Chapter 5, Problem 5.63P

The Keystone Pipeline in the Chapter 6 opener photo has D = 36 in. and an oil flow rate Q = 590,000 barrels per day (1 barrel = 42 U.S. gallons). Its pressure drop per unit length, $△p/L$ , depends on the fluid density $\rho$ , viscosity $\mu$ , diameter D, and flow rate Q. A water-flow model test, at 20°C, uses a 5-cm-diameter pipe and yields $△p/L\approx 4000$ Pa/m. For dynamic similarity, estimate $△p/L$ of the pipeline. For the oil take $\rho =860{\text{kg/m}}^{\text{3}}$ and $\mu =0.005\text{kg/m}\cdot \text{s}$ .