1. AE-May-2015-04-BS-7

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04-BS-7 May 2015 Page 1 of 15

NATIONAL EXAMINATIONS

May 2015

04-BS-7 MECHANICS OF FLUIDS

Three (3) hours duration

-----------------------------------------------------------------------

Notes to Candidates

1. This is a Closed Book examination.

2. Exam consists of two Sections. Section A is Calculative (9 questions) andSection B is Analytical (4 questions).

3. Do seven (7) questions from Section A (Calculative) and three (3)questions from Section B (Analytical). Note that the Analytical Questionsdo not require detailed calculations but do require full explanations.

4. Ten (10) questions constitute a complete paper. (Total 50 marks).

5. All questions are of equal value. (Each 5 marks).

6. If doubt exists as to the interpretation of any question, the candidate is urgedto submit, with the answer paper, a clear statement of any assumptions made.

7. Candidates may use one of the approved Casio or Sharp calculators.

8. Reference information for particular questions is given on pages 7 to 10. Allpages of questions attempted are to be returned with the AnswerBooklet, showing diagrams generated or where readings were taken andwhich data was used. Candidates must write their names on thesepages.

9. Constants are given on page 11.

10. Reference Equations are given on pages 12 to 15.

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SECTION A CALCULATIVE QUESTIONS

Do seven of nine questions. So/ufions to These questions must be set outlogically with all intermediate answers and units given.

QUESTION 1

Refer to the adjoining illustration. Use thedifferential elevations in metres andcentimetres as given in the figure. Pipe Acontains benzene and pipe B contains carbon 40 cmtetrachloride while the U-tube containsmercury. Determine the pressure in pipe A ifthe pressure in pipe B is 200 kPa.

2.Refer to Constants on page 11 for specificgravities.

(5 marks )

3.

QUESTION 2

Refer to the adjoining sketch. For theconditions shown in the figure, find the force F 5required to lift the concrete-block gate if the ~~concrete density is 2400 kg/m3. The density of '~'—'sea water is 1025 kg/m3. All dimensions are in Ssa watermetres.

(5marks)2 diem

QUESTION 3

Refer to the Examination Paper Attachments Page 7 Jounama Dam.

This drawing shows an elevation and cross section of the spillway for the dam.Calculate the total horizontal force on the pivots of each radial gate when the dam isat its full supply level.

(5 marks )

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QUESTION 4

The diameters of the suction and dischargepipes of a pump are 150 mm and 100 mm,respectively. The discharge pressure is readby a gauge at a point 1.5 m above the centerline of the pump, and the suction pressure isread by a gauge 0.5 m below the center line.The pressure gauge reads a pressure of 150kPa and the suction gauge reads a vacuum of30 kPa (negative gauge pressure) whengasoline having a specific gravity of 0.75 ispumped at the rate of 0.035 m3/s. Calculatethe electrical power required to pump the fluid ifthe pump efficiency is 75%.

(5 marks

u2 100 mm..~—.

—j—T

1.5 m

~— ~0.5 m~~ ~ .._.~__ i _ ~

150 m m V~

QUESTION 5

A pitot-static tube is used for measuring the air flow in a duct. A differentialmanometer containing water is connected between the dynamic and staticmeasuring points of the pitot-static tube. If the reading on the manometer is 24 mm,determine the air velocity in the duct. If the same air velocity were measured using adifferential pressure gauge instead of a manometer, determine the differentialpressure reading on the gauge in kPa.

(5 marks )

QUESTION 6

A wind turbine is operating in a wind of 10 m/sthat has a density of 1.2 kg/m3. The diameterof the windmill is 4 m. The constant pressure(atmospheric) streamline passing the turbineblade tip has a diameter of 3 m upstream of thewind turbine and 4.5 downstream. Assume thatthe velocity distributions are uniform and the airis incompressible. Determine the thrust due tothe wind on the wind turbine.

~~~~►~~~~~~~.~►~

(5 marks

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04-BS-7 May 2015 Page 4 of 15

QUESTION 7

Refer to the Examination Paper Attachments Page 8 Moody Diagram.

A concrete water supply pipeline of 1 m diameter is laid over a distance of 10 km.The outlet of the pipe is 40 m lower than the inlet. Determine the flow rate in thepipe. Neglect entrance and exit losses. Assume an absolute roughness of 1 mm.

Show on the diagram where values have been plotted and read.

Hint: Guess velocities and plot corresponding friction factor versus Reynoldsnumber on Moody diagram for each chosen velocity.

(5marks)

QUESTION 8

Refer to the Examination Paper AttachmentsPage 9 Moody Diagram.

Determine the head loss in an annular duct oflength 5 m where the annulus has an outerdiameter of 25 mm and an inner diameter of 18mm and water flows within the annulus(between the inner and outer diameters) at arate of 0.5 litres/s. The duct is made of copperdrawn tubing.

Show on the diagram where values have been plotted and read.

(5 marks

QUESTION 9

Refer to the Examination Paper Attachments Page 10 Drag Coefficients ofCyclists.

The chart shows drag coefficients of cyclists in different configurations. Determinethe maximum speed in km/h that a regular cyclist should be able to maintain on astandard (no aerodynamic components) racing bicycle during a two hour cyclingrace. Neglect rolling resistance. Note that the drag force has to be calculated sincethat given in the table is only at a speed of 20 mph (8.9 m/s or 32 km/h) and will bedifferent for the speed to be calculated.

Human generated power can be determined from the following equation which givesaverage power in kW over a given period of time where t is in minutes.

P = 0.373 — 0.097 logo t for healthy young men

(5 marks

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04-BS-7 May 2015 Page 5 of 15

SECTION B GRAPHICAL AND ANALYTICAL QUESTIONS

Do three of four questions. These questions do not require detailedcalculations but complete written explanations must be given to support theanswers where descriptive answers are required.

QUESTION 10

Explain how pipe roughness (assuming surface roughness height E »laminarsublayer thickness S) affects the velocity profile in a pipe. Sketch typical velocityprofiles for pipes of different roughness assuming fully developed turbulent flow.Assume that the flow rate is the same in each case.

(5 marks )

QUESTION 11

... '.cs.

Axis Vertical Axis Horizontal

A cylindrical drum with a height equal to its diameter can either be stood on its end(axis vertical) or put on its side (axis horizontal) to drain water through a hole at itslowest point. Determine with explanations the following:

(a) The orientation in which the drum will drain more quickly.

(b) The reason why one orientation gives a shorter time to drain than the other.

(c) An alternative orientation which will give a shorter draining time than either ofthe given orientations.

(5 marks )

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04-BS-7 May 2015 Page 6 of 15

QUESTION 12

—+-

-~~--~_— ~i

FLAT PLATE CURVED PLATE

A flat plate and curved plate are subject to horizontal jets having the same flow rateand velocity. State which will be subject to the greater force when stationary andexplain why this would be the case. When moving in the same direction as the jetstate which plate will give the best transfer of energy (from jet to plate). Explain froman energy aspect the reason for you answer.

QUESTION 13

Consider a closed shower cubical, square in plan view,which is closed by drawing a curtain across the openside. When taking a hot shower with the curtain closedthe curtain tends to blow inwards. Explain why this isso and state the fundamental fluid mechanics principlesthat create this phenomenon. Hence suggest how onecould calculate the angle of the curtain 8 clarifying whatbasic parameters would be required.

(5marks)

(5marks)

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04-BS-7 May 2015 Page 11 of 15

04-BS-7 MECHANICS OF FLUIDS

GENERAL REFERENCE INFORMATION

CONSTANTS

In engineering calculations a high degree of accuracy is seldom attained due to theneglect of minor influences or the inaccuracy of available data. For consistency incalculations however the following reasonably accurate constants should be used:

Atmospheric Pressure po = 100 kPaGravitational Acceleration g = 9.81 m/s2Specific Gravity of Water = 1.00Specific Gravity of Glycerine = 1.26Specific Gravity of Mercury = 13.56Specific Gravity of Benzene = 0.90Specific Gravity of Carbon Tetrachloride = 1.59Density of Water p = 1000 kg/m3Density of Sea Water p = 1025 kg/m3Density of Concrete p = 2400 kg/m3Density of Air p = 1.19 kg/m3 (at 20°C), p = 1.21 kg/m3 (at 15°C)Absolute Viscosity of Water ,u = 1.0 x 10-3 Ns/m2Absolute Viscosity of Air ,u = 1.8 x 10"5 Ns/m2Surface Tension of Water Q = 0.0728 N/m (at 20°C)Specific Heat of Water cP = 4.19 kJ/kg°CSpecific Heat of Air cP = 1005 J/kg°CSpecific Heat of Air cP = 718 J/kg°CGas Constant for Air R = 287 JJkg°KGas Constant for Helium R = 2077 J/kg°KGas Constant for Hydrogen R = 4120 J/kg°K

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04-BS-7 May 2015 Page 12 of 15

NOMENCLATURE FOR REFERENCE EQUATIONS (SI UNITS)

a Width mA Flow area, Surface area m2CV Calorific value J/kgcp Specific heat at constant pressure J/kg°Cb Width mD Diameter mE Energy JF Force Ng Gravitational acceleration m/s2h System head mh~ Head loss mH Pump or turbine head m

Moment of inertia m4k Ratio of specific heatsk Loss coefficientK ConstantL Length mm Mass kgM Mass flow rate kg/sN Rotational speed rev/sp Pressure Pa (N/m2)P Power W (J/s)q Specific heat J/kgQ Flow rate m3/sr Radius mR Specific gas constant J/kg KT Temperature KU Blade velocity m/sv Specific volume m3/kgV Velocity m/sV Volume m3w Specific work J/kgW Work Jy Depth mz Elevation mn Efficiency~ Dynamic viscosity Ns/m2v Kinematic viscosity m2/sp Density kg/m36 Surface tension N/mt Thrust Nr Shear stress N/m2

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04-BS-7 May 2015 Page 13 of 15

REFERENCE EQUATIONS

Equation of State

pv=RTp=pRT

Universal Gas Law

p v~ =constant

Compressibility

R = -oivopViscous Force and Viscosity

F = µ A du/dyµ = ti / (du/dy)v= µ/p

Capillary Rise and Internal Pressure due to Surface Tension

h = (6 cos 8 / p g) x (perimeter /area)p = 26/r

Pressure at a Point

P=P9h

Forces on Plane Areas and Centre of Pressure

F = A9Y~AYP = Y~+ ~~~Y~A

Moments of Inertia

Rectangle: I~ = b h3 / 12Triangle: I~ = b h3 / 36Circle: I~ = n D4 / 64

Surface Area of Solids

Sphere: A = n D2

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Volumes of Solids

Sphere: V = n D3 / 6Cone: V = n D2 h / 12Spherical Segment: V = (3 a2 + 3 b2 + 4 h2) n h / 2 g

Continuity Equation

p, V, A, = p2 V2 A2 = M

General Energy Equation

p~~P~9+z~+VIZ / 2 g+gin~9i"N/in~9= p2/peg+z2+V22 / 2 g+h~+go~c~9+Wa~c~9

Bernoulli Equation

p~~PJ+z~+V~2 / 2 9=p2~P9+z2+V22 / 2 g

Momentum Equation

Conduit: FR = p~ A - p2 A - M (V2 - V~)Free Jet: FR = - p Q (V2 - V~)

Flow Measurement

Venturi Tube: Q = [C A2 / {1 - (D2 / D~)4}~~2][2 g Oh]~~2Flow Nozzle: Q = K A2 [2 g oh]'~2Orifice Meter: Q = K Ao [2 g Oh]'~2

Flow over Weirs

Rectangular Weir: Q = Cd (2 / 3) [2 g]'~2 L H3~2

Power

Turbomachine: P= p g Q HFree Jet: P = '/2 p Q V2Moving Blades: P = M DV U

Aircraft Propulsion

Fthrust — M ~Vjet ' Vaircraft~

Pthrust — M ~Vjet - Vaircraft~ Vaircraft

Ejet = '~z ~Ujet2 ' Vaircraft2~1 2 2

Pjet = ~ M (Vjet - Vaircraft

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04-BS-7 May 2015 Page 15 of 15

Efuel = CVfuel

Pfuel = Mfuel C~fuel

~thermai = Pjet ~ Pfuel

~lpropulsion — Pthrust ~ Pjet — 2 Vaircraft ~ ~Ujet + Vaircraft~

coverall — thermal X propulsion

Wind Power

F'tota~ _ '~ p Ar V~ 3Pmax = 8/27 p AT V~ 3

HmaX = F'maX ~ Ptota~ = 16/27

Reynolds Number

Re=dVp/µ

Flow in Pipes

h~ = f(L/D)(V2 / 2 g)De = 4 (flow area) / (wetted perimeter)D = De for non-circular pipesL = Ltota~ -F- Le for non-linear pipes(L / D) = 35 k for Re ~ 104

Drag on Immersed Bodies

Friction Drag: Ff = Cf '/2 p V2 B L (B = ~c D)Pressure Drag: Fp = CP '/2 p V2 ATotal Drag: Fo = Co '/2 p V2 A

Aircraft Wing: F~ = C~'/z p V2 AWin9Aircraft Wing: Fo = Co'/2 p V2 Aw;,,9

Karmen Vortex Frequency

f ~ 0.20 (V / D) (1 - 20 / Re)