Question 6.9: Water flows through a 1.2 m diameter pipeline constructed fr......

Understanding Hydraulics [985713]

Water flows through a 1.2 m diameter pipeline constructed from smooth concrete pipes for which k = 0.60 mm. The hydraulic gradient ( $S_{F}$ ) is 1 in 250 and n is 1.005 × $10^{- 6}$ m²/s. Calculate the mean velocity of flow using the Colebrook–White equation.

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k = 0.60 mm = 0.00060 m. $S_{F}$ = 1/250 = 0.004. Using equation (6.19):

v = –  2 \sqrt{2gDS_{F}} \log \left\lgroup\frac{k}{3.7D} + \frac{2.5v}{D\sqrt{2gDS_{F}} } \right\rgroup

v = – 2 \sqrt{19.62 \times 1.2 \times 0.004} \log \left\lgroup\frac{0.00060}{3.7 \times 1.2} + \frac{2.5 \times 1.005 \times 10^{-  6}}{1.2 \sqrt{19.62 \times 1.2 \times 0.004} } \right\rgroup

v = – 0.614 log(0.000135 + 0.00000682)

v = – 0.614 × – 3.848

v = 2.363 m / s

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