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The University for businessand the professions

Degree TitleBEng (Hons)/ MEng (Hons) in Mechanical EngineeringBEng (Hons) / MEng (Hons) in Aeronautic EngineeringBEng (Hons) / MEng (Hons) in Automotive Engineering

BEng (Hons) / MEng (Hons) in Air Transport EngineeringBEng (Hons) / MEng (Hons) in Energy Engineering

Module Code Exam TitleME2109 Fluid Mechanics

Part 2 Examination

Date Time?? May 2011 ?? (2.5 hours)

Division of Marks: All questions carry equal marksInstructions to students: Answer any THREEfrom FIVEquestions

Number of answer books to be provided: 1 with Graph paper

Whether or not calculators etc are permitted:Yes, Casio FX83/85 MS/ES.Whether or not dictionaries etc are permitted: No.Any stats tables or other additional materials: Data Sheet attached.Whether or not the exam paper can be removed from the exam room: No

External Examiner: Professor R Crookes

Internal Examiner: Dr J M NouriDr S Prince

School of Engineering and Mathematical Siences

Department Mechanical Engineering and Aeronuotics

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Question 1

(a) Water of density =1000kg/m3 and kinematic viscosity =1x10-6m2/s, is pumpedup at 0.212x10-4m3/s through an inclined pipe. Assuming that the flow is steady, thevelocity profile for the fully developed laminar flow is given by

2

2

4

)(

4

1r

d

dz

ghpdu

where d(p-gh)/dzis the Pizometric pressure gradient in the direction of the flow (i.e.z), r is the radial distance from the pipe centre, z is the distance along the pipe

centreline, gis the acceleration due to gravity, is the dynamic viscosity of water andd is the pipe diameter. Using the above equation and considering the flow ratethrough a cylindrical fluid element show that:

(i) The mean flow rate may be expressed

dz

ghpddQ

)(

128

4

[5 marks]

(ii) the mean flow velocity of the fluid is half the maximum velocity.[4 marks]

(iii) the wall shear stress may be expressed

dz

ghpddw

)(

4

[3 marks]

(iv) when the local velocity is the same as the mean velocity, the radial positionis given by r=0.354d.

[3 marks]

(b) If the pipe diameter is 15 mm and its length is 65 m, verify that the flow is laminarby neglecting end effect.

[2 marks]Also calculate:

(i) the friction factor,f.[1 marks]

(ii) the total head loss using the Darcy equation.

[2 marks]

(iii) the average wall shear stress.[2 marks]

(iv) the Pizometric pressure difference over the given length of the pipe.[2 marks]

The Manning friction factor equation is

u

f w

2

8

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Question 2

(a) A three-reservoir arrangement, shown in Figure Q2, is set up with each reservoirconnected to a common junction J by three identical pipes. The elevations of thewater surfaces in reservoirs are 25, 20 and 6.5 m above an arbitrary datum level.With each pipe, the length, diameter and wall surface roughness is such that the

head losses (in meters) due to friction are equal to 22000Q12, 21000Q22, 20000Q32,for pipes 1, 2 and 3, respectively, where Qis the flow rate in m3/s. Determine:

(i) the hydraulic grade head HJat the common junction J. High accuracy is notrequired. A good estimate value derived from plotting a graph will beacceptable.

[12 marks](ii) Determine the flow rate in each pipe.

[3 marks]

Figure Q2

(b) Two water reservoirs A and B are joined with a long pipe of length L. Calculatethe percentage increase in the flow rate obtainable if, from two third of the pipe (awayfrom reservoir A), another pipe of the same diameter and roughness is added inparallel to it. Neglect all losses except friction and assume constant and equal friction

factor for all pipes and the same head, h, inboth cases.[10 marks]

Elevation 25m

20m

6.5m

Pipe 1, Q1

Pipe 2, Q2

Pipe 3, Q3

J

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Question 3

(a) Describe briefly the boundary layer , BL, development over a flat plate, with help

of a schematic diagram. Define the boundary layer thickness, , and the Reynoldsnumber and give the transitional Reynolds numbers for both rough and smoothsurfaces.

[6 marks]

(b) Use the momentum thickness concept to show that the drag coefficient at the

back end of a plate can be expressed as CD= 2/cper wetted side where is themomentum thicknessand cis the chord length of the plate.

[3 marks]

(c) A glider with a smooth wing of 33 m long and a chord length, c, of 3.5 m flies at 49m/s. If the air density and kinematic viscosity are 1.21 kg/m3and 1.45x10-5m2/s:

(i) calculate the position, from the leading edge of the glider, of laminar toturbulent flow transition.[3 marks]

(ii) calculate the total drag force, assuming the boundary layers are whollyturbulent and the momentum thickness is given by

Re

036.0

2.0

c

c

x

[4 marks]

(iii) calculate the power dissipated.[2 marks]

(d) A 1-m2fishing net consists of cylindrical threads arranged on a square mesh of 20mm spacing. The threads has diameter 1 mm and its density is 2600 kg/m 3.Calculate the terminal velocity of the net as it settles vertically down in seawater ofdensity 1030 kg/m3. Take the drag coefficient as CD=1.1.

[7 marks]

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Question 4

(a) State the main differences between the positive displacements pumps (PDP) anddynamic pumps.

[4 marks](b) Show, with the help of a schematic diagram, that the kinetic energy available at

the exit of a nozzle jet for impulse turbine is avj

HCg

VKE 2

2

2 , where Cvis the velocity

coefficient, Hais total available head and Vjis the jet velocity.

[6 marks]

(c) A small impulse wheel turbine is to be used to drive a generator at speed of 890rpm. The total head available is 120 m which provides a discharge of 45 l/s. If theturbine efficiency is 79%, the velocity coefficient is Cv=0.96 and the velocity ratio of

wheel to jet is =0.48, determine:

(i) the power developed[2 marks]

(ii) the speed of the wheel[2 marks]

(iii) the diameter of the wheel[1 marks]

(iv) the jet diameter.[2 marks]

Note that the velocity ratio is =U/ Vj

(d) The net positive suction head, NPSH of a pump is 4.1 m. The pump is fixedabove a supply tank with a suction head of 3.7m and delivering a flow rate of 0.0262m3/s. The suction pipe is 8.9 m long with a friction factor f=0.035 and negligible pipe

secondary losses. If the atmospheric, pa, and water vapour,pv, pressures are 101.3

kPa and 3.14 kPa, respectively:

(i) express the Dracy equation in terms of flow rate, Q.[1 marks]

(ii) determine the minimum diameter of the suction pipe to avoid cavitation[7 marks]

NPSH is expressed as

hhg

p

g

pNPSH fs

va

where hf is the head loss in the pipe and hs is the

suction head.

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Question 5

An aircraft is in steady level flight at an altitude where the pressure relative to sea

level is 0.5052 and the ambient temperature is 260K. The pitot-static pressuredifference on the aircraft reads 13490 Pa.

(a) Determine the dynamic pressure.

[10 Marks]

(b) At a particular position on the wing the local pressure coefficient is0.7.

Determine the local Mach number at this location.

[4 Marks]

(c) Also, at the position on the wing at which the flow becomes locally sonic,determine:

(i) the static pressure,

[2 Marks]

(ii) the value of the pressure coefficient

[2 Marks]

(iii) the local airspeed.

[7 Marks]