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Pipe Flow Friction Chart
Bachelor of Engineering (Honours) in Mechanical Engineering – Award
(Bachelor of Engineering in Mechanical Engineering – Award)
(NFQ – Level 8)
Autumn 2005
Fluid Mechanics
(Time: 3 Hours)
Instructions Answer FIVE questions. All questions carry equal marks
Examiners: Dr. G Kelly Mr. J. Hegarty Prof. J. Monaghan
Q1. (a) Discuss the use of Dimensional Analysis in the solving of problems involving fluid flow. Where and how is it used? (10 marks) (b) The discharge through a horizontal capillary tube is thought to depend upon pressure drop per unit length, the tube diameter, and the viscosity. Find the form of the equation. (10 marks)
Q2. (a) Describe two basic types of similarity which are used in the design and analysis of model testing programmes. Outline difficulties if any, in achieving similarity in model testing. (10 marks) (b) A piping system which normally carries water is to be tested with a 1/5 scale model using air to determine pressure losses. The prototype transports water at a velocity of 0.45 m/s through a duct of diameter 4.25m. Determine the velocity and quantity of air required for the model to ensure similarity. Assume the density of air and water are 1.23 kg/m^3 and 1000 kg/m^3 respectively. The viscosity of air and water are 1.78 x 10 - kg/ms and 1.140 x 10 -3^ kg/ms respectively. (10 marks)
Q3. (a) Show how the inlet and outlet velocity triangles for a centrifugal pump are obtained. (6 marks) (b) A centrifugal pump has an impeller of outer radius r 2 and inner radius r 1 with corresponding peripheral velocities of u 2 and u 1. If the flow enters the impeller radially, obtain an expression for the work done per unit weight on the fluid by the impeller in terms of u 2 and the velocity of whirl at the outlet vw 2. (8 marks) (c) The diameter of the impeller to a centrifugal pump is 1.2 m and its peripheral speed is 9 m/s. Water enters radially and is discharged from the impeller with a velocity whose radial component is 1.5 m/s. The vanes of the impeller are curved backwards at exit and make an angle of 30° to the periphery. If the pump discharges 3.4 m^3 per minute, what will be the turning moment on the shaft? (6 marks)
Q4. (a) Discuss the effects of operating identical pumps in series and in parallel. ( marks) (b) A centrifugal pump having four stages in parallel delivers 11m^3 /min of water against a head of 24.7m, the diameter of the impellers being 225mm and the speed of revolution 1700 rev/min. A second pump is to be made up with a number of identical stages in series, of similar construction to the first pump, to run at 1250 rev/min, and to deliver 14.5 m^3 /min against a head of 248m. Find the diameter of the impellers and the number of stages required. (12 marks)
Q5. (a) Describe, and illustrate graphically, the interaction between a pump and a system with which it is operates. In this context what is meant by the operating point? ( marks) (b) A water supply system consists two reservoirs joined by 840m of 0.15m diameter pipe with an absolute roughness of 6 x10 -6^. The water is pumped form the lower to the upper reservoir by a centrifugal pump whose characteristics are shown in the table below. The difference between water levels is 3m. Neglecting all losses except friction determine the rate of flow between the reservoirs and the power consumed by the pump. Take the dynamic viscosity of water μ as 1.14x10 -3^ kg/ms. (12 marks) Q [m^3 /s] 0.01 0.014 0.017 0.019 0. H [m] 9.5 8.7 7.4 6.1 0. η [%] 65 81 78 68 12
10 3 2 4 10 4 2 4 10 5 2 4 10 6 2 4 101024 7 8
Reynolds Number Re = ρ μ ud (logarithmic scale)
Friction Factor
(^) f (logarithmic scale)
0 002
0 004
0 007
0 009
0 01
0 016
0 025
0 02
0.00080.
Relative roughness
(^) k / d
Fully developed turbulence - rough pipes
Smooth pipes
criticalregion
Material k Glass, Brass, Copper, Lead smooth Steel, wrought iron 46 μm Ashphalted cast iron 120 μm Galvanized iron 150 μm Cast iron 260 μm
f (^) Re
Laminar flow = 16
unstable transition region
