CC0047 Semester 2, 2014 Page 1 of 9Time Allowed: 1.5 Hours + 10 minutes reading timeThis examination paper consists of 9 pagesINSTRUCTIONS TO CANDIDATES1. This exam paper must not be removed from the exam room2. Answer all questions.3. Questions are not of equal value.4. Non-programmable, University approved calculators and drawing instruments arepermitted.5. This is a closed-book exam.6. Some additional useful information is attached to this question paper.7. The exam will be marked out of a total of 100 marks.ConfidentialSEAT NUMBER: ………………………………………STUDENT ID: ………………………………………….SURNAME: …………………………………………….GIVEN NAMES: …………………………………..AMME2200/5200Thermodynamics and FluidsFinal Examination: Paper 2 – Fluid MechanicsSemester 2, 2015CC0047 Semester 2, 2014 Page 2 of 9Part A: Multiple ChoiceAnswer all Part A questions on the multiple choice answer sheet provided.An sixteen (16) page booklet has been provided for your rough working for Part A.It must be submitted but will not be marked.Full marks for a correct answer. No marks for an incorrect answer.Question 1 [7 marks]A supply crate with a mass of 250kg is to be dropped into a remote location from anaeroplane. To slow the descent of the crate a low porosity parachute is deployed asshown in Figure 3.1. The parachute has a drag coefficient CD = 1.2. To ensure theintegrity of the delivered goods, the maximum allowable (i.e. terminal) velocity of thecrate is 7m/s. Which of the following answers is closest to the required minimumdiameter of the parachute?Hint: You may assume that the drag force on the crate is insignificant compared to theparachute drag. Use an air density at 200C and standard pressure.Figure 3.1: A supply crate attached to a parachute.A) 7.2 m B) 9.4 m C) 11.2 m D) 2.3 mlow porosity parachutecrate, m = 250kgdiameter, DCC0047 Semester 2, 2014 Page 3 of 9Question 2 [7 marks]The velocity of a two dimensional flow can be represented mathematically asV u i j = + vwhere iand jare unit vectors in the x and y directions of a Cartesian space,respectively. A certain flow has an x-direction velocity given byyxu = 7y3 + 4 .Which ONE of the following answers represents a valid y-direction velocity in a twodimensional, steady-state, incompressible flow?A) v = 0B) yyx= +2 2v 2C) xyx= +2 2v 2D)yxv = -7 y3 – 4Question 3 [7 marks]Fresh water at 250C is supported above a submerged gate consisting of a steel platehinged to a vertical wall at location A and pressed against the ground at location B asshown in Figure 3.1 below. On the underside of the gate there is air at standardatmospheric pressure. The plate has a width (into the page) of 5 m. Which of thefollowing answers is closest to the resultant pressure force acting on the gate?Figure 3.1: A submerged gate supporting a volume of fresh water.A) 1267 kN B) 3024 kN C) 1970 kN D) 442 kN7 m4 mCC0047 Semester 2, 2014 Page 4 of 9Question 4 [7 marks]A new car design was tested at a reduced scale in a wind tunnel at 200C and standardatmospheric pressure. The model car was a 1/4th scale replica of the prototype. Ofparticular interest to the design engineers was the drag force at the freeway cruisingspeed. To investigate this design point they tested the model car at 100 m/s and foundthat the drag force on the model was 900 N. Which of the following answers is closestto the prototype cruise speed and drag force?A) 100 km/h, 1800 N B) 110 km/h, 1100 N C) 90 km/h, 1800 N D) 90 km/h, 900 NQuestion 5 [7 marks]A centrifugal pump for pumping fresh water is configured as shown in Figure 5.1. Thepump geometry is defined by r1 = 100mm, r2 = 300mm, b = 50mm. The angle ofimpeller blade at the inlet is β1. The inlet is designed so that there is no swirl in theincoming flow.Figure 5.1: Centrifugal pump configuration.During workshop testing the rotational speed, ω, of the pump is slowly increased andwhen ω = 1500rpm it is observed that the inlet flow is shockless. At that point thevolume flow rate of water is measured at 0.7m3/s. Which of the following answers isclosest to the angle β1?A) 450 B) 500 C) 550 D) 600ωβ1β2r1r2b rr1 2 CC0047 Semester 2, 2014 Page 5 of 9Question 6 [7 marks]Fresh water flows through a three-way pipe junction as shown in Figure 6.1. The inlet isdenoted as location 1, and the outlets as locations 2 and 3. The pipe diameters atlocations 1 and 2 are as indicated in the figure.Figure 6.1: A three-way pipe junction.At the inlet, the flow has a uniform velocity of 5 m/s. At each of the outlets there is afully developed laminar pipe flow having a parabolic velocity profile of the form= –2( ) max 1rRU r Uwhere r is the radial coordinate and Umax is the velocity at the centreline of the pipesection. If the centreline velocity at location 2 is 8 m/s, which of the following answersis closest to the mass flow rate at location 3?A) 3.2 kg/s B) 2.9 kg/s C) 4.1 kg/s D) 5.1 kg/sQuestion 7 [7 marks]A pitot tube connected to a mercury filled manometer is immersed in a flow of air closeto the Earth’s surface where the absolute pressure is 100 kPa. The stagnation gaugepressure recorded by the pitot tube is 23 mm Hg. Which of the following answers isclosest to the speed of the air flow?A) 2.2 m/s B) 71 m/s C) 34 m/s D) 88 m/sQuestion 8 [7 marks]Two flat, horizontal, squares plates of side length 5 m are separated by a 1mm thick filmof SAE-30 lubricating oil. A constant horizontal force of 22.5 kN is applied to the topplate while the bottom plate is fixed in place. Which of the following answers is closestto the steady-state speed of the top plate?A) 30 m/s B) 9 m/s C) 3 m/s D) 5 m/sU1 = 5 m/sU2 (r)U3D1 = 30 mm (r)D2 = 10 mmCC0047 Semester 2, 2014 Page 6 of 9Part B: Worked-Solution QuestionsAnswer both of the Part B questions in the eight (8) page answer booklet.Show full working for questions in this section.Clearly state any assumptions you decide to make.Solutions should be legible. Marks may be deducted for working which isunreadable or difficult to follow.Question 9 [22 marks]The flow of air around a symmetric wing is visualised, revealing the flow patternsketched in Figure 9.1. Upstream of the wing the flow has a uniform velocity ofmagnitude U. The wing deflects the flow so that at a short distance downstream of thewing, the velocity profile increases linearly from a minimum magnitude of U/2 at thecentreline to the freestream value, U, at a distance L above the centreline. The deflectionof a streamline is shown in the figure. Since the length of the wing into the page, b, ismuch larger than the chord length, c, the flow is two-dimensional. The pressuresupstream and downstream are equal.Figure 9.1: Flow visualisation near a wing.a) Sketch a fully labelled control volume of the flow. Clearly label the control volume(CV), control surface (CS), external forces and fluid fluxes across the CS. (4 marks)b) Using the principle of conservation of mass, derive an expression for H in terms ofL. (6 marks)c) Using the principle of conservation of linear momentum, derive and expression forthe drag force on the wing in terms of density, U, L and b. (12 marks) streamlineHLU/2c UU CC0047 Semester 2, 2014 Page 7 of 9Question 9 [22 marks]The drag force on the international space station orbiting around the Earth depends onthe mean free path between gas molecules λ (a length), the density ρ, the characteristiclength of the space station L, and the mean speed of gas molecules relative to the spacestation c. The dimensional form of the functional relationship can be expressed asFD = g(λ, ρ, L, c)Find a non-dimensional form of this functional relationship which would be useful forconducting experiments.To solve this problem you should apply the Buckingham Pi Theorem using thefollowing recipe.1. List the set of n dimensional parameters involved.2. List the set of m primary dimensions (e.g. M, L, t).3. List the dimensions of all dimensional parameters.4. Select m repeating variables.5. Combine the remaining n – m parameters in turn with those selected in step 4and make them into a non-dimensional group.CC0047 Semester 2, 2014 Page 8 of 9Additional Formulae and Useful InformationFluid properties and natural constantsAir at 200C and standard atmospheric pressure density, ρ = 1.2 kg/m3 dynamic viscosity, µ = 1.81 x 10-5 Ns/m2Fresh water at 200C density, ρ = 998 kg/m3 dynamic viscosity, µ = 1.01 x 10-3 Ns/m2SAE-30 Oil at 200C density, ρ = 917 kg/m3 dynamic viscosity, µ = 0.30 Ns/m2Mercury at 200C density, ρ = 13550 kg/m3 dynamic viscosity, µ = 1.56 x 10-3 Ns/m2Acceleration due to gravity, g = 9.81 m/s2Ideal Gas Equation of StateIntegral forms of the fundamental conservation equationsContinuity:Linear momentum:Angular momentum:Bernoulli equation:Differential forms of the fundamental conservation equations Continuity:∂+dρ ρ= 0∂ρρ Navier-Stokes equation (x –direction):Centre of pressure + ⋅ = 0 ∫ dV ∫ V dAdtdCV CS ρ ρV dV V V dAdtdFCV CS∑ ∫ + ∫ ⋅ = ρ ρconstant2 2+ + gz =P Vρ (r V ) dV (r V ) V dAdM∑ 0 = ∫ × ρ ∫ ρdtCVCS + ×⋅ ∂+∂∂+∂wzvyuxdt∂ ∂+∂ ∂+∂ ∂+∂ ∂ = – ∂ ∂+∂ ∂+∂ ∂+∂ ∂222222zuyuxuPxguzwuyvuxuutρ ρ x µRxxcFg Iy′ = y + ρ sinθ ˆˆ.RTPρ =CC0047 Semester 2, 2014 Page 9 of 9Parallel axis theoremMoments of area (Note: 2nd moments are taken about the centroid of area)Common non-dimensional numbersReynolds number:Froude number: VgLFr =Weber number:Lift and drag coefficients:Turbomachinery Radial flow machines: T Q r V rV = – ρ ( 2 2 1 1 t t )Axial flow machines: T Q r V rV = – ρ ( 2 2 1 1 t t )P Q u V u V = – ρ ( 2 2 1 1 t t )P Qu V V = – ρ ( t t 2 1) μρVLRe =σρV2 LWe =V AFCV AFCL L D D212212ρ ρ= =2I xx = I xˆxˆ + Ayc

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