Prof. T.T. Al-Shemmeri

Engineering Fluid Mechanics Solution
Manual

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Engineering Fluid Mechanics Solution Manual
© 2012 Prof. T.T. Al-Shemmeri & bookboon.com (Ventus Publishing ApS)
ISBN 978-87-403-0263-9

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Engineering Fluid Mechanics Solution Manual

Contents

Contents
Book Description:

5

Author Details:

5

1

Chapter One Tutorial Problems

6

2

Chapter Two Tutorial Problems

13

3

Chapter hree Tutorial Problems

21

4

Chapter Four Tutorial Problems

28

5

Chapter Five Tutorial Problems


31

Sample Examination Paper

33

Class Test – Fluid Mechanics

34

Formulae Sheet

44

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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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Engineering Fluid Mechanics Solution Manual

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:

w?

1.2

o ON /3V /3

?
? N4V /3
/5
t
ON

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

Itcfkgpv ?

v ?o

w?

1.3

Chapter One Tutorial Problems


fX 30347
?
? 37 u /3
f{ 20297

fX
? 2026: z37 ? 20942 Rc0u
f{

o 2026:
?
? 70479 z32 /7 o 4 1 u
;35
t

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:
(a)

P = F/A

C?

r
6


F4 ?

Hence the weight

r
6

z 20232 4 ? 90:76 z32 /7 o 4

=PxA/g
= 2 x 105 x7.854x10-5 / 9.81
= 1.60 kg

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Engineering Fluid Mechanics Solution Manual

1.4

Chapter One Tutorial Problems

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:

*707 / 3+ z32 7
R
?
? 66097o Ycvgt
j?
t 0i
3247 z;0:3
1.5

he U-tube manometer shown below, prove that the diference in pressure is given by:

  d 2 
P1 − P2 = r .g .z 2 1 +   
  D  

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Engineering Fluid Mechanics Solution Manual

Chapter One Tutorial Problems

Solution:
he relationship between liquid columns and the area of cross section is based on the conservation of

matter, ie continuity equation, hence:
volume 1 = volume 2

|3 zC3 ? |4 zC4
jgpeg › |3 ?

| 4 z*r 1 6+ zf 4
f
? |4 z* + 4
4
*r 1 6+ zF
F

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

H 3? H 4
R3 - t0i0|3 ? R4 - t0i0|4
hence

R3 / R4 ? t0i0* |4 / |3 +
? t0i0|4 z ]3 - *f 1 F +4 _
Clearly if D is very much larger than d then (d/D)2 is very small so

R3 / R4 ? t0i0|4
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]

307o"

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9

208o"

c"


Engineering Fluid Mechanics Solution Manual

Chapter One Tutorial Problems

Solution:
Area of laminar

C""""

3
?" r *3047+4"?"3044:"o4"
6

Depth to centroid

je""


3
?" *2082"-"3072+"?"3027"o"
4

Resultant Force
F

= r g A hc = 9.81 x 1200 x 1.228 x 1.05
= 15180 N

www.job.oticon.dk

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Engineering Fluid Mechanics Solution Manual

1.7

Chapter One Tutorial Problems

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.
[Ans: 17%]

Solution:


Ygkijv"
Y"

H"

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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Engineering Fluid Mechanics Solution Manual

1.8

Chapter One Tutorial Problems

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:

Y"
H"

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

= Weight force + Payload

he Upthrust is F

= r x g xVL = 1.2 x 9.81 x(px(4/3)x33) =1331.4 N

Weight of balloon gas

= r xVL = 0.6 x 9.81 x(px(4/3)x33) =666 N

Weight of equipment

= 50 kg = 50x9.81 = 490.5 N

herefore the payload that can be lited
P

=F-W
= 1331.4 – (666 + 490.5)
= 175 N = 17.9 kg.

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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
Q

= A2 V2 + A3 V3
= (p/4) D22x V2 + (p/4) D32x V3
= (p/4) 0.012x 0.3+ (p/4) 0.0152x 0.6
= 2.356x10-5 + 10.6x10-5
= 12.96 x10-5 m3/s

since


S ?" C3 "z"X3
^X3 ?

S

r
6

z 2024

4

? 206347 o 1 u "

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Engineering Fluid Mechanics Solution Manual

2.2

Chapter Two Tutorial Problems

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

r3
572 z325
?
? 57089:o "
ti 3222 z;0:3
X34
3:4
?
? 380736o "
4i 4 z;0:3
z1 = 36m
he total head = 35.678 + 16.514 + 36 = 88.192 m

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Engineering Fluid Mechanics Solution Manual

2.3

Chapter Two Tutorial Problems


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.
Ans (0.16 kg/s)

Solution:

(i)

p1 - p2 = rm x g x h
= 830 x 9.81 x 0.080 = 651 Pa

4* r3 / r4 +
4 z87306
""" ?
? 56025 o 1 u
4
304 z]3 / *;2 1 3:2+ 6 _
t ]3 / * C4 1 C3 + _

(ii)

x4 ?

(iii)

m = Cd V2 A2 x r

C4 ?

Q

r
6

z202;4 ? 8058 z32/5 o4

= 0.62 x 34.03 x 0.00636 x 1.2
= 0.161 kg/s

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Engineering Fluid Mechanics Solution Manual

2.4

Chapter Two Tutorial Problems

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.
Ans: (320 N/m2, 158 kN/m2)

Solution:
a) For air
Re


= r V D/m = 1 x 1 x 0.01/ 1 x 10-5 = 1000 i.e. laminar

f = 16/Re=16/(1000)= 0.016
therefore

hf = 4 xfx

L v2
D 2g

322
34
j h ? 6 z20238 z
z
? 5408 o
2023 3;084
R ? t 0i0j h ? 302 z;0:3z5408 ? 542 P 1 o

"
4

b) for water
Re

= r V D/m
= 1000 x 1 x 0.01/ 1 x 10-3 = 104 i.e. turbulent low

f


= 0.079/Re0.25
= 0.079/(104)0.25 = 0.0079

therefore

hf = 4 xfx

L v2
D 2g

322
34
jh ? 6 z20229; z
z
? 3803 o
2023 3;084
R ? t 0i0j h ? 3222 z;0:3z3803 ? 379;63 ? 37: mP 1 o4

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Engineering Fluid Mechanics Solution Manual

2.5

Chapter Two Tutorial Problems

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.
Ans: (33.6 kW)

Solution:
V = Q/A = 0.05/(p x 0.152/4) = 2.83 m/s
Re = rVD/m = 1000 x 2.83 x 0.15/0.001 = 4.244 x 105
k/D = 0.15/150 = 0.001;

From Moody diagram f = 0.0051

6 h N x 4 6 z 2022:z322 40:54
jh ?
?
? :092: o "
z
F 4i
2037
4 z ;0:3
hsys = Hf + Hz + Ho = 8.708 + 50 + 0 = 58.808 m
Input power R ?

t0i0S0J u{u 3222 z ;0:3z 2027z 7:092:
?
? 550773 mY "
j oj r
20; z 20;

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Engineering Fluid Mechanics Solution Manual

2.6

Chapter Two Tutorial Problems

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:

C?

r
6

F4 ?

r
6

z 20297 4 ? 6063: z32 /5 o 4

Hz ? tCX 4 *3 / equs +
Hz ? 3222 z 6063: z32 /5 z 52 4 z *3 / 2+
Hz ? 5;98 P

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Engineering Fluid Mechanics Solution Manual

2.7

Chapter Two Tutorial Problems


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:

C3 ?
C4 ?

r
6

r
6

z 206 4 ? 203478 o 4
z 204 4 ? 202536 o 4

S
20 7
?
? 50;9; o 1 u
r
C3
4
z 206
6

20 7
S
x4 ?
?
? 370;37 o 1 u
r
C4
z 204 4
6
x 3?

/Hz"-"r3C3"/"r4"C4"equ"s"?"t" X% "*X4"equ"s"/X3+"
"
/Hz"-""522z325z203478"Î"422z325z202536z3?"3222z207z*370;37/50;9;+
"
/"Hz"-"""598:2""""/"84:5?7;8:""
Hence
Fx = 25429 N
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Engineering Fluid Mechanics Solution Manual

2.8

Chapter Two Tutorial Problems

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:

4

4

r
r3 x3
x5
- |3 ? 5 - |5
ti 4i
ti 4i
2 - 2 - 508 ? 2 -

4

x5
-2
4i

jgpeg › X5 ? 4 z ;0:3z 508 ? :0626 o 1 u
"
r 4
r
4

5
"S ? CzX ? 6 F zX ? 6 z 20297 z :0626 ? 20259 o 1 u
5
r
;:
" 03z32
- 2 ? 4 - 706
" z ;0:3
ti
3222

^"R4 ? ;:03z32 5 / 706 z ;:32 ? 67348 Rc

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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
Ans (6.169m)


Solution:

"











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Engineering Fluid Mechanics Solution Manual

4

Chapter Three Tutorial Problems

4

X4 ? X3 - 4cu
X ? 4 z ;0:3z 4 ? 80486 o 1 u
PUN <

ÂH ? 2

o0i /

3
t0X 4 0Ch zEf ? 2
4

;72 /

r

3
z304 z 80486 40* +F 4 z306 ? 2
4
6

uqnxg › F ? 8039 o
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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Engineering Fluid Mechanics Solution Manual

Chapter Three Tutorial Problems

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

Weight

= 9.81 x(1.2 + Load )

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:

HN
87 z32 5
EN ?
?

*3 1 4+t0C0X 4 *3 1 4+z 20;8 z 4907 zX 4
E F ? 2024 - 20283zE N

4

Ç
87z32 5
? 2024 - 20283z È
4 Ù
É *3 1 4+z 20;8 z 4907 zX Ú

4

hence

HF ?

3
3
t0X 4 0Ch zE F ? z 20;8 zX 4 z 4907z*2024 - 3609; z32 7 zX / 6 +
4
4

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Engineering Fluid Mechanics Solution Manual


Chapter Three Tutorial Problems

Power

R ? HF zX ? 20486X 5 - 30;74 z32 9 X /3
X ? 922 mo 1 j ?

922 z3222
? 3;60666 o 1 u
5822

hence

E N ? 3609; z32 7 z*3;60666+ / 6 ? 2035
E F ? 2024 - 20283z 2035 4 ? 20243
R ? 20486 z3;60666 5 - 30;74 z32 9 1 3;60666 ? 4263 mY
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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