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Cork Institute of Technology
Bachelor of Engineering (Honours) in Mechanical Engineering- Stage 2
(NFQ Level 8)
Summer 2006
Fluid Mechanics
(Time: 3 Hours)
Instructions Answer FIVE questions. All questions carry equal marks
Examiners: Dr. G Kelly Mr. J. E. Hegarty Prof. M. Gilchrist
Q1. (a) Derive an expression for the velocity of flow issuing from a pipe of length L used to empty a reservoir when the pipe outlet is a distance h below the surface of the water in the reservoir. Ignore all losses except friction. (8 marks) (b) A cylindrical tank, 0.9m in diameter is emptied through a 50mm diameter pipe of length 3.6m by opening the valve at the end of pipe. After opening the valve for a period of 2 minutes, the level in the reservoir fell to 1.2m above the outlet. Calculate the level in the reservoir prior to opening the valve and the hence or otherwise estimate the volume discharged through the pipe. Ignore all losses except friction and assume a friction factor of f = 0.01 for the pipe. (12 marks)
3.6m
d= 50mm
D= 0.9m h
3.6m valve
d= 50mm
D= 0.9m h
valve
Q2. (a) A reservoir with a head H discharges through a pipeline of length L. Using rigid column
theory derive the following expression ∆ H = gLdvdt for the head rise ∆H resulting from
the closure of a valve located at the end of the pipeline. Ignore all losses. (6 Marks)
(b) Show how this equation ∆ H = gLdtdv may be used to derive an expression which
describes the development of flow on opening the valve. ( Marks) (c) A valve positioned at the discharge end of a 30m pipe is opened at a time when the level in the tank supplying the reservoir is 6m above the pipe inlet. Calculate the time taken to accelerate the flow to 50% of its final velocity. Assume that the final velocity is 2.128 ms-1^. (6 Marks)
Q3. (a) Describe the principle and operation of an orifice plate meter. Write down the equations governing the flow through such a meter. Outline why a typical discharge coefficient is significantly different to unity. (8 marks) (b) An orifice plate is to be used to measure the velocity of airflow through a 2m diameter duct. The mean velocity in the duct will not exceed 15 ms-1^ and a water tube manometer having a maximum difference between water levels of 150mm is to be used. Assuming Cd is 0.64 determine a suitable orifice diameter to make full use of the manometer range. Take the density of air to be 1.2 kgm-3^. (12 marks)
d
H
L
valve
d
H
L
valve
(i) Derive an expression (in terms of Q, r, and h) for the convective acceleration of the air at a point A which is a distance r from the centre of the disks where Q is the constant rate of air discharge in the pipe, r is a radial distance from the centreline of the pipe, and h is the disk separation. Assume a negligible change in air density. (6 Marks) (ii) If D = 0.10 m, h = 0.01 m, and Q = 0.380 m^3 /s, determine the velocity in the pipe and the convective acceleration at point A where r = 0.2m. (6 Marks)
Q7. (a) Derive an expression for the magnitude and direction of the resultant force generated due to the deflection of a jet of fluid by a curved vane through an angle θ. State all assumptions used. (10 Marks) (b) A jet of water having a velocity of 15m/s impinges tangentially on a stationary vane whose section is in the form of a circular arc with a subtended angle of 120o^. Find the magnitude and direction of the reaction on the vane when the discharge from the jet is 0.45 kgs-1^. (
Marks)
V 60°
120°
V
y
x
V 60°
120°
V
y
x
Cork Institute of Technology
2
2
2
2
2
4
4
4
4
4
310
410
510
10
6
10
7
10
8
Reynolds Number (logarithmic scale)
ρ ud^ μ
Re
Friction Factor f (logarithmic scale)
0 025 0 020.0180 0160 0140.0120 010 0090.0080 0070 006 0.005 0 004 0.0030 0025 0.
0.050.040.03 0.020.0150.010.0080.0060.004 0.0020.0010.00080.00060.00040.00020.00010.00005 0.
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
Re f^
Laminar flow
unstable transition region
