Chapter 8, Problem 8.9P

In Chapter 1, it was stated that for incompressible liquids, flow work could usually be neglected in the steady-flow energy equation (Equation I. 12d). In the trans-Alaska pipeline, the high viscosity of the oil and long distances cause significant pressure drops, and it is reasonable to question whether flow work would be significant. Consider an $L=\text{ 1}00\text{km}$ length of pipe of diameter $D=\text{ 1}.\text{2 m}$ , with oil flow rate $m=\text{ 5}00\text{ kg}/\text{s}$ . The oil properties are $\rho =900{\text{kg/m}}^3,c_p=2000\text{J/kg}\cdot \text{K},\mu =0.765\text{N}\cdot {\text{s/m}}^2$ . Calculate the pressure drop, the flow work, and the temperature rise caused by the flow work.