Discussion
Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, f = 0.0225) of length 500 m. The volumetric flow rate is 0.2 m3/s. The head loss (in m) due to friction is (assume g = 9.81 m/s2)
Answer: A
The head loss is about 116.18 m.
Find the velocity, then apply the Darcy-Weisbach equation:
\[ \begin{aligned} A &= \tfrac{\pi}{4}(0.2)^{2} = 0.031416\ \text{m}^{2} \\ v &= \frac{0.2}{0.031416} = 6.366\ \text{m/s} \end{aligned} \]
\[ \begin{aligned} h_{f} &= \frac{fLv^{2}}{2gD} \\ &= \frac{0.0225 \times 500 \times 6.366^{2}}{2 \times 9.81 \times 0.2} \\ &= \frac{455.9}{3.924} = 116.2\ \text{m} \end{aligned} \]
232.36 is twice the correct value, the result of dropping the 2 in 2g. 0.116 is the right digits with the decimal point moved three places, and 18.22 does not come from the Darcy-Weisbach equation with these data.
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