Let's analyze the question from the image: **Question:** Consider air flowing at \( U = 1.2 \, \text{m/s} \), \( \mu = 1.42 \times 10^{-5} \, \text{kg/m.s} \), and \( \nu = 1.47 \times 10^{-5} \, \text{m}^2/\text{s} \) on a flat plate having a length of 1 m and a width of 0.5 m, respectively. Then the length up to which the flow of air will be laminar is: Options: - 0.25 m - 0.375 m - 0.725 m - 0.545 m ### Solution: The flow will be laminar up to the point where the Reynolds number (\( Re_x \)) reaches the critical value, typically \( Re_{cr} = 5 \times 10^5 \) for flow over a flat plate. The Reynolds number is given by: \[ Re_x = \frac{U x}{\nu} \] Set \( Re_x = 5 \times 10^5 \): \[ 5 \times 10^5 = \frac{1.2 \cdot x}{1.47 \times 10^{-5}} \] Solve for \( x \): \[ x = \frac{5 \times 10^5 \times 1.47 \times 10^{-5}}{1.2} \] \[ x = \frac{7.35}{1.2} \] \[ x = 0.6125 \text{ m} \] Let's check the closest value in the options: - 0.25 m - 0.375 m - 0.725 m - 0.545 m The closest value is **0.545 m**. ### **Final Answer:** **0.545 m** is the length up to which the flow of air will be laminar.