Question 7.P.19: Determine the diameter of the pipe (smooth) required to conv......
Determine the diameter of the pipe (smooth) required to convey 150 l of kerosene over a length 1000 m with the loss of head by friction limited to 10 m of kerosene. Density = 810 kg/m³, kinematic viscosity = 2.37 × 10^{–6} m²/s
In this problem also as in P. 7.18, trial is necessary. Assume f = 0.012
Neglecting dynamic head, As u = Q/A,
10 = [(0.012 × 1000)/(2 × 9.81 × D)] × [(0.15 × 4)/(πD²)]²
∴ u = (4 × 0.15)/πD², Simplifying
D^{5} = [(0.012 × 1000)/(2 × 9.81 × 10)] × [(0.15² × 4²)/π²] \\ = 2.231 × 10^{–3}
∴ D = 0.295 m and u = 2.195 m/s
Re = 0.295 × 2.195/2.37 × 10^{–6} = 0.273 × 10^{6}
Refer eqn. 7.11.11, f = 0.0032 + (0.221/Re^{0.0237}) = 0.0146
Assuming f = 0.014, to repeat the procedure
10 = [(0.014 × 10000)/(2 × 9.81 × D)] × [(0.15 × 4)/πD²]²
∴ D^{5} = [(0.014 × 1000)/(2 × 9.82 × 10)] [(0.15² × 4²)/π²] = 2.6 × 10^{–3}
D = 0.304 m, u = 0.15 × 4/π × 0.304² = 2.065 m/s
Re = 2.065 × 0.304/2.37 × 10^{–6} = 0.265 × 10^{6} \\ f = 0.0032 + 0.221/(0.265 × 10^{6})^{0.237} = 0.01466
The answer can be refined further using this value of f and reworking on the same lines.