chapter one fluid flow properties of fluid

Chapter one fluid flow properties of fluid

Qahtan A. Mahmood

Introduction

Fluid mechanics is a branch of physics concerned with the mechanics of fluids (liquids,

and gases,) and the forces on them. Fluid mechanics has a wide range of applications

Fluid mechanics can be divided into:

Fluid statics, the study of fluids at rest;

: مخل القح الت سلطب المبئع ف حبلخ السكن عل العبء الذ حت دراسخ المائع ف حبلخ السكن

Fluid kinematic is deal with fluid velocity type

:كبن تتم دراسخ سزعخ المبئع كفخ تغزب ثه وقطخ اخز كفخ تغز دراسخ المائع ف حبلخ الحزكخ

االوجة السزعخ مع الضغظ المسلظ ثه وقطته ف

Fluid dynamics, the study of the effect of forces on fluid motion,

دراسخ المبئع مه حج الق الت سلطب ف حبلخ الحزكخ

If a fluid affected by changes in pressure and temperature, it is said to be

Compressible fluid

مائع قبثلخ لالوضغبط حج تغز حجم المبئع ثتغز الضغظ درجخ الحزارح مخل الغبساد اثخزح الماد

Incompressible fluid,

السائل ف الحققخ المبئع الذ مائع قبثلخ لالوضغبط حج تغز حجم المبئع ثتغز الضغظ درجخ الحزارح مخل

مخل ذي الخبصخ ذع مبئع مخبل لس لذا المبئع جد,المبئع الحقق تغز حجم قلال ثتغز الضغظ درجخ

الحزارح كن عل وعه

Real fluid can be divided into:

Newtonian تجع قبون وته

Non Newtonian ال تجع قبون وته

https://en.wikipedia.org/wiki/Physics

https://en.wikipedia.org/wiki/Mechanics

https://en.wikipedia.org/wiki/Fluid

https://en.wikipedia.org/wiki/Liquid

https://en.wikipedia.org/wiki/Gas

https://en.wikipedia.org/wiki/Force

https://en.wikipedia.org/wiki/Fluid_statics

https://en.wikipedia.org/wiki/Fluid_dynamics


Qahtan A. Mahmood

1-1 Physical Properties of Fluids

1. DENSITY AND SPECIFIC GRAVITY

Density is defined as mass per unit volume [symbol: ρ (rho)]

Specific Volume [symbol: υ (upsilon)]

Is defined as the volume per unit mass, that is

Weight density or specific weight [symbol: (gamma).]

Is defined as weight per unit volume, that is,

Specific gravity or relative density[symbol: SG]

Is defined as the ratio of the density of a substance to the density of some

standard substance at a specified temperature (usually water at 4°C, for which H2O =

1000 kg/m3). That is,


Qahtan A. Mahmood

2- Pressure

Pressure is the (compression) force exerted by a fluid per unit area.

(

)

The pressure developed at the bottom of a column of any liquid is called hydrostatic

pressure and is given by

3- Energy and specific heats

Potential energy is the work required to move the system of mass m from the

origin to a position against a gravity field g:

Kinetic energy is the work required to change the speed of the mass from zero to

velocity V.

In the analysis of systems that involve fluid flow, we frequently encounter the

combination of properties U and Pv. For convenience, this combination is called

enthalpy h. That is,


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Where P/ is the flow energy, also called the flow work, which is the energy per unit

mass needed to move the fluid and maintain flow.

The internal energy U represents the microscopic energy of a non-flowing fluid per unit

mass,

Whereas enthalpy h represents the microscopic energy of a flowing fluid per unit mass

as shown in figure below

The total energy of a simple compressible, E of a substance is the sum of the internal,

kinetic, and potential energies on a unit-mass basis, it is expressed as (e = U + KE+ PE).

The fluid entering or leaving a control volume possesses an additional form of energy

the flow energy P/ . Then the total energy of a flowing fluid on a unit-mass basis

becomes

Where h = P/ + U is the enthalpy, u is the velocity, and z is the elevation of the system

relative to some external reference point

The differential and finite changes in the internal energy and enthalpy of an ideal gas

can be expressed in terms of the specific heats as


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For incompressible substances, the constant-volume and constant-pressure specific

heats are identical. Therefore, cp= cv= c for liquids, and the change in the internal

energy of liquids can be expressed as U = cave T.

Noting that constant for incompressible substances, the differentiation of

enthalpy h = U + P/ gives dh = dU + dP/ . Integrating, the enthalpy change becomes

h =U +P/ = cave T +P/

Therefore h =U = cave T for constant-pressure processes, and h =P/ for

constant-temperature processes of liquids.

4- The ideal gas equation of state

Any equation that relates the pressure, temperature, and density (or specific volume) of

a substance is called an equation of state. The simplest and best-known equation of

state for substances in the gas phase is the ideal-gas equation of state, expressed as

Where: Ru is the gas universal constant, Ru = 8.314 (kJ/kmol .K). The ideal gas

equation can be written as follows:

The constant R is different for each gas; for air, Rair = 0.287 kJ/kg.K. The molecular

weight of air M=28.97 kg/kmol.

5- Dynamic viscosity [symbol: μ (mu)]

The viscosity of a fluid is a measure of its resistance to shear or angular deformation.


Qahtan A. Mahmood

6- Kinematic viscosity [symbol: ν (nu)]

It is the ratio of the dynamic viscosity to mass density of fluid,

7. Surface tension [symbol: σ (sigma)]

The surface of a liquid is apt to shrink, and its free surface is in such a state where each

section pulls another as if an elastic film is being stretched. The tensile strength per unit

length of assumed section on the free surface is called the surface tension. Liquid

droplets behave like small spherical.

The pulling force that causes this tension acts parallel to the surface and is due to the

attractive forces between the molecules of the liquid. The magnitude of this force per

unit length is called surface tension σ s and is usually expressed in the unit N/m (or

lbf/ft in English units).

Let d as the diameter of the liquid drop, σ as the surface tension, and p as the increasing

in internal pressure.

التتز السطح ظبزح فشبئخ تحذث إحز جد قح تمبسك ثه جشئبد المبدح السبئلخ، حج تعط السائل

صفخ األغشخ المتمبسكخ، تحذث إحز تعزض الجشئبد المجدح داخل السبئل لق الشذ مه كل االتجببد، فتلغ

تتأحز ثبلق المجدح ف األسفل الجاوت، ممب كل مىمب األخز، أمب الجشئبد المجدح عل سطح السبئل ف

جعل السطح مشذدا لألسفل؛ فظز عل ئخ غشبء.


Qahtan A. Mahmood

1-2 the flow rate

Volumetric flow rate [symbol: Q]

It is the volume of fluid transferred per unit time.

Where: A is the cross sectional area of flow normal to the flow direction.

Mass flow rate [symbol: m]

It is the mass of fluid transferred per unit time.

Mass flux or (mass velocity) [symbol: G]

It is the mass flow rate per unit area of flow,

1-3 Newton’s Law of Viscosity and Momentum Transfer

Consider a fluid layer between two very large parallel plates separated by a distance L

as shown in figure (1-1). Now a constant parallel force (F) is applied to the upper plate

while the lower plate is held fixed. The fluid in contact with the upper plate sticks to the

plate surface and moves with it at the same velocity, and the shear stress ( ) acting on

this fluid layer is

Where: A is the contact area between the plate and the fluid.

y is the vertical distance from the lower plate.


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Figure (1-1) The behavior of a fluid in laminar flow between two parallel plates

In steady laminar flow, the fluid velocity between the plates varies linearly

between 0 and V, and thus the velocity profile and the velocity gradient are

The velocity gradient is directly proportional to the shear stress

Fluids for which the rate of deformation is proportional to the shear stress are called

Newtonian fluids.

Most common fluids such as water, air, gasoline, and oils are Newtonian fluids. Blood

and liquid plastics are examples of non-Newtonian fluids

In one-dimensional shear flow of Newtonian fluids, shear stress can be expressed by the

linear relationship


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A plot of shear stress versus the rate of

deformation (velocity gradient) for a

Newtonian fluid is a straight line whose

slope is the viscosity of the fluid, as shown

in Figure (1-2). Note: that viscosity is

independent of the rate of deformation

figure (1-2): The rate of deformation (velocity gradient)

The shear force acting on a Newtonian fluid layer (or, by Newton’s third law, the force

acting on the plate) is

The viscosity of liquids decreases with temperature, whereas the viscosity of gases

increases with temperature

This is because in a liquid the molecules possess more energy at higher temperatures,

and they can oppose the large cohesive intermolecular forces more strongly. As a result,

the energized liquid molecules can move more freely.

In a gas, on the other hand, the

intermolecular forces are negligible,

and the gas molecules at high

temperatures move randomly at

higher velocities. This results in

more molecular collisions per unit

volume per unit time and therefore

result greater resistance to flow.


Qahtan A. Mahmood

Consider a fluid layer of thickness L within a small gap between two concentric

cylinders, as shown in figure (1-3) below such as the thin layer of oil in a journal

bearing.

Figure (1-3): Cylindrical moving

The gap between the cylinders can be modeled as two parallel flat plates separated by a

fluid.

the wetted surface area of the inner cylinder to be A = 2RL

torque can be expressed as

Where L is the length of the cylinder and n is the number of revolutions per unit time,

Equatio1-3 can be used to calculate the viscosity of a fluid by measuring torque at a

specified angular velocity. Therefore, two concentric cylinders can be used as a

viscometer, a device that measures viscosity.


Qahtan A. Mahmood

1-4 Newtonian and non-Newtonian fluids

Plot the relationship between shear stress and rate of deformation as shown in Figure

(1-4). The slope of the curve on the () versus du/dy chart is referred to as the apparent

viscosity of the fluid.

For Newtonian fluids, the relationship between shear stress and rate of

deformation is linear.

For non-Newtonian fluids, the relationship between shear stress and rate of

deformation is not linear, and are divided into

a) Fluids for which the apparent viscosity increases with the rate of deformation

(such as solutions with suspended starch or sand) are referred to as dilatant .

b) The fluid becoming less viscous as it is sheared harder ( such as some paints,

polymer solutions, and fluids with suspended particles) are referred to as

pseudoplastic or shear thinning fluids.

c) Some materials such as toothpaste can resist a finite shear stress and thus behave

as a solid, but deform continuously when the shear stress exceeds the yield stress

and thus behave as a fluid. Such materials are referred to as Bingham plastics

Figure (1-4): Plot the relationship between shear stress and rate of deformation


Qahtan A. Mahmood

Example (1.1)

One liter of certain oil weighs 0.8 kg calculates the specific weight, density, specific

volume, and specific gravity of it.

Solution:

Specific weight

Density

Specific volume

Specific gravity

Example (1.2)

Determine the specific gravity of a fluid having viscosity of (4.0 c.poise ) and kinematic

viscosity of (3.6 c.stoke)

Solution


Qahtan A. Mahmood

Example (1.3)

A flat plate of area 2x104 cm

2 is pulled with a speed of 0.5 m/s relative to another plate

located at a distance of 0.2 mm from it. If the fluid separated the two plates has a

viscosity of (1.0 poise), find the force required to maintain the speed.

Solution

Example (1.4)

A shaft of diameter 10 cm having a clearance of 1.5 mm rotates at 180 rpm in a bearing

which is lubricated by an oil of viscosity 100 c.p. Find the intensity of shear of the

lubricating oil if the length of the bearing is 20 cm and find the torque.

Solution:

The linear velocity of rotating is


Qahtan A. Mahmood

The torque is equivalent to rotating moment

T=FR =F (D/2) =3.95N*(0.1/2)m=0.1975J

Example (1.5)

A plate of size 60 cm x 60 cm slides over a plane inclined to the horizontal at an angle

of 30°. It is separated from the plane with a film of oil of thickness 1.5 mm. The plate

weighs 25kg and slides down with a velocity of 0.25 m/s. Calculate the dynamic

viscosity of oil used as lubricant. What would be its kinematic viscosity if the specific

gravity of oil is( 0.95)

Solution:

Component of W along the plane =W cos(60) =W sin(30)

= 25 (0.5) = 12.5 kg

F = 12.5 kg (9.81 m/s2) =122.625 N

τ = F/A = 122.625 N/(0.6 x0.6) m2 = 340.625 Pa

chapter one fluid flow properties of fluid

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