1 School of Mechanical and Chemical Engineering SEMESTER 1, 2012 EXAMINATIONS ENSC3003 Fluid Mechanics FAMILY NAME: ____________________________ GIVEN NAMES: ______________________ STUDENT ID: SIGNATURE: ________________________ This Paper Contains: 18 pages (including title page) Time allowed: 3 hours 10 minutes INSTRUCTIONS: This paper contains 5 questions, a table of constants and conversions (1 page), a general equation sheet (3 pages), and the equations of motion in Cartesian and Cylindrical coordinates (4 pages). Students should attempt all 5 questions Each question is worth 30 marks, for a total of 150 marks PLEASE NOTE Examination candidates may only bring authorised materials into the examination room. If a supervisor finds, during the examination, that you have unauthorised material, in whatever form, in the vicinity of your desk or on your person, whether in the examination room or the toilets or en route to/from the toilets, the matter will be reported to the head of school and disciplinary action will normally be taken against you. This action may result in your being deprived of any credit for this examination or even, in some cases, for the whole unit. This will apply regardless of whether the material has been used at the time it is found. Therefore, any candidate who has brought any unauthorised material whatsoever into the examination room should declare it to the supervisor immediately. Candidates who are uncertain whether any material is authorised should ask the supervisor for clarification. Supervisors Only – Student left at:
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Fluid Mechanics ENSC3003 Examination Paper 2012 Semester 1
Fluid Mechanics ENSC3003 Examination Paper 2012 Semester 1
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School of Mechanical and Chemical Engineering
SEMESTER 1, 2012 EXAMINATIONS
ENSC3003 Fluid Mechanics
FAMILY NAME: ____________________________ GIVEN NAMES: ______________________
STUDENT ID: SIGNATURE: ________________________
This Paper Contains: 18 pages (including title page) Time allowed: 3 hours 10 minutes
INSTRUCTIONS: This paper contains 5 questions, a table of constants and conversions (1 page), a general equation sheet (3 pages), and the equations of motion in Cartesian and Cylindrical coordinates (4 pages). Students should attempt all 5 questions Each question is worth 30 marks, for a total of 150 marks
PLEASE NOTE
Examination candidates may only bring authorised materials into the examination room. If a supervisor finds, during the examination, that you have unauthorised material, in whatever form, in the vicinity of your desk or on your person, whether in the examination room or the toilets or en route to/from the toilets, the matter will be reported to the head of school and disciplinary action will normally be taken against you. This action may result in your being deprived of any credit for this examination or even, in some cases, for the whole unit. This will apply regardless of whether the material has been used at the time it is found. Therefore, any candidate who has brought any unauthorised material whatsoever into the examination room should declare it to the supervisor immediately. Candidates who are uncertain whether any material is authorised should ask the supervisor for clarification.
Supervisors Only – Student left at:
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Question 1 (30 points total) (a) (15 points) Gas enters a pipe system at section 1 at a velocity of 5.2 m/s and a temperature
of 125˚C, and leaves at section 2, where the temperature is 80˚C. The pipe diameter at section 1 is 200 mm, and the pipe diameter at section 2 is 250 mm. The gauge pressures at sections 1 and 2 are 600 kPa and 400 kPa respectively. The system is at steady state. Determine the following;
The mass flow rate (in kg/s) at section 1 The mass flow rate (in kg/s) at section 2 The flow velocity (in m/s) at section 2 You may assume that at 300 K and standard atmospheric pressure, the density of the gas is
0.7 kg/m3. (b) (10 points) A body of water is held back behind a 5 metre long diamond shaped wall, as
illustrated in the diagram below (the diamond is a square rotated to a 45 degree angle). The water surface is level with the top of the wall, and atmospheric pressure acts at the surface. Calculate the horizontal and vertical components of the pressure force (in Newtons) acting on the dam wall. Your answer must identify the direction in which the force acts. You may use "shortcuts" in determining your answers, and assume that the density of water is 1000 kg/m3.
(c) (5 points)
The temperature of a liquid undergoing laminar flow in a horizontal circular pipe is decreased. If the pressure gradient is unchanged, how will this affect the volume flow rate in the pipe? Justify your answer.
2 metres
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Question 2 (30 marks total)
A liquid is transported through a horizontal circular pipe of radius R via pressure-driven flow, as illustrated below. The pressure at the upstream end of the duct (z=0) is Po, and at the downstream end (z=L) is PL. The flow may be regarded as laminar and isothermal, and the oil is a Newtonian liquid; the duct may be regarded as stationary. (a) (20 marks) Starting with the appropriate form of the Continuity Equation and Equations of
Motion (attached at the end of the examination paper), derive an equation for determining the z component of velocity in the pipe at steady state. Be sure to identify all assumptions and boundary conditions. You may use the attached equation sheets – submit any marked equation sheets with your examination booklet.
(b) (5 marks) Derive an equation for the volume flow rate of oil through the pipe at steady state.
You must show all working for full credit. (c) (5 marks) In a modified version of this system, the pipe radius tapers from R at z=0 to a
radius of 0.5R at z=L. While continuing to assume isothermal laminar flow, re-derive the differential forms of the continuity equation and z-direction momentum balance for the tapered pipe (NOTE – do not integrate the resulting equations)
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Question 3 (30 marks total)
A centrifugal mixing device, as illustrated in the diagram below, is being developed to stir small quantities of blood for experimental procedures. The proposed device is confined within a cylinder 2 cm in diameter and 10 cm tall, and uses a stirrer 1 cm in diameter. The proposed operating speed for the stirrer is 20 rpm. Blood is very viscous, and significant surface vortex can develop. If this vortex becomes large enough to reach the stirrer, the delicate cells within the blood will be severely damaged by the extreme shear gradients arising. It is therefore proposed to build a large scale model using an alternative fluid in order to investigate the phenomenon. Due to material restrictions, it has been established that the model cylinder diameter (DCM) must be 10 cm. If the specific gravity of blood is 1.1, and the viscosity of blood at room temperature is 2.0 cP, determine (i) The other dimensions (height HM and stirrer diameter DSM) of the model (ii) The kinematic viscosity required of the model fluid (in m2/s) (iii) The speed (in rpm) of the stirrer in the model system
DS
DC
H
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Question 4 – 30 Marks Total A centrifugal pump is to be installed to transfer water (ρ=1000 kg/m3, μ=0.001 Pas) between two reservoirs via the system illustrated in the diagram below. (a) (16 marks) The pump curve for the proposed pump is provided overleaf. Calculate the
system curve, plot it on the chart provided, and determine the duty point for the proposed system. To plot the system curve, calculating 3 points on the curve will be sufficient. (NB please detach the finished chart and submit it with your solutions). Charts for the friction factor and fitting loss factors are provided.
(b) (6 points) It is proposed to increase the flow delivered through the system by operating a
second identical pump with the original pump. Using the system curve you have calculated and the pump curve provided, determine the optimal arrangement of the two pumps (in terms of maximising flow rate) and the resulting duty point.
(c) (3 points) If the pump efficiency at the duty point is 76%, calculate the pump power (in
watts) that must be supplied by the motor when the pump is operating at the regular (single pump) duty point.
(d) (5 points) At the duty point, the NPSHR for the proposed pump is 9.2 metres. Under
extreme conditions, the water level in the supply reservoir may fall to as low as 1.5 metres above the pump inlet centreline. Assuming that the friction losses in the suction side pipework can be considered to be negligible (for the purpose of NPSH calculation only), is the pump safe from cavitation ? Show working to support your answer. The vapour pressure (head) of water at 293 K is 0.238 m (H2O)
PPipework
Length 675 metresDiameter 450 mmCommercial Steel
90 degreeLong radius
Fully OpenGate Valves
Swing CheckValve
11.5 metres
90 degreeLong radius
90 degreeLong radius
Sharp entrance4.3 metres
(to pump centreline)
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Pump Curve for Question 4
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Question 5 - 30 marks total The pipe section shown below is incorporated in an oil delivery system (for the oil, SG=0.9, μ=2.5 centipoise). The flow velocity at section 1 is 1.5 m/s. The absolute pressures at section 1 is 450 kPa. The system is at steady state, and the pipe section is horizontal (so that body forces may be neglected). It may be assumed that β=1.05 for this system. (a) (14 points) Calculate the absolute pressure (in Pa) at section 2. For the purposes of this
calculation, it may be assumed that the straight pipe losses in the pipe are negligible. Fitting losses, however, must be taken into account. The loss factor chart was provided for question 4.
(b) (16 points) Determine the magnitude (in Newtons) and direction of the force exerted on the
pipe section by the flowing oil
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Constants Gravity 9.81 m/s2 Density of Water 1000 kg/m3 Viscosity of Water 0.001 Pas Atmospheric Pressure 1.015 x 105 Pa
Common Unit Conversions
Density
1 lb/ft3 16.02 kg/m3
Force 1 lbf 4.448 N 1 dyn 1 x 10-5 N
Length 1 foot 0.3048 m 1 inch 0.0254 m
Mass 1 pound (lbm) 0.04536 kg 1 ton (2000 lb) 907.0 kg
Pressure 1 atmosphere 1.015 x 105 Pa 1 mm H2O 9.806 Pa 1 mm Hg 133.3 Pa 1 psi 6895 Pa