Question

Two reservoirs are connected by a 5000 m long and 1.5 m diameter C.I pipe with f = 0.01 . The difference in water levels in two reservoir is 25 m. Determine the increase in discharge if the C.I pipe is replaced with a smooth steel pipe of same size with f = 0.005.

Answer 1

$H_L=\dfrac{32f_1LQ_1²}{π²gd_1 ⁵}$

$Q_1= \sqrt{\dfrac{Hπ²gd_1 ⁵}{32f_1L}}$

$Q_1 = \sqrt{\dfrac{25π²×9.81×1.5⁵}{32×0.01×500}}= 10.72m³/s$

$Q_2= \sqrt{\dfrac{Hπ²gd_2 ⁵}{32f_2L}}$

$\sqrt{\dfrac{25π²×9.81×1.5⁵}{32×0.005×500}} = 15.16m³/s$

$Q= Q_1+ Q_2=15.16m³/s- 10.72m³/s= 4.44m³/s$