Question

Figure 4 Water pipes taking water from Trawsfynydd Lake to Maentwrog hydroelectric power station

Question 3

This question is worth 12 marks.

The water from the lake in Question 2 flows along the river and enters a hydroelectric power plant through large inlet pipes with a circular cross-section of internal diameter $0.850m$ , similar to those shown in Figure 4.

Figure 4 Water pipes taking water from Trawsfynydd Lake to Maentwrog hydroelectric power station

• a.Explain why the velocity of the water is greatest at the centre of the inlet pipe and sketch a typical velocity profile across the pipe. You should be able to answer Question 3(a) in no more than 50 words. (2 marks)

• b.Describe the difference between laminar and turbulent flow using diagrams to support your answer. You should be able to answer Question 3(b) in no more than 100 words. (2 marks)

• c.The volumetric flow rate of water through each inlet pipe is $1.50m^{3}S^{-1}$ . Assuming that the density of the water is unchanged from that in the lake, and that the dynamic viscosity of the water is $1.002 x10^{-3}Pas$ , determine whether the flow in the inlet pipe is laminar or turbulent. (5 marks)

• d.The inlet pipes feed the turbine in a power station. Just before entering the turbine, the inlet pipe narrows to a circular cross-section of diameter $0.350 m$. Given that water is incompressible and has a velocity of $2.64ms^{-1}$ (to 3 s.f.) just before the pipe narrows, show that the flow velocity just after the restriction and before it enters the turbine is $15.6ms^{-1}$ (to 3 s.f.). State any assumptions you make. (3 marks)

Answer 1

The main reason for velocity being maximum at centre of the inlet pipe is due to, Friction od inner surface pipe Viscosity of the fluid when any fluid runs through pipe the velocity of water or the taken fluid near it's wall is less because of the friction the wall exerts. As we move towards the centre of pipe ie, away from the walls the friction decreases and hence the velocity increases, ie, velocity of water or any fluid of different viscosity moves faster \r\n Laminar flow: - Motion of the fluid particles is very orderly, all particles moving in straight lines parallel to the pipe walls. Encountered when highly viscous fluid such as oil flows in small pipes or narrow passage. \r\n Turbulent flow: - Motion is locally, completely random but the overall direction of flow is one way. In practice, most flows are turbulent The friction factor reached maximum when flow become fully turbulent. Reynold's number R_e = rho VD/mu rho rightarrow