the VG orientation angle as the independent variable, the boundary layer separation position as the dependent variable, and freestream velocity as a controlled variable is correct because the researchers systematically manipulated the angle across trials, measured the resulting separation position, and held the velocity fixed at 45 m/s throughout Experiment 1.

Step-by-Step Solution

Identify the variable intentionally altered by the experimenters across trials.

The researchers changed the VG orientation angle (

\theta

) from

0^\circ

20^\circ

, making it the independent variable.

The independent variable is the factor systematically manipulated by the experimenter to observe its effects.

Identify the response parameter measured as a result of changing the independent variable.

The normalized separation position (

x_s/c

) was measured for each angle, making it the dependent variable.

The dependent variable represents the outcome or measured data that responds to changes in the independent variable.

Identify the experimental factors kept unchanged across all trials.

Freestream velocity (

v = 45\text{ m/s}

), angle of attack (

\alpha = 12^\circ

), and ambient temperature (

T = 20^\circ\text{C}

) remained constant, making them controlled variables.

Controlled variables are parameters deliberately kept constant to ensure that changes in the dependent variable are solely attributable to the independent variable.

Key Concept

Classification of Experimental Variables

Estimated Time:1m 40s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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