Consider the flow of oil at 10 degree C in a 1.9m-diameter pipeline at an average velocity of 0.5 m/s. A 1500-m-long section of the pipeline passes through icy waters of a lake at 0 degree C. Measurements indicate that the surface temperature of the pipe is very nearly 0 degree C. Given:
rho = 893.6 kg/m3
mu = 2.326 kg/m. s
cp = 1839 J/kg. degree C
k = 0.1460 W/m. degree C
v = 2.592 times 10^-3 m^2/s
Pr = 28.750
If the pressure drop is 15.4kPa, what is the pumping power required to overcome the pressure losses and to maintain the flow of oil in the pipe?