Question 5.2: A tanker carrying toluene is unloaded, using the ship’s pump...

Cross-sectional area of pipe =\frac{\pi}{4}\left(225 \times 10^{-3}\right)^{2}=0.0398 m ^{2}

Minimum fluid velocity =\frac{1000 \times 10^{3}}{5 \times 3600} \times \frac{1}{0.0398} \times \frac{1}{874}=1.6 m / s

Reynolds number =\left(874 \times 1.6 \times 225 \times 10^{-3}\right) / 0.62 \times 10^{-3} =507,484=5.1 \times 10^{5} (5.4)

Absolute roughness commercial steel pipe, Table 5.2 = 0.046 mm

Relative roughness = 0.046/225 = 0.0002

Friction factor from Figure 5.7, f = 0.0019

Total length of pipeline, including miscellaneous losses, =900+600 \times 225 \times 10^{-3}=1035 m

Friction loss in pipeline, \Delta P_{f}=8 \times 0.0019 \times\left(\frac{1035}{225 \times 10^{-3}}\right) \times 874 \times \frac{1.62^{2}}{2} =78,221 N / m ^{2} (5.3)

Maximum difference in elevation, \left(z_{1}-z_{2}\right)=(0-30)=-30 m

Pressure difference, \left(P_{1}-P_{2}\right)=(1.05-1.1) 10^{5}=-5 \times 10^{3} N / m ^{2}

Energy balance

\begin{array}{c}9.8(-30)+(-5 \times 103) / 874-(78,221) / 874-W=0 \\W=-389.2 J / kg ,\end{array} (5.5)

Power =(389.2 \times 55.56) / 0.7=30,981 W , \quad \text { say } 31 kW (5.6a)