Question

Water is slowly drained from a large reservoir using two horizontal plastic pipes connected in series. The pipes are smooth and located at the bottom of the reservoir, as shown below. The first pipe has a diameter D1 = 10 cm and length L1 = 10 m, while the second pipe has a diameter D2 = 5 cm and a length L2 = 40 m (see schematic below). The water level in the reservoir is constant and equal to H = 20 m. The water density and dynamic viscosity are given as p = 1000 kg/ m3 and j = 10-3 Pa * s, respectively. 20 m Water tank Pipe 1 Pipe 2 10 m 40 m Please answer the following question: By neglecting all the localised viscous losses, evaluate the volumetric flow rate Q. [20 marks]

Answer 1

Viscous losses are neglected so only minor losses needed to be considered

Now there are three region for these losses

1. at entrance of Pipe 1

2. Sudden contraction from pipe 1 to pipe 2

3. at the exit from pipe 2

velocity in pipe 1 = Flow rate / Cross-section 1 = Q/($\pi$/4*0.1^2)= 127.324 Q m/s

Velocity in pipe 2 = Flow rate / Cross-section 2 = Q/($\pi$/4*0.05^2)=509.29 Q m/s

K entrance (loss coefficient =0.5)

loss at entrance = Kentrance * V1^2/2g = 0.5*127.3242Q2/19.62= 413.13 Q2

loss at contraction =K V2^2/2g

р. 65,0.4) О. 9 О- - С. - o 2 О.Ч Nu x 0.05 0.2.S 2 Р И, ко1

K= 0.4 at A2/A1 = 0.25

0.4*509.29 2/19.62 = 5287.99 Q^2

loss at exit = V22/2g = 13219..99 Q^2

so 20 = (413.13+ 5287.99+13219.99 )Q^2

Q=0.0325 m3/s or 3.25 litres/s Ans