Fluid Mechanics 1 | My Assignment Tutor

CC9100 Semester 1, 2015 Page 1 of 10Time Allowed: 2 Hours + 10 minutes reading timeThis examination paper consists of 10 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: …………………………………..AMME2261 / AMME9261Fluid Mechanics 1Final ExaminationSemester 1, 2015CC9100 Semester 1, 2015 Page 2 of 10Part A: Multiple Choice QuestionsAnswer all Part A questions on the multiple choice answer sheet provided.A sixteen (16) page booklet has been provided for your rough working for Part A.It must be submitted but it will not be marked.Full marks for a correct answer. No marks for an incorrect answer.Question 1 [7 marks]A triangular vertical gate is fitted to control fresh water flow in an open irrigationchannel as shown in Figure 1.1. Since the gate is closed the water is not flowing and theforce on the gate is due to hydrostatic pressure only. The water level is to the top of thegate as shown.Figure 1.1: Triangular gate in an irrigation channel.Which of the following answers is closest to the magnitude of the resultant horizontalforce, FR, acting on the gate?A) 134.1 kN B) 44.1 kN C) 7.67 kN D) 36.9 kNQuestion 2 [7 marks]The velocity of a two dimensional flow can be represented mathematically asV u i j  = + vwhere iand jare unit vectors in the x and y directions of a Cartesian space,respectively. A certain flow has an x-direction velocity given byu =+.Which ONE of the following answers represents a valid y-direction velocity in a twodimensional, steady-state, incompressible flow?A)v = 0 3xy 2 4x + 5y B) v = -3×2 + 7C) v = 7×2 – y(y 2 + 4)+ 1D)yy y1v = – 3 – 4 +CC9100 Semester 1, 2015 Page 3 of 10Question 3 [7 marks]Model tests are conducted during the design phase of a new autonomous submarine.The model tests are performed on a 1/5th scale model in an atmospheric pressure windtunnel with the aim of determining the drag force. The prototype is designed to operatewell below the ocean surface so that wave making drag is negligibly small. Which ofthe following answers is closest to the wind tunnel speed required to achieve dynamicsimilarity with the prototype operating in sea water at 2 knots? You may assume thatboth the air and sea water are at 200C.Note that 1 knot = 1.852 km/h.A) 145 knots B) 115 knots C) 215 knots D) 175 knotsQuestion 4 [7 marks]Figure 4.1 shows streamlines for an ideal, steady, incompressible, frictionless flow ofair over a cylinder of radius R. In the figure U = 11 m/s is the free stream velocity farupstream and downstream of the cylinder where the gauge pressure is 0 kPa. The radialand angular coordinates are r and θ , respectively. The air is at 200C.Figure 4.1: Frictionless flow over a cylinder.Which ONE of the following statements about the magnitude and location of themaximum gauge pressure is TRUE?A) Pmax = 24.5 Pa, r = R, θ = 00B) Pmax = -24.5 Pa, r = R, θ = 900C) Pmax = -72.6 Pa, r = R, θ = 900D) Pmax = 72.6 Pa, r = R, θ = 00rθUCC9100 Semester 1, 2015 Page 4 of 10Question 5 [7 marks]A barge has a uniform rectangular cross section of width 2L and vertical draft of heightH as shown in Figure 5.1. The centre of gravity, G, is at the waterline height.Figure 5.1: Schematic of a floating rectangular hull.If L = 2.5m and H = 1.85 m which ONE of the following statements about themetacentric height (GM ����) and the barge’s stability is TRUE?A) GM ���� = 0.20m, unstableB) GM ���� = 0.20m, stableC) GM ���� = -0.20m, unstableD) GM ���� = -0.20m, stableQuestion 6 [7 marks]A centrifugal pump is used to pump fresh water at a power station. The pump isconfigured as shown in Figure 6.1, with r1 = 100mm, r2 = 300mm and b = 50mm. Theangle of the impeller blades at the inlet and outlet are β1 = 550 and β1 = 350, respectively.The inlet is designed so that there is no swirl.Figure 6.1: Centrifugal pump configuration.When operating at a speed of ω = 1500rpm the pump delivers a volume flow rate of0.7m3/s. Which of the following answers is closest to the ideal (i.e. frictionless) torquethat is required to drive the pump under these conditions?A) 4324 Nm B) 9715 Nm C) 6542 Nm D) 7653 Nmωβ1β2r1r2b rr1 2 CC9100 Semester 1, 2015 Page 5 of 10Question 7 [7 marks]A volcanic plume puts ash into the atmosphere to an altitude of 7000m. Thecharacteristic ash particle is a sphere with a diameter of 70 µm and a density of 850kg/m3. Which of the following answers is closest to the length of time it takes for aparticle to settle to the ground?You may use the following assumptions:– Each ash particle is isolated from other particles.– An ash particle falls vertically downwards at a constant speed equal to itsterminal velocity.– The density and kinematic viscosity of the air are independent of altitude and aregiven by ρ = 0.75 kg/m3 and ν = 1.5 x 10-5 m2/s.– The drag coefficient may be obtained from Stokes’ relation, CD = 24/Re.A) 9.6 hours B) 8.9 hours C) 10.2 hours D) 15.4 hoursQuestion 8 [7 marks]Sea water flows through a pipe that is inclined at 30 to the horizontal as shown in Figure8.1. The pipe has a diameter of 0.1m. The flow Reynolds number is 1600. The pressuredifference is measured between two points, A and B, which are separated by a distanceof 300m.Figure 8.1: Inclined pipe carrying sea water.Which of the following answers is closest to the magnitude of that pressure difference?(Hint: the pressure difference results from the height difference between the two pointsand pressure loss to the walls due to friction).A) 17 Pa B) 157875 Pa C) 157858 Pa D) 132878 PaA 30300 m BCC9100 Semester 1, 2015 Page 6 of 10Part 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]A typical jet engine test stand is shown in Figure 9.1, together with some test data. Fuelenters the top of the engine vertically at a rate of 2% of the mass flow rate of the inletair. The engine is tested in a laboratory that is at standard atmospheric pressure andtemperature (i.e. P = 101.3 kPa and T = 298 K).Figure 9.1: Jet engine on a test stand in a laboratory.a) Sketch a fully labelled control volume of the flow. Clearly label the control volume(CV), control surface (CS), external forces including pressure forces, and fluidfluxes across the CS. (4 marks)b) Calculate the mass flow rate of air through the engine. You may assume that air isan ideal gas with a gas constant of R = 287 J/kgK. (6 marks)c) Using the principle of conservation of linear momentum, calculate the horizontalengine thrust. You may assume that the flows across the engine inlet and outlet areuniform. (12 marks)(gauge) (gauge)CC9100 Semester 1, 2015 Page 7 of 10Question 10 [22 marks]An engineering company has been hired to optimise the design of a particular brand ofgolf balls. To increase the flight length the drag force should be minimised. It is knownthat the drag force, FD, is dependent on the diameter, D, dimple size, d, the speed ofrotation, ω, velocity, V, air density, ρ, and air viscosity, µ. The dimensional form of thefunctional relationship can be expressed asFD = f (D, d,ω,V , ρ, µ)a) Find a non-dimensional form of this functional relationship which would be usefulfor conducting experiments. (10 marks)You may apply the Buckingham Pi Theorem using the following recipe.1. List the set of n dimensional parameters involved.2. List the set of m primary dimensions .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.b) Tests are conducted on a model golf ball in a wind tunnel. The model golf ball hasa diameter that is twice that of the prototype diameter. Determine the model airspeed and model speed of rotation that are required for dynamic similarity to aprototype golf ball moving at 30 m/s and rotating at 300 revolutions per minute(rpm). You may assume that the density and viscosity of the model air are the sameas those of the prototype air. (5 marks)c) At the model test conditions described in part b), the engineers observed that theminimum drag occurs when the dimple depth is 3% of the model diameter. If theprototype golf ball has a diameter of 42 mm, what is the prototype dimple depth?(2 marks)d) For the model test conditions described in parts b) and c) the minimum drag forceon the model golf ball is 2 N. What is the equivalent drag force on the prototypeball? (5 marks)CC9100 Semester 1, 2015 Page 8 of 10Additional 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/m2Sea water at 200C density, ρ = 1025 kg/m3 dynamic viscosity, µ = 1.07 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):  + ⋅ = 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 µ.RTPρ =CC9100 Semester 1, 2015 Page 9 of 10Centre of pressureParallel axis theoremMoments of area (Note: 2nd moments are taken about the centroid of area)Stability analysisMetacentric height:Common non-dimensional numbersReynolds number:Froude number: VgLFr =Weber number:Lift and drag coefficients:μρVLRe =σρV2 LWe =V AFCV AFCL L D D212212ρ ρ= =RxxcFg Iy′ = y + ρ sinθ ˆˆ2I xx = I xˆxˆ + AycBGVIGMsubmerged= –0CC9100 Semester 1, 2015 Page 10 of 10Turbomachinery 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)Laminar pipe flow relationsPressure loss due to wall friction: 8 constant= – 4 Q =dPµdxRπ

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