Engineering fluid mechanics soluton manual

Download free eBooks at bookboon.comEngineering Fluid Mechanics Solution Manual 6 Chapter One Tutorial Problems 1 Chapter One Tutorial Problems 1.1 Show that the kinematic viscosity has

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Download free eBooks at bookboon.com

2

Prof T.T Al-Shemmeri

Engineering Fluid Mechanics Solution Manual

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Engineering Fluid Mechanics Solution Manual

ISBN 978-87-403-0263-9

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Engineering Fluid Mechanics Solution Manual Book Description

Book Description:

Title – Engineering Fluid Mechanics Solution Manual

Author – Prof T.T Al-Shemmeri

Fluid Mechanics is an essential subject in the study of the behaviour of luids at rest and when in motion

he book is complimentary follow up for the book “Engineering Fluid Mechanics” also published on BOOKBOON, presenting the solutions to tutorial problems, to help students the option to see if they got the correct answers, and if not, where they went wrong, and change it to get the correct answers

Author Details:

Prof Tarik Al-Shemmeri – BSc, MSc, PhD, CEng

Professor of Renewable Energy Technology at Stafordshire University

Current research interests in Renewable Energy and Environmental Technology

Lecturing topics include: Energy management and Power generation

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6

Chapter One Tutorial Problems

1 Chapter One Tutorial Problems

1.1 Show that the kinematic viscosity has the primary dimensions of L2T-1

Solution:

he kinematic viscosity is deined as the ratio of the dynamic viscosity by the density of the luid

he density has units of mass (kg) divided by volume (m3); whereas the dynamic viscosity has the units

of mass (kg) per meter (m) per time (s)

Hence:

3 4 5

3 3

/ /

1.2 In a luid the velocity measured at a distance of 75mm from the boundary is 1.125m/s he luid

has absolute viscosity 0.048 Pa s and relative density 0.913 What is the velocity gradient and shear stress at the boundary assuming a linear velocity distribution? Determine its kinematic viscosity

[Ans: 15 s-1, 0.72Pa.s; 5.257x10-5 m2/s]

Solution:

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Engineering Fluid Mechanics Solution Manual Chapter One Tutorial Problems

u f{

fX Itcfkgpv

0

297 2

1.3 A dead-weight tester is used to calibrate a pressure transducer by the use of known weights

placed on a piston hence pressurizing the hydraulic oil contained If the diameter of the piston

is 10 mm, determine the required weight to create a pressure of 2 bars

[Ans: 1.6 kg]

Solution:

4 7 4

4 2232 9:76 326

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8

1.4 How deep can a diver descend in ocean water without damaging his watch, which will withstand

an absolute pressure of 5.5 bar?

Take the density of ocean water, r = 1025 kg/m3

[Ans: 44.75 m]

Solution:

Use the static equation: r"?"t"i"j"

Hence the depth can be calculated as:

Ycvgt o z

z i

R

:3 0

; 3247

32 + 3 7 0 7

* 0

=

−

2 2

2

1 1

D

d z

g P

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4 4

+ 6 1

*

+ 6 1

*

F

f z

| zF

zf z

|

r r

For the “U” tube manometer that the height diferent in the two columns gives the pressure diference, therefore:

0 0 0

hence

+ 0*

* ]

3 R i |

R / ? t 0 0

1.6 A lat circular plate, 1.25 m diameter is immersed in sewage water (density 1200 kg/m3) such

that its greatest and least depths are 1.50 m and 0.60 m respectively Determine the force exerted

on one face by the water pressure,

[Ans: 15180 N]

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1.7 A rectangular block of wood, loats with one face horizontal in a luid (RD = 0.9) he wood’s

density is 750 kg/m3 Determine the percentage of the wood, which is not submerged

For stable condition

Upthrust = weight force or

F = W

he Upthrust due to Buoyancy = rseawater g Vx

he total weight of submersed wood = rwood g VL

herefore the portion of block that is NOT submerged is

1- Vx/VL = (rwood / rwater ) = 1 - 750 / 900 = 17%

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12

1.8 An empty balloon and its equipment weight 50 kg, is inlated to a diameter of 6m, with a gas

of density 0.6 kg/m3 What is the maximum weight of cargo that can be lited on this balloon,

if air density is assumed constant at 1.2 kg/m3?

[Ans: 17.86 kg]

Solution:

H"

Y"

Since the system is stable according to Newton’s second law of motion:

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Engineering Fluid Mechanics Solution Manual Chapter Two Tutorial Problems

2 Chapter Two Tutorial Problems

2.1 A 20 mm dam pipe forks, one branch being 10 mm in diameter and the other 15 mm in diameter

If the velocity in the 10 mm pipe is 0.3 m/s and that in the 15 mm pipe is 0.6 m/s, calculate the rate of low in cm3/s and velocity in m/s in the 20 mm diameter pipe

(129.6 cm3/s, 0.413 m/s)

Solution:

Total mass low into the junction = Total mass low out of the junction

ρ1Q1 = ρ2Q2 + ρ3Q3 When the low is incompressible (e.g if it is water) ρ1 = ρ2 = ρ

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14

Chapter Two Tutorial Problems

2.2 Water at 36 m above sea level has a velocity of 18 m/s and a pressure of 350 kN/m2 Determine

the potential, kinetic and pressure energy of the water in metres of head Also determine the total head

Ans (35.68 m, 16.5 m, 36 m, 88.2 m)

Solution:

Take each term separately

o z

z i

:3 0

; 3222

4i

X4

:3 0

; 4

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2.3 he air supply to an engine on a test bed passes down a 180 mm diameter pipe itted with an

oriice plate 90 mm diameter he pressure drop across the oriice is 80 mm of parain he coeicient of discharge of the oriice is 0.62 and the densities of air and parain are 1.2 kg/m3

and 830 kg/m3 respectively Calculate the mass low rate of air to the engine

*]

+

*

4 3 4

3

4

C C

r r x

;2

*3]403

60873

4

6 ?/

?

(iii) m = Cd V2 A2 x r

4 5 4

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16

2.4 Determine the pressure loss in a 100 m long, 10 mm diameter smooth pipe if the low velocity

is 1 m/s for:

a) air whose density 1.0 kg/m3 and dynamic viscosity 1 x 10-5 Ns/m2

b) water whose density 10003 kg/m3 and dynamic viscosity 1 x 10-3 Ns/m2

L xfx

hf

2 4

; 2 0 3 0 0

8 0 54 84 0 3;

3 23 0 2

322 238 0 2 6

o P z

z j

i R

o z

z z j

L xfx

hf

2 4

379;63 3

0 38 :3 0

; 3222 0

0

3 0 38 84 0 3;

3 23 0 2

322 229;

0 2 6

o mP z

z j

i R

o z

z z

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2.5 Determine the input power to an electric motor (hm = 90%) supplying a pump (hp = 90%)

delivering 50 l/s of water (r = 1000 kg/m3, m = 0.001 kg/ms) between two tanks with a diference

in elevation of 50m if the pipeline length is 100m long in total of 150 mm diameter, assume a friction factor of 0.008 and neglect minor losses

z z

z i

x F

N h

:3

;4

:5437

2

32222:

264

00

S i R

r o

;2

92:

7:

272:3

;3222

00

0

00

?

j j

t

"

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18

2.6 A jet of water strikes a stationary lat plate “perpendicularly”, if the jet diameter is 7.5 cm and

its velocity upon impact is 30 m/s, determine the magnitude and direction of the resultant force

on the plate, neglect frictional efect and take water density as 1000 kg.m3

Ans (3970 N)

Solution:

o z z

Hz ? 3222 6 0 63: 32/ 5 524 * 3 / 2 +

P

Hz 5;98 ?

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2.7 A horizontally laid pipe carrying water has a sudden contraction in diameter from 0.4m to 0.2m

respectively he pressure across the reducer reads 300 kPa and 200 kPa respectively when the low rate is 0.5 m3/s Determine the force exerted on the section due to the low, assuming that friction losses are negligible

Ans: (25.5 kN)

Solution:

o z

C

o z

C

00

25362426

34782626

4 4

4

4 4

u

o z

C

S x

u

o z

0

1

000

;37

37426

72

;9;

5626

72

4 4

4

4 3

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20

2.8 A siphon has a uniform circular bore of 75 mm diameter and consists of a bent pipe with its crest

1.8 m above water level and a discharge to the atmosphere at a level 3.6 m below water level Find the velocity of low, the discharge and the absolute pressure at crest level if the atmospheric pressure is 98.1 kN/m2 Neglect losses due to friction

Ans (0.0371 m3/s, 45.1 kN/m2)

Solution:

5

4 5 5 3

4 3 3

4

x i

r

| i

x i

-t t

u o z

z X

jgpeg

i x

1 0

0 0

0

5

4 5

626 : 8 5 :3

; 4

2 4 2 8 5 2

-? - -

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Engineering Fluid Mechanics Solution Manual Chapter Three Tutorial Problems

3 Chapter Three Tutorial Problems

3.1 If the vertical component of the landing velocity of a parachute is equal to that acquired

during a free fall of 2m, ind the diameter of the open parachute (hollow hemisphere) if the total weight of parachute and the person is 950N Assume for air at ambient conditions, Density = 1.2 kg/m3 and Cd = 1.35

Get in-depth feedback & advice from experts in your

topic area Find out what you can do to improve

the quality of your dissertation!

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22

Chapter Three Tutorial Problems

zE C X i

o

H

PUN

u o z

z X

cu X

X

f

4 3 2

486 8 4 :3

; 4 4

4

4 3

4

0 0 0

<

1 0

0

? /

6 486 8 4 3 4

3

;72 / 0 0 40* r + 4 0 ?

o F

uqnxg › ? 80 39

3.2 A buoy is attached to a weight resting on the seabed; the buoy is spherical with radius of 0.2m

and the density of sea water is 1020 kg/m3 Determine the minimum weight required to keep the buoy aloat just above the water surface Assume the buoy and the chain has a combined weight of 1.2 kg

Ans (33 kg)

Solution:

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Since the system is stable and motionless, Newton’s second law of motion reduces to:

Weight = Upthrust (Buoyancy)

Fb = Fg

Volume of sphere = (4.pi/3) x R3 = 0.0335 m3

he Upthrust is FB = rluid x VL x g =1020 x 0.0335x9.81= 335.3 N

Hence the payload = (335.3 / 9.81) – 1.2 = 32.98 kg

3.3 An aeroplane weighing 65 kN, has a wing area of 27.5 m2 and a drag coeicient (based on wing

area) CD=0.02+0.061 xCL2 Assume for air at ambient conditions, Density = 0.96 kg/m3 Determine the following when the crat is cruising at 700 km/h:

1 the lit coeicient

2 the drag coeicient, and

3 the power to propel the crat

Ans (0.13, 0.021, 2040 kW)

Solution:

zX z

z

z X

+1

*00+1

zX z

z

z z

zE

749

;8243

3287283

2242283

2242

4 4

5 4

ÙÚ

ÈÉ

Ç-

?-

?

00

+1

*0

00

0

hence

zX z z

z zX z

zE C X

4

34

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24

Chapter Three Tutorial Problems

Power

u o

z j

mo X

X z X

zX H

6663;65822

3222922922

32

;743486

1

00

hence

z E

z z E

F

N

24323522832242

3526663;632

9;

36

4

6 7

?-

?

00

0+0

*0

mY z

z

3.4 A racing car shown below is itted with an inverted NACA2415 aerofoil with lit to drag given

as: Cd=0.01 + 0.008 x Cl2

he aerofoil surface area is 1 m2 and the car weight is 1 kN; the car maintains a constant speed

of 40 m/s, determine at this speed:

1 he aerodynamic drag force on the aerofoil

2 he power required to overcome this drag force

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Assume for air at ambient conditions, take Density = 1.2 kg/m3

Ans (18 N, 0.7 kW)

Solution:

23:8:

22639322:

223222:

2232

263936234343

32

34

3

4 4

4

5 4

00

000

0

00

+1

*00+1

*

?-

E

z z z

z X

C

H E

N F

N

P z

z z z zE

C X

4

3 4

mY z

zX H Rqygt ? F ? 39 0 ; 62 ? 2 0 939

3.5 Air lows over a sharp edged lat plate, 3m long and 3m wide at a velocity of 2 m/s

1 Determine the drag force

2 Determine drag force if the plate was mounted perpendicular to the low direction assume

Cd = 1.4

For air, take density as 1.23 kg/m3, and kinematic viscosity as 1.46x10-5 m/s2

Ans (0.05N, 31N)

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z z

z zN

X

F

n

22429 2 54:

3

32 7 32 33 6 32 68 3

5 4

7

7 7

0 Tg

z z z z zE

X C

4

3 4

2

P z

z z z z zE

X C H

3

6 3

4 4

0 0 +

* 0 0

3.6 (a) An airplane wing has a 7.62m span and 2.13m chord Estimate the drag on the wing (two

sides) treating it as a lat plate and the light speed of 89.4 m/s to be turbulent from the leading edge onward

(b) Determine the reduction in power that can be saved if the boundary layer control device is installed on the wing to ensure laminar low over the entire wing’s surface

For air, take density as 1.01 kg/m3, and kinematic viscosity as 1.3x10-5 m/s2

Ans (358 N, 86%)

Solution:

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