Fluid Mechanics Tutorial

COPYRIGHT

Published by :
Politeknik Sultan Azlan Shah
Behrang Stesen, Behrang
35950 Perak
Tel : 05-4544431
Faks : 05-4544993
Email : http://www.psas.edu.my
First Published 2022
All right reserved. No parts of this publication may be reproduced stored in a retrieval
system, or transmitted in any form or by any means, electronic, mechanical,
photocopying or otherwise without permission of Sultan Azlan Shah Polytechnics.

PERPUSTAKAAN NEGARA MALAYSIA
Fluid Mechanics Tutorial
ISBN

i

AN INTRODUCTION OF FLUD MECHANICS
TUTORIALS BOOK

This is a tutorial book on fluid mechanics. By doing an exercise intensively, we believe that
might help students to get a better understanding of what they learned. Furthermore, it helps
to memorise the formulas and equations related to this subject. This book also provided a
simple note to enhance more understanding.
Most of the tutorial’s questions are based on the diploma level of polytechnic. Hopefully, this
book can help with a better understanding of the specific topic.

Thank you.

iii

CONTENTS i

Copyright Declaration ii

Contents iii

An Introduction of Fluid Mechanics Tutorials Book 1

Topic 1 2
3
1.1 Fluid Mechanics. 4
1.2 Concepts of dimension, SI and Imperial 5
1.3 Fundamental and Derived Quantity. 6
1.4 Fluid Properties.
1.4 Tutorial 1 12
13
Topic 2 14
2.1 Relationship between Pressure and Depth 15
2.2 Formula of Pressure 20
2.3 Tutorial 2.1 21
2.3 Pascal Law 23
2.4 Hydraulic Jack Operation 27
2.5 Tutorial 2.2 33
2.6 Manometer, U-tube, Barometer, Piezometer 41
2.7 Tutorial 2.3 42
2.8 Types of flow 43
2.9 Discharge and Mass Flowrate 44
2.10 Continuity Equation Law 49
2.11 Tutorial 2.4 58
2.11 Bernoulli’s Theorem, Pipe, Venturi, Orifice, Pitot
2.12 Tutorial 2.5 ii

1

FLUID MECHANICS

Fluid Mechanics is the study of fluid flow that is used to analysis of various application
that operate based on liquid body such as power turbines/pumps

FLUID MECHANICS

A substance which Studies that deals with the
deforms continuosly under motion and forces on
the application of shear objects
force Object in this case means
A substance that can FLOW rpeasrtticolresartehamt oavriengeither at

Statics Dynamics

2

Concepts of dimension, SI and Imperial

• A dimension is a measure of a physical variable (without numerical values)r
while a unit is a way to assign a number or measurement to that dimension.
For exampler length is a dimensionr but it is measured in units of feet (ft) or
meters (m).
• The SI system (International System of Units) is the modern metric system of
measurement and the dominant system of international commerce and trade.
• The Imperial Unit is also called The British Imperial because it came from the
British Empire that ruled many parts of the world from the 16th to the 19th
century. After the U.S gained independence from Britainr the new American
government decided to keep this type of measurementr even though the metric
system was gaining in popularity at the time.

3

Fundamental and Derived Quantity

A fundamental quantity is a quantity from which other quantities may
be derived; for example, length and time are fundamental quantities
from which a quantity such as speed is derived. The S.I. System of
units is based on seven (7) fundamental quantities as seen Table 1
below.
A derived quantity is produced when two (2) or more fundamental
quantities are combined, either by multiplication or division as shown
in Table 2 below.

Table 1: Fundamental Quantity

Table 2: Derived Quantity

process Restoring process

4

Fluid Properties

5

Tutorial 1

Question 1
What is the volume in m³ of this syrup if it has a density of 0.63 g/mL and a mass of 78 g?
Answer:

Step 1: List down the information

Step 2: Unit Conversion (if necessary)

Step 3: Apply the correct formula

6

Question 2
A piece of cooper has a mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide and 9.5 mm
tick. Calculate density (kg/m³) and specific volume.
Answer:

7

Question 3
Determine the specific weight, w (in kN/m3) weight and specific gravity, S of fluid if the
of fluid is 10 N and the volume is 500 cm3.
Answer:

8

Question 4
Determine the specific weight, ω (in kN/m³ ) and specific gravity, S of fluid if the weight
of fluid is 10 N and the volume is 500 cm³.
Answer:

9

Question 5
Calculate the specific weight, density, specific volume, and specific gravity of 1 liter of
petrol weights 7 N.
Answer:

10

Question 6
Given the mass of fluid is 500 g and the volume is 200 cm³. Calculate:

i. Mass density of fluid
ii. Specific weight of fluid
iii. Specific volume of fluid
iv. Specific gravity of fluid
Answer:

11

Topic 2:

12

The Relationship between Pressure and Depth

Pressure and depth have a directly proportional relationship. This is due to the greater
column of water that pushes down on an object submersed. Conversely, as objects are
lifted, and the depth decreases, pressure is reduced.

13

PRESSURE
Unit: N/m² or Pa

14

Tutorial 2.1

Question 1
Calculate the pressure at a point of 1 km depth in the sea bed in pascal and bar units. Given
the density os sea water is 1025 kg/m³.
Answer:

15

Question 2
Find the height of water column which is equivalent to the pressure of 3.5 kN/m² . Take
into consideration specific weight of water is 9810 N/m³.
Answer:

16

Question 3
The pressure at a point in the sea bed is 100.55 bar.

a. What is this pressure as a head of fresh water with density 1000 kg/m³?
b. What is this pressure as a head of mercury with spesific gravity 13.6?
Answer:

17

Question 4
Calculate the pressure in kN/m² due to a coloumn of 0.4 m of:

a. Water
b. Oil (mass density of 900kg/m³) -
c. Brine (S = 1.1)
d. Mercury (S = 13.6)
Answer:

18

Question 5
The pressure intensity at a point in a fluid is given 4.9 kN/m² . Find the corresponding height of
fluid for:

a. Water
b. Oil (S = 0.9)
Answer:

19

Pascal’s Law

20

Hydraulic Jack Operation According to Pascal’s Law

21

22

Tutorial 2.2

Question 1
A force, F of 650 N is applied to the smaller cylinder of a hydraulic jack. The area, A1 of
a small piston is 15 cm² and the area A2 of a larger piston is 150 cm². What load, W can
be lifted on the larger piston if:

a. the pistons are at the same level.
b. the large piston is 0.65 m below the smaller piston.
c. the small piston is 0.40 m below the larger piston.
Consider the mass density ρ of the liquid in the jack is 10³ kg/m³.

23

Question 2
A hydraulic jack consists of a small and a large cylinder with diameters of 7 cm and 20 cm
respectively. The required force, F to lift up a load, W is 400 N. If the large piston is 15 cm
higher than the small one, determine the weight, W that can be lifted if the specific weight of oil
is 8730 N/m³.

24

Question 3
A force, F of 900 N is applied to the smaller cylinder of a hydraulic jack. The area, A1 of
a small piston is 22 cm² and the area A2 of a larger piston is 250 cm². What load, W
can be lifted on the larger piston if:
a. The pistons are at the same level.
b. The large piston is 0.65 m below the smaller piston.

25

Question 4
A hydraulic jack has a diameter ratio between the two pistons of 8:1. The diameter of large
piston is 600 mm, and it is required to support a mass of 3500 kg. The jack is filled with
hydraulic fluid of specific gravity 0.8. Calculate the force required on the small piston:

a. When the two pistons are at the same level.
b. When the small piston is 2.6m below than the large piston.

26

Manometer

Manometer is one of the oldest pressure measurement devices still
in use today.

A manometer is one of the most accurate devices for measuring
pressure in the lower ranges.

Since manometers are so accurate, they are often used as
calibration standards.

All manometers operate on the principle that changes in pressure
will cause a liquid to rise or fall in a tube.

There are several different types of manometers such as u-tube
manometer, barometer and piezometer.

27

U-tube Manometer

U-tube manometer is probably the most common manometer in use today.
A common u-tube manometer consists of a U-shaped tube of glass filled
with some liquid. Typically, the liquid is mercury, water and light oils.
It’s worth saying here that mercury was a common manometer fluid in
the past, but has largely been replaced due to its environmental and
health hazards.

28

29

30

Barometer

A Barometer consists of a glass tube with one end sealed. An
evacuated tube has its open end submerged in an open
container of mercury.

The pressure exerted by the column of mercury is balanced
by the pressure of the atmosphere. The glass tube is
calibrated in pressure units.

Any liquid could be used in a barometer, but mercury is used
because of its high specific gravity.

A mercury barometer needs to be at least 30 inches tall. A
water-filled barometer would have to be more than 33 feet

high!
Atmospheric pressure = ρgh

31

Piezometer

Piezometer is one of the simplest forms of manometers. It can
be used for measuring moderate pressures of liquids.

The setup of piezometer consists of a glass tube, inserted in the
wall of a vessel or of a pipe. The tube extends vertically upward to
such a height that liquid can freely rise in it without overflowing.
The pressure at any point in the liquid is indicated by the height of
the liquid in the tube above that point.

Pressure at point A can be computed by measuring the height
to which the liquid rises in the glass tube.

The pressure at point A is given by P = ρgh, where ρ is the
density of the liquid.

32

Tutorial 2.3

Question 1
A U-tube manometer shown in figure below is used to measure the gauge pressure of
water (mass density ρ = 1000 kg /m³). If the density of mercury is 13.6 × 10³ kg/m³,
what will be the gauge pressure at A if h1 = 0.45 m and D is 0.7 m above BC.

33

Question 2
A U-tube manometer shown in figure below is used to measure the gauge pressure of a fluid P
of density ρ = 1000 kg/m³. If the density of the liquid Q is 13.6 × 10³ kg/m³, what will be
the gauge pressure at A if h1 = 0.15 m and h2 = 0.25 m above BC. Take into consideration P
atm = 101.3 kN/m².

34

Question 3
U-tube manometer as shown in figure below, measure the pressure difference at points A and
B. Fluid P is oil (S = 0.85 ) and Fluid Q is mercury (S = 13.6 ). Calculate the pressure
difference if h = 2.0 m, h2 = 0.35 m and h1 = 0.5 m.

35

Question 4
Figure shows a differential manometer connected at two points A and B. At A, air pressure
is 10 kN/m². Find the absolute pressure at B. Given ρ water = 1000 kg/m³.

36

Question 5
An inverted U tube as shown in the figure below is used to measure the pressure difference
between two points A and B which has water flowing. The difference in level h = 0.3 m, a =
0.25 m and b = 0.15 m. Calculate the pressure difference PB – PA if the top of the
manometer is filled with oil of relative density 0.8.

37

Question 6
Figure below shows a u-tube manometer that used to measure the pressure difference between
pipe P and pipe Q that contains water. If the fluid in u-tube is oil with specific gravity of 0.9,
calculate the pressure difference between these two pipes in kN/m². Given M=80 cm and
N=25 cm.

38

Question 7
A pressure tube is used to measure the pressure of oil (mass density, 640 kg/m³) in a
pipeline. If the oil rises to a height of 1.2 m above the centre of the pipe, what is the gauge
pressure in at that point? (gravity = 9.81 m/s².

39

Question 8
What is the atmospheric pressure in N/m² if the level of mercury in a Barometer tube is
760 mm above the level of the mercury in the bowl? Given the specific gravity of
mercury is 13.6 and specific weight of water is 9.81×10³ N/m³.

40

Types of Flow

Steady Flow and Unsteady Flow

A flow is said to A flow is said to
be steady flow if be unsteady

different fluid flow if different
properties and fluid properties
fluid velocity
and fluid
does not change
with respest to velocity change
with respest to
time.
time.

Uniform and Non-uniform Flow

The velocity is the same
magnitude and direction
at every point in the fluid.

The velocity is not
the same at every
point in the flow

Laminar and Turbulent Flow

- The flow of fluid is smooth
and highly ordered.

- The fluid layers move
parallel to each other and do

not cross each other.

- The flow of fluid is chaotic
and not in any order.
- The fluid layers cross each
other nad do not move
parallel to each other.

41

Discharge and Mass Flowrate

Discharge, Q
The volume of liquid passing through a given cross-section in unit time is
called the discharge. It is measured in cubic meter per second (m³/s), or
similar units and denoted by Q.

Mass Flowrate, ṁ
The mass of fluid passing through a given cross section in unit time is called the
mass flow rate. It is measured in kilogram per second (kg/s), or similar units and
denoted by ṁ.

42

Continuity Equation Law

For continuity of flow in any system of fluid flow, the total amount of
fluid entering the system must equal the amount leaving the

system. This occurs in the case of uniform flow and steady flow.
1. Continuity Equation in Single Pipe

2. Continuity Equation in Branch Pipe

43

Tutorial 2.4

Question 1
For the pipe in figure below, the following data are given:
Find:
a. The discharge, Q
b. The fluid velocity at station 2, v2

44

Question 2
Water flows through a pipe with a diameter of 50 mm. Then the pipe split into two, one of the
pipes has a diameter 25 mm with the velocity of flow 0.4 m/s and the other one has a
diameter 15 mm with the velocity 0.6 m/s. Calculate the velocity in the main pipe.

45

Question 3
A pipe is split into 2 pipes which are BC and BD as shown in the figure below. The following
information is given:
Calculate:
a. discharge at section A if vA = 2 m/s
b. velocity at section B and section D if velocity at section C = 4 m/s

46