Question

Water flows from one large reservoir to another via a pipeline which is 0.9 m in diameter, 15km long, and for which f-0.04. The difference in height between the water surface levels in the two reservoirs is 50m. (a) Ignoring the minor losses in the pipeline, calculate the flow rate between the two reservoirs. (b) Assuming that the pipeline entrance and exit are sharp and that the minor losses are as in Table 1, calculate the discharge now. What is the difference between the answers to parts (a) and (b)? [15] Table 6.1 Head losses in pipelines Type of loss Equation to calculate head loss Example Friction (Darcy equation) DI Sudden expansion (sharp increase in diameter or exit from pipeline) Sudden contraction (sharp entrance to pipeline or reduction in diameter) n=0.5 Notation: = head loss due to friction minor head loss 2 = Darcy friction factor indicating pipe roughness (dimensionless) (Note: in the UK 2 = 4f, in the USA i = f) L= pipe length (m) V= mean velocity (m/s) D = pipe diameter (m) g= acceleration due to gravity (m/s) subscript 1 = upstream velocity before change of section subscript 2=downstream velocity after change of section.

Answer 1

celus: t soll 0.9m K - 0 15000m - =0 @ Ignoring minor losses, we have (Acc. to U.S.) L o s hy the Daje kone or 12.1 or a² = 0.5954 (m/2 or a = 0.772 m3/ e hi= the tth),+ lk , + X or 50 = flur to.subt So I DI 1920 or 10049.280 je poor xitos 3+15] 0.9-79 00 02-0.594 = 0.4708 m². Therefore (Aa=0.772-0.7708 WIT IS8=1,2 X 10 3 m/ P