A 2 km long pipe of 0.2 m diameter connects two reservoirs.

A 2 km long pipe of 0.2 m diameter connects two reservoirs. The difference between water levels in the reservoirs is 8 m. The Darcy-Weisbach friction factor of the pipe is 0.04. Accounting for frictional, entry and exit losses, the velocity in the pipe (in m/s) is

Frictional loss

h_f =	fLV²
	d × 2g

Loss of head at entrance,

h_L =	0.5V²
	2g

Loss at exit of pipe

h_c =	V²
	2g

∴ 8 =	fLV²	+	0.5V²	+	V²
	d × 2g		2g		2g

⇒ 8 =	0.04 × 2000 × V²	+	V²	+	0.5V²
	2 × g × 0.2		2g		2g

⇒ 8 = 20.3873 V² + 0.07645 V²
⇒ V = 0.625 m/s ≌ 0.63 m/s