As I have discussed the pressure now I will explain fluid mechanics. The definition of fluid mechanics is as follows:
Fluid mechanics deals with the properties and characteristics of fluid at rest.
Some of the important key points related to the fluid statics are as follows:
Fluid statics has many properties just as hydrostatics when the fluid is in a liquid state and acts as aerostatics when it is in a gaseous state.
The only stress that is in fluid statics is the normal ones other than that there is no shear stress.
The main application of fluid statics is to determine the forces that are acting on the floating or the submerged bodies.
That is a brief introduction to fluid statics further I will explain the forces that are acting on submerged and floating bodies. So without wasting any time let us start.
The structure of the surface and the forces that are acting on the surface is explained as follows:
As the name suggests, there is a plane surface on which liquid flows and the surface is resting.
The fluid pressure is equally distributed onto the surface.
So the set of parallel forces is formed on the surface as a result of hydrostatics forces.
As one side of the surface is facing the fluid pressure whereas the other side is sometimes exposed to the atmosphere and as the result is zero resultant.
The working principle along with all the equations that are acting on the surface are explained as follows:
First of all, as I have discussed earlier that one side of the plate is completely exposed to the atmosphere and has atmospheric pressure whereas the other side of the plate is completely submerged in the fluid as shown in the diagram.
The horizontal surface intersects the plane surface at some angle so that line is considered to be x-axis.
Po is the absolute pressure i.e., the pressure that is above the fluid (liquid) also known to be local atmospheric pressure if the fluid or liquid is exposed to the atmosphere.
The equation of absolute pressure is:
P=P0+ρgh
P=P0+ρg ysinθ (equation 1)
Here h is the vertical distance of a specific point to a surface and y is the distance of a point from the x-axis from the point O as shown in the diagram.
Now the next step is to find the resultant hydrostatics force and for that, the equation is as follows:
FR=∫APdA
Here we will substitute the value of P from equation 1 and equation 2 will look like this:
FR=∫A(P=P0+ρg ysinθ) dA
FR=P=P0A+ρg sinθ∫AydA
∫AydA is the first moment of the area as it is in the y-coordinate and the value is as follows:
yc=1A∫AydA
By substituting the value, we get the final result:
FR=P0A+ρgyc sinθA
FR=P0+ρghcA
FR=PcA
FR=PavgA
The final result will be stated theoretically:
The final resultant force is equal to the pressure at the centroid surface and the area.
The structure of the surface and the forces that are acting on the surface is explained as follows:
As the name shows that the curved surface is submerged in liquid and the hydrostatic forces are determined.
In this part we have applied the integration of pressure forces that fluctuates when the direction of the surfaces changes.
The final force (resultant) is equal and opposite to the force that is acting on the curved surface.
The working principle along with all the equations that are acting on the surface are explained as follows:
Here the weight of the enclosed liquid is as follows:
W=ρgυ
Here V is the volume of fluid and that is in a downward direction as shown in the figure.
the vertical and horizontal forces will be:
the horizontal force component on a curved surface:
FH=FX
the vertical force component on the curved surface
FV=Fy+W
The final result will be:
the horizontal and the vertical component of the hydrostatic force of a curved surface are both equal in case of magnitude and line of action.
The horizontal and vertical component is an equal hydrostatic forces acting on horizontal projection along with the weight of the fluid.
I hope you enjoyed reading the article and have an extensive overview of the pressure and fluid statics. Thanks for reading.
The article will cover essential aspects of fluid statics and pressure forces applied to the fluid. The article will start with the absolute pressure gauge and the variation of pressure with depth in different gravitational field manometers and barometers, respectively. Then I will explain the forces that deal with fluids, such as hydrostatic force, buoyant force, etc. So, dear friends, without wasting any time, let’s start.
The definition of pressure according to fluid mechanics is as follows:
Pressure is the normal force applied by a fluid per unit area.
The units of pressure Pascal is too small to deal with in practical cases. For instance,
Kilopascal: 1kPa=103Pa
Mega Pascal: 1MPa=106Pa
The three common pressure units used are standard atmosphere bar and kilogram-force per square centimeter.
1bar=105Pa=0.1MPa=100kPa
1atm=101,325Pa=101.325kPa=101325 bars
1 kgf/cm2=9.807 N/ cm2=9.807×m2=9.807×104Pa
=0.9807bar
=0.9679 atm
The unit of pressure in the English system is pound-force per square inch (psi or lbf/in2)
The actual pressure at a given position is called absolute pressure. The pressure is measured relative to an absolute vacuum or absolute zero pressure.
The difference between the absolute and local atmospheric pressure is called gage pressure.
The pressure below the atmospheric pressure is called vacuum pressure.
All three of these pressures are interrelated with each. Other, and this is visible with the formulae as mentioned below:
Pvac=Patm-Pabs
Pgage=Patm-Pabs
The following diagram shows the relation of the pressures from the below-mentioned diagram:
We all know there is no fluid pressure change at rest and in the horizontal position. This phenomenon can further be elaborate on a few points:
Assuming a thin layer horizontally of fluid followed by force balance at any point. The pressure increases as the depth increase as there are more layers of fluids, and these layers are being balanced by the pressure increasing.
An example can explain the whole phenomenon.
Toto show how pressure changes with the change in depth. We assumed a rectangular fluid element, as shown in the diagram.
The length, width, and heights are mentioned on the diagram.
The pressure of the fluid is constant, whereas force balance in z direction vertically will be:
∑Fz=maz=0
P2△x-P1△x-ρg△x△z=0
Now, we will divide the above equation with delta x △xand will get the below-mentioned equation:
△P=P2-P1=ρg△z=sz
Here, one of the most important things is that the s is the specific weight of fluid.
The final statement to be noted is that there is an increase in pressure linearly with an increase in depth.
It is essential to note that the pressure force applied by the fluid is always normal at some points to the surface.
As pressure is a scalar quantity, sometimes it seems to be vector one. The pressure will be the same in any fluid at any point. To prove this point, let us discuss a scenario.
Let us consider fluid element (a wedge shape/ right-angled triangle) at equilibrium.
The mean pressures at three surfaces are mentioned as P1, P2, and P3, respectively.
The diagram shows the points clearly.
Here, the value along the pressure is the surface area.
According to Newton’s second law, the force in the direction of x and z is as follows as △y=1:
∑Fx=max=0 P1△z-P3Isinθ = 0 (1)
∑Fz=maz=0 P2△x-P3Icosθ-12ρg△x△z = 0 (2)
Here, the value of w is the weight of the fluid, and the value is as follows:
W=mg
W=ρg△x△z/2
The value of △x and △z are as follows:
x = I cos θ
△z=I sinθ
So, by substituting all the values in equations 1 and 2 and then diving equation 1 with △z and equation 2 with △x then, the final result will be:
P1-P3= 0 (3)
P2-P3-12ρg△z=0 (4)
Here, in equation 3 △, z drops to 0, and the final result will be:
P1=P2=P3=P
Numerous devices are used to measure fluid pressure and work on different principles. These devices are explained below briefly.
The definition of a manometer is explained as follows:
A manometer is a device in which fluid columns measure pressure differences.
The important key points about the manometer are explained below:
the manometer is used to measure small or moderate pressure differences.
If pressure is at a specific position inside any gas tank, then the pressure anywhere in the tank will be the same. But here important point to be noted is that it is for gases only as their gravitational effect is negligible.
The basic diagram of the manometer is shown as follows:
As we can see, two points in a basic barometer and a height h. So the pressure at point 1 will be the same throughout the tank so that P1=P2 and the pressure will be by the equation:
P2=Patm+ρgh
Here, h is the height of column fluid, which is in static equilibrium, and as we can see, the column is exposed to the atmosphere.
is the density of the fluid, and Patm is the atmospheric pressure.
Here, one important point to be noted is that the height of the tube is independent of the area of the tube.
The definition of the barometer is as follows:
A barometer is a device that is used for the measurement of atmospheric pressure.
The following are some important key points related to the barometer:
The structure of the barometer is the inversion of a tube filled with mercury in a container, which is exposed to the atmosphere.
The diagram shows the structure of the barometer;
Toto calculates the formula of the atmospheric pressure; we will follow the above diagram. As you can see, there is a point B, so this B equals atmospheric pressure. Point C inside the tube is assumed to have zero pressure as there are only mercury vapors above point C, and pressure above that point is low compared to the atmospheric pressure, so for ease, the pressure is taken to be zero. The formula of pressure is as follows:
Patm=ρgh
There are many other pressure-measuring devices that are in use in our daily life, and they are briefly explained as follows:
Bourdon Tube is a pressure measuring device consisting of a hook like a hollow metal tube that is connected to a dial indicator. There is a fluid inside the tube that is pressurized. When this fluid is being pressurized up to a point then the needle that is on the dial is deflected. The needle is read to zero when the tube is exposed to the atmosphere.
There are special types of pressure detectors that can convert the pressure effect into electrical energy and they are called pressure transducers.
When the mechanical pressure is created when the electric potential is applied to a crystalline form. Such kinds of devices are called Piezoelectric transducers.
In the introduction, I will extensively explain the property r and how to impact them are so. Let us start. Then I explain properties that are related to fluid flow.
First of all, I will start with the word Property. The definition of property is as follows:
The word property is defined as any characteristic of the system. There are two main types of the property named intensive and extensive.
Example
The examples of property are as follows
Temperature -T
Pressure - P
Mass – m
Following is a brief explanation of the types of properties.
The intensive properties are the ones that are independent of mass, temperature, density, and pressure. Therefore, they are presented in lowercase letters. But here stands an exceptional case, i.e., the temperature and pressure are only denoted with uppercase letters.
The examples of intensive property are as follows:
Velocity - v
Specific Internal Energy - u
Temperature - T
Charge Density - ne or ρ
Molality - m or b
The extensive property is the ones that depend on the size or extent of the system. They are presented by the uppercase letter, but here is an exceptional case for the mass presented by a lowercase letter.
Extensive properties are usually derived, so the following are some examples.
Total Energy
e= E/m
Specific Volume
v=V/m
The specific property is the ones that depend on that are derived from either extensive or intensive ones.
One of the simple examples of a specific property is the density of water; as we know, it is an intensive property. So the extensive property (derived ones) is the mass of water volume divided by the volume. Here both the mass of water and volume are extensive properties.
The term continuum is related to matter in this way: the matter is made of atoms, and their distance and compactness vary from state to state. As in solids, atoms are closely packed, whereas, in liquids, there is some distance. However, in gases, the atoms are spaced widely. So in the continuum, the matter is defined as continuous and homogenous with no holes.
The primary purpose of using a continuum is to treat properties as a point function, and there are no jump discontinuities as the properties vary in space continually. This only applies when the system size is large compared to the space in molecules. It is practically applicable in almost every case except exceptional cases.
At the start of the discussion, I discussed the properties such as intensive and extensive observed during the fluid flow. Now some more properties play a distinct role in the fluid flow and their importance. So without wasting any time, let’s start.
The density is defined as;
Density is mass per unit volume.
ρ=m
It is defined as
The specific density is the reciprocal of density, i.e., volume per unit mass.
υ=Vm
There are numerous factors on which the density depends. The most important of all is the temperature and the pressure, which change the nature of the substance.
In gases, an increase in pressure will decrease the temperature and vice versa.
Compared to gases, solids and liquids are incompressible, so an increase or decrease in pressure is negligible.
In solids and liquids, the temperature is an essential factor that changes the density compared to the pressure. For instance, at the pressure of 1atm, the density of water changes from 998kg/m3 to 975kg/m3. So the difference is about 2.3 percent which is negligible in many cases.
The definition is as follows:
The density of the substance is relative to the density of the well-known substance.
SG=H2O
As relative gravity is a dimensionless quantity, so the SI unit of it is as same as the density one, i.e., kg/L or g/cm3 (0.001 times density in kg/m3)
Specific Gravity of Substances
The following is the list of some substances with specific gravity at 0˚C.
Substance |
SG |
Blood |
1.05 |
Air (at 1 atm) |
0.0013 |
Wood |
0.3-0.9 |
Gasoline |
0.7 |
Gold |
19.2 |
Seawater |
1.025 |
Ethyl Alcohol |
0.79 |
The definition of specific weight is as follows:
The weight of a unit volume of a substance is known as specific weight.
s=ρg
The definition of vapor pressure is as follows:
Vapor pressure is the pressure applied by the vapor of a pure substance at the state of equilibrium with its liquid at a given temperature.
Some important key points related to the vapor pressure are as follows:
It is presented by Pv.
Vapor pressure is as same as saturation pressure Pv.=Psat.
Sometimes, vapor and partial pressure are considered one thing, but they have two different definitions and applications.
Increase in temperature increases the vapor pressure.
The following table shows water saturation or vapor pressure at different temperatures.
Temperature ˚C |
Saturation or Vapor Pressure kPa |
-10 |
0.260 |
-5 |
0.403 |
0 |
0.611 |
5 |
0.872 |
10 |
1.23 |
15 |
1.71 |
20 |
2.34 |
Some important terms are related to vapor pressure, and they are named saturation temperature and saturation pressure, respectively.
Saturation pressure is the pressure at which changes in the state of a pure substance occur at a given temperature. It is represented by Psat.
Saturation temperature is the temperature at which changes in the state of a pure substance occur at a given pressure. It is represented by Tsat.
The definition of partial pressure is as follows:
Partial pressure is the pressure of gas or vapors with a combination mixture of gases.
Some important key points related to partial pressure:
Partial pressure of water vapors has some atmospheric pressure, and the value is 0.3.
The absence of liquid equalized or less than the partial pressure of vapors to the vapor pressure.
At the state of equilibrium, the presence of partial and vapor pressure in the system then the system is saturated.
In open lakes, the evaporation rate is managed by the vapor and partial pressure differences.
As we know, vapor bubbles in the liquid collapse when they are moved or swept from low regions. The result is the production of high-pressure waves that creates destruction. The reason for explaining this is that the phenomenon is related to cavitation, and the vapor bubbles formed are called cavitation bubbles. The phenomenon mentioned above is called cavitation as it is the leading cause of destruction and causes performance to drop off.
Some important key points related to cavitation:
In designing hydraulics pumps and turbines, this phenomenon (cavitation) is prioritized
In flow systems, cavitation is not considered as they result in poor performance, turbulence and noise.
For checking whether cavitation is present in the flow system or not, cavitation is observed by a unique tumbling sound.
We are well known for the term that energy cannot be created nor destroyed but can be transformed from one form to another. There is various form of energy that we observe in our daily life.
So I will recall some of the vital energy that is used during the fluid flow:
The basic concept of kinetic energy is that anybody or system (comprised of energy) is in motion relative to the reference frame and is said to have kinetic energy.
K.E = 12v2
Here, v stands for the velocity of the system or body relative to the reference frame.
The potential energy is the energy possessed by the body or system due to elevation in the gravitational field.
P.E =gz
Here, g represents the gravitational acceleration, whereas z represents the elevation of the system or body concerning the reference position.
Thermal energy is the energy that is related to the temperature. So it is defined as the energy in the system responsible for temperature.
Q=c ∆T
Here ∆T represents the temperature difference, whereas c represents the specific heat.
After discussing all the energy, one important term related to fluid flow is the Enthalpy. So let us discuss enthalpy.
The enthalpy is the combination of internal energy and the product of volume and pressure. The enthalpy value is calculated with the help of pressure, temperature, and volume, respectively. The energy conservation law says that internal energy changes equal heat transfer. The enthalpy change is assumed to equal the heat transfer if the work changes the volume at constant pressure.
H=E +PV
Here, H is the enthalpy, E stands for internal energy, P stands for pressure, and V stands for the system volume.
The sum of all the energy of flowing fluid is called total energy.
eflowing=K.E+P.E+Enthalpy
eflowing=h+V22+gz
There is an expansion in fluids when they are heated, and they contract when they are cooled. This means that temperature and pressure are two essential parameters responsible for contraction and expansion. The temperature and pressure also change the volume or density of the fluids. But volume or density varies differently from fluid to fluid. So, two properties are related to the volume or density changes to the change in pressure. And they are named Bulk Modulus of Elasticity and Coefficient of volume expansion.
So let’s explain these two properties without wasting any time.
There is a similarity in solids’ and liquids' expansion and contraction principles. So, the definition of the bulk modulus is as follows:
Bulk Modulus of Elasticity is a property that is the ratio of change in pressure relative to the volume.
κ = -v(Pv)T= ρ(P∂ρ)T (1)
The formula can also be presented concerning the finite changes, as shown below.
κ≅ -∆P∆vv≅-∆P∆pp
Here ∆vv and ∆pp are dimensionless.
The unit of κ is psi or Pa.
Here, the temperature is kept constant, so the bulk modulus of elasticity presents the change in pressure to the change in volume and density of the fluid.
The above equation proves that the incompressible substance coefficient of compressibility (Bulk modulus of Elasticity) is infinite.
Increase in pressure decreases the volume.
The negative sign indicates Pv is a negative quantity, whereas the bulk modulus value is positive.
An important key point related to Bulk Modulus of Elasticity:
Bulk modulus of elasticity is also known as the coefficient of compressibility or bulk modulus of compressibility.
If the value of bulk modulus is significant, then firstly, the fluid is incompressible, and then a large amount of pressure is required for a small amount of fractional change in the volume.
When the equation is being differentiated, then
From the equation, it is evident an increase in one quantity decreases the other and vice versa. From equation 1, we will differentiate the ρ=1/v, and we will get dρ=-dv/v2. So after cancellation, the final result will be:
dρ=-dvv
The inverse of the coefficient of compressibility is called isothermal compressibility.
The formula is as follows:
α=1=-1v(∂v∂P)T=1(∂ρ∂P)T
It is observed that there is a drastic change in liquid density when it is increased or decreased. A property named coefficient of volume expansion is responsible for the fluid density difference at constant pressure and variable temperature.
𝛃=-1v(∂v∂T)P=-1(∂ρ∂T)P
The coefficient of volume expansion is represented by beta.
At the infinite changes, the formula is shown below:
-∆vv∆T=-∆pp∆T
Here, the pressure is kept constant.
Important key points related to the coefficient of volume expansion:
Increase in temperature increases the value of as they have a direct relationship.
∆T represents the temperature difference in the equation.
If we define viscosity, the most reasonable and appropriate term will be resistance. When the fluid flows, there exist layers of viscosity at that point. There are intermolecular forces in fluid when the fluid is more viscous. So the definition of viscosity will be:
Viscosity is a property that represents the internal resistance of a fluid to motion.
One of the best examples is the pouring of honey. As you observe, honey is dense and very has strong internal resistance.
η=2ga2(∆ρ)9v
We assume a sphere that is dropped onto the fluid, and then the fluid’s viscosity is measured.
Here ∆ρ is the density difference between the fluid and surface
a is the radius of the sphere
G is the acceleration due to gravity
Important key points related to viscosity:
When one layer moves adjacently to the other, some friction exists, which we named viscosity. The layers are moving at some distance and are named dy. The velocities of the fluids are u and u+du, respectively.
The graphical presentation of the layer velocity versus the distance is shown below.
The graph will explain the trends of velocity and distance. As mentioned, two layers are moving adjacently to each other, so the layer that is on top imposes shear stress on the lower layer, and the lower layer, in response, causes shear stress on the upper one.
There are two primary types of viscosity, and they are explained briefly as follows.
Following are some essential key points related to kinematic viscosity:
Kinematic viscosity is the ratio between dynamic viscosity and fluid density.
The formula of kinematic viscosity is as follows:
υ=
Here υ is the kinematic viscosity η is the absolute or dynamic viscosity, and ρ is the density of the fluid.
When the temperature decreases, kinematic viscosity also decreases.
Following are some essential key points related to dynamic or absolute viscosity:
Dynamic viscosity is the ratio of shear stress to the shear strain of motion.
Dynamics viscosity helps in the interaction of the molecules dealing with mechanical stress.
I hope you enjoyed reading the article and have an extensive overview of the fluid-flowing properties. Thanks for reading.
Fluid mechanics is considered to be one of the essential branches of Mechanical Engineering. Fluid Mechanics comprises two words, fluid, and mechanics, with different meanings and research criteria. In this article, I will extensively introduce fluid mechanics and its importance in daily life. So without wasting any time, let us start:
We remember in the early classes, we used to study three states of matter, and afterward, they became four named:
The definition of fluid is the state of matter that can be liquid or solid. We might have noticed that whenever the matter is in any stage, the criteria to know its state is to understand how much stress it can bear, and we name that stress as shear stress that changes its shape. But this situation mostly happens in solid or liquid cases. When the stress is applied, the substantial changes shape and reform into a new one. But up to a limit that cannot destroy its ultimate form. The stress applied to a solid is directly proportional to the strain, whereas, in liquids, the stress is directly proportional to the strain rate.
As mentioned that fluid mechanics comprises of two terms, so now I will define what mechanics is and how much it is essential in our today’s life.
Here are two essential terminologies:
The branch of mechanics in which bodies are at rest is called statics. It is a vast study of internal and external forces in a structure
Example:
The best example of statics is when you are standing on a plane on the rigid ground. The force of gravity and the reaction force as the reaction of gravitational force, both these forces act as statics and help in maintaining the state of rest.
The branch of mechanics which studies the bodies in motion is called dynamics. The study is all related to the movement and what is the cause of it.
Example:
The example of moving the body and dealing with all the forces that are acting on and their effect is categorized in dynamics.
Fluid Mechanics is the sub-category defining the fluid’s nature at rest or in motion.
The types of fluid mechanics are as follows:
Example:
It involves the mass flow rate of oil through the pipeline, study of the pattern weather forecast, and blood circulation.
Example:
The best example of fluid statics involves drinking with a straw. The mechanism happening inside is that when we reduce the pressure at the top of the straw, inside the liquid the atmosphere pushes the liquid up to the mouth.
Fluid statics and dynamics are divided into compressible and incompressible fluid as well as real and ideal fluids. So real is divided into the laminar and turbulent flow, and this goes on.
As I discussed earlier, fluid flow is classified, and they vary from type to type.
By reading their names, you get an idea of what a laminar and turbulent flow is. So laminar flow is one in which fluid flows smoothly without any turbulence. Usually, highly viscous fluid with low viscosity is characterized as laminar flow. Whereas turbulent flow is the one in which fluid flow is not smooth. And they have high velocities.
The compressible and incompressible flows depend upon one of the significant factors density. The flow is incompressible when the density is constant or nearly constant throughout the flow. Incompressible flows characterize most liquids. The compressible flows are opposite to the incompressible ones; they don’t have constant throughout. One of the best examples of compressible flow is gases.
In these types of flow, viscosity is one of the essential vital elements. Every fluid has some viscosity value. So the flows with a significant amount of frictional effect are said to be viscous. Inviscid flows are where viscosity is neglected or to some extent.
As the name shows, the flow covered with a solid boundary is considered internal flow. The liquid is flowing in a pipe or a wire. At the same time, the external flow is defined as an unbounded flow. The fluid flowing over the pipe or the fluid over the ball is exemplified as external flow. And the flow inside a pipe covered is said to be internal flow.
The names are enough to define the nature of the flows. So steady or uniform flows are said to be steady flows. And the unsteady one is opposite to the steady one that does not have any uniformity.
Natural flows are the one that flows naturally. But the theoretical example will be the one that flows due to the buoyancy effect. The forced fluids are the ones that are forced to flow with the help of external means. An example of forced flow is a fan or pump.
The nature of the fluid varies from type to type. The following are some vital types of fluids.
Real fluids possess viscosity. Viscosity is defined as resistance or opposition. Eliminating the ideal cases, all the fluids are examples of real fluids.
The ideal fluids are the one that has no viscosity at all. As I have mentioned just now that all the fluids have viscosity. So ideal fluids are just an ideal case study.
Both of them have two different properties. The Newtonian fluids are the ones in which the shear stress is directly proportional to the shear strain, and in non-Newtonian fluids, they are not proportional to each other.
The ideal plastic fluids are the ones in which shear stress is directly proportional to the shear strain. The shear stress value is also more than the yield value. These fluids are velocity gradient ones and have significant importance.
Fluid mechanics is considered one of the vast branches of mechanical engineering that covers all the fundamental laws of physics. It is not wrong to say those fluid mechanics depend on these laws, and they are named as follows:
Second Law of Thermodynamics
Conservation of mass
Conservation of linear momentum
Conservation of energy
Conservation of angular momentum
As I have briefly discussed all the types of fluids, the following is their graphical presentation.
The properties are one of the significant features of everything. The fluids also have some properties. The following are some essential properties of the fluid.
The word viscosity means thickness. According to the definition, viscosity is defined as the fluid’s property related to friction and resistance.
When one layer moves adjacently to the other, some friction exists, which we named viscosity. The layers are moving at some distance and are named dy. The velocities of the fluids are u and u+du, respectively.
The graphical presentation of the layer velocity versus the distance is shown below.
The graph will explain the trends of velocity and distance. As mentioned, two layers are moving adjacently to each other, so the layer that is on top imposes shear stress on the lower layer, and the lower layer, in response, causes shear stress on the upper one.
According to physics, density is defined as the mass to volume ratio. So the fluid mass to fluid volume ratio is the density of the fluid. In liquids, the density is constant, but in gases, it’s variable.
The specific weight is defined as the ratio between the weight of the fluid and volume. Thus the weight density is defined as the weight per unit volume of fluid and is denoted by w.
Mathematically,
w=Weight of FluidVolume of Fluid
w=Mass of Fluid×Acceleration due to cycleVol. of fluid
w=Mass of Fluid×gVol. of Fluid
w=ρg
The specific volume is defined as the volume of a fluid by a unit mass or volume. This property applies to gases.
Mathematically,
Specific Volume = Vol. of fluidMass of fluid
Specific Volume=1Mass of FluidVol.
Specific Volume=1
The thermodynamic property is the salient feature of gas and liquid. We know that when liquids are compressed, they form gas, so thermodynamics is one of the critical features of gases.
The equation below shows a connection between the pressure, specific volume, absolute temperature, and gas constant.
p=RT
The definition of a system is as follows:
The system is the quantity of matter or a specific region specified for research or study.
As you can see from the diagram, an imaginary or real wall or a surface separates the system from the surroundings. So a system can be open, close, or isolated (special case). So following is a brief explanation of all the types of systems.
Open System
In the open system, the volume is controlled and the energy and mass can easily pass through the boundary of the control volume.
Close System
In the closed system, the mass is controlled and cannot cross the boundary. The energy can cross the boundary easily and volume is also not fixed.
Isolated System
In the isolated system, the energy cannot cross the boundary.
The definition of dimensions is as follows:
The Definition of units is as follows:
There are two types of units explained below briefly.
Some basic dimensions are given the names and they are as follows:
Dimensions |
Units |
Mass |
m |
Temperature |
T |
Length |
L |
Time |
t |
Some dimensions are assigned names in terms of primary dimensions and they are as follows:
Dimensions |
Units |
Volume |
V |
Energy |
E |
Velocity |
V |
Two kinds of units are commonly used in today’s world and that is;
The English system does not have an apparent systematic and numerical base. It is considered to be one of the most difficult systems to memorize. In almost every country metric SI units are widely used but the United States is the only country that has not fully opted for the metric system rather they use the English system in many states.
Example
12 in =1 ft
1 mile =5280 ft
4 qt =1 gal
It is one of the most commonly used and feasible units. The metric SI units are widely used in industries and countries like England. There are seven basic fundamental dimensions introduced and their units in SI are as follows:
Dimension |
Unit |
Length |
meter (m) |
Mass |
Kilogram (kg) |
Time |
Second (s) |
Temperature |
Kelvin (K) |
Electric Current |
Ampere (A) |
Amount of light |
Candela (cd) |
Amount of Matter |
Mole (mol) |
There are numerous examples of fluid mechanics in our daily life. The following examples are some crucial parameters that cover fluid mechanics.
Our heart is an integral part of the human body that pumps blood to all body parts through arteries and veins. In this modern era of science and technology, many scientists have designed artificial hearts that work on the working principle of fluid dynamics and transmit blood and pumps like the original heart.
Our homes are one of the best examples of fluid mechanics. The piping, sewage, hot and cold water pipes, natural gas, and LPG work on fluid mechanics principles. Moreover, our refrigerator, air conditioning, heating, cooling, and insulating system are all examples of fluid mechanics.
We find various examples in our cars, planes, buses, and ships. Fluid mechanics covers all the fields associated with fuel transportation, from the fuel tanks to the cylinders, fuel pumps, carburetors, etc. It covers all the cooling heating systems of automobiles, lubrication systems, power steering, and radiator cooling.
Fluid mechanics is used in many medical devices such as glucose monitors, heart assistance devices, etc.
It is beneficial for eliminating pollution from the atmosphere, cleaning water, cleaning sewage systems, and controlling floods.