11. A log 2 m in diameter and 12 m long is towed at a constant speed of 3 m/s in
ID: 2087375 • Letter: 1
Question
11. A log 2 m in diameter and 12 m long is towed at a constant speed of 3 m/s in fresh water at 20°C. What is the drag force, in kN, on this log if it is towed lengthwise (water facing log end)? (a)65 (d) 12.7 (b ) 275 (e) 50.8 (c)5.2 12. In Prob.11, what is the required towing power in kW? (a) 0.35 (d) 192.2 (b)38.1 (c) 13.6 (e) 62.3 14. In Prob.11, what would the drag force be in kN if the log was towed widthwise (water facing I log length) (Use interpolation to find Co from Table 7.2)? (a ) 25 (d) 322 (b)98 (c)216 (e) 149Explanation / Answer
L/D = 12 / 2 = 6
11.
Frontal area A = 3.14 / 4 * 2^2 = 3.14 m^2
For flat faced cylinder with L/D = 6, we get Drag coefficient based on frontal area Cd = 0.9
Drag force = Cd * A * 1/2 * rho * V^2
= 0.9 * 3.14 * 1/2 * 1000 * 3^2
= 12717 N
= 12.7 kN
12.
Towing power = F * V
= 12.7 * 3
= 38.1 kW
13.
Reynolds number Re = V*D / neu
= 3 * 2 / (0.8927*10-6)
= 6.72*10^6 . So the flow is turbulent.
For turbulent flow over cylinder, Drag coeff Cd = 0.3
Frontal area A = D*L = 12 * 2 = 24 m^2
Drag force = 0.3 * 24 * 1/2 * 1000 * 3^2
= 32400 N
~ 32.2 kN (It looks like in option d the decimal point has been missed)
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