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To compute the Reynolds number, we need the airstream speed (V), pipe diameter (D), the air kinematic viscosity (谓) at 25掳C. Using this data, we can calculate the Reynolds number as follows: \( Re = \frac{VD}{谓} \) For air at 25掳C and 1 atm pressure, 谓 is approximately \( 15.52 脳 10^{-6}\, \mathrm{m^2/s} \) (you can find this value in a table or online resources). Now, we have: D = 0.025 m (25 mm diameter) V = 15 m/s (airstream speed) Now, calculate the Reynolds number: \( Re = \frac{(15\, \mathrm{m/s})(0.025\, \mathrm{m})}{15.52 脳 10^{-6}\, \mathrm{m^2/s}} \approx 24,172 \)

To compute the drag coefficient, we can use an empirical correlation based on the Reynolds number (Re) for flow over a circular cylinder. For a Reynolds number of approximately 24,172 as computed in Step 1, the drag coefficient is Cd 鈮� 0.4 (you can find this value in a table or online resources).

To compute the drag force per unit length, first, we need to calculate the dynamic pressure of the airstream. To do this, we need the density (蟻) of air at 25掳C and 1 atm pressure (approximated as \(1.184\, \mathrm{kg/m^3}\)), the airstream speed (V), and the drag coefficient (Cd) as calculated in Step 2. Next, we can calculate the dynamic pressure (q) of the airstream and drag force (Fd) per unit length: \( q = \frac{(1/2)蟻V^2} \) \( Fd = \mathrm{Cd} \cdot q \cdot d \) Now, calculate the dynamic pressure and drag force per unit length: \( q = \frac{(1/2)(1.184\, \mathrm{kg/m^3})(15\, \mathrm{m/s})^2} \approx 132.87\, \mathrm{N/m^2} \) \( Fd = (0.4) (132.87\, \mathrm{N/m^2})(0.025\, \mathrm{m}) \approx 1.33\, \mathrm{N/m} \) Therefore, the drag force exerted on the pipe per unit length is approximately 1.33 N/m.

To compute the Nusselt number, we need the Prandtl number (Pr) of air at 25掳C and 1 atm pressure (approximated as 0.706), and the Reynolds number (Re) as calculated in Step 1. Using the Reynolds number, the Prandtl number, and an empirical correlation for flow over a circular cylinder, we can calculate the Nusselt number as follows: \( Nu 鈮� 0.3 + \frac{(0.62\,Re^{1/2}\,Pr^{1/3})}{(1 + (0.4/Pr)^{2/3})^{1/4}}(1 + (\frac{Re}{282000})^{5/8})^{4/5} = 152.59 \) Now, compute the convective heat transfer coefficient (h) using the Nusselt number and pipe diameter (D): \( h = \frac{Nu \cdot k_{air}}{D} \) For air at 25掳C and 1 atm pressure, the thermal conductivity (k) is approximately \(0.026\, \mathrm{W/(m \cdot K)}\). Now, calculate the convective heat transfer coefficient (h): \( h = \frac{(152.59)(0.026\, \mathrm{W/(m \cdot K)})}{0.025\, \mathrm{m}} \approx 158.95\, \mathrm{W/(m^2 \cdot K)} \)

Finally, we can calculate the rate of heat transfer per unit length by multiplying the convective heat transfer coefficient (h) by the surface area per unit length (A) and by the temperature difference (螖T) between the surface temperature and the airstream temperature: \( q = h \cdot A \cdot 螖T \) For a circular pipe, the surface area per unit length (A) is the circumference of the pipe, or \( A = 蟺D \). Now, insert the known values and compute the rate of heat transfer per unit length: \( q = (158.95\, \mathrm{W/(m^2 \cdot K)}) (蟺 \cdot 0.025\, \mathrm{m})(100^{\circ} \mathrm{C} - \,25^{\circ} \mathrm{C}) \approx 372.99\, \mathrm{W/m} \) In conclusion, the drag force exerted on the pipe per unit length is approximately 1.33 N/m, and the rate of heat transfer from the pipe per unit length is approximately 372.99 W/m.