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Contents:
Contents:
A brief history of Fluid Mechanics, Application of Fluid Mechanics, Dimensions and Units
Properties of Fluids
Density, Specific Volume, Specific Weight, Specific Gravity
Viscosity, Newton's Law of Viscosity, Coefficient of Dynamic and Kinematic Viscosity, Effect of Temperature
Surface Tension and Capillarity Effect
Vapour Pressure, Compressibility and Speed of Sound
Lecture 01: (16 Aug 2023)
Introduction to Course, Course Policies, Course Outcomes and Brief History of Fluid Mechanics
Introduction to Course, Course Policies, Course Outcomes and Brief History of Fluid Mechanics
Fluid Mechanics is one of the classical subjects in the engineering sciences, which has application in almost all the disciplines of the engineering. In the end of the 18th century many theoretical and experimental researches were carried out and basic equations governing the fluid flows were available. Methods to solve these equations for engineering flows were developed in the second half of the 20th century. The chronological summary of the important scientists who carried out the research in the field of fluid mechanics are shown in below figure.
Definition of Fluid
A fluid is a substance that deforms continuously due to the application of shear stress independent of its magnitude. This continuous deformation due to the application of shear stress causes a flow. Figure 2 shows the deformation of both solids and liquids due to the application of shear stress.
The rate of deformation of the fluids depends on the fluid’s viscosity, μ. Both liquids and gases are regarded as fluids.
Fluid Mechanics is the science that deals with the behaviour of fluids at rest or in motion and the interaction of fluids with solids or other fluids at the boundaries.
Fluid mechanics can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.
Approaches to study fluid mechanics
Analytical Approach - This method is by solving the governing equations of the fluid motion by using principles of mathematics and obtaining specific solutions for various problems.
Experimental Approach - This method is by utilizing the experimental setups to visualize flows and thus understanding the phenomenon.
Computational Approach - This method adopts the numerical methods to solve the governing equations of the fluid motion and obtaining numerical solutions for various problems.
Lecture 02: (21 Aug 2022)
Application and Significance of Fluid Mechanics, Units and Dimensions,
Application and Significance of Fluid Mechanics, Units and Dimensions,
Properties of Fluids - Density, Specific Weight, Specific Volume and Specific Gravity
Properties of Fluids - Density, Specific Weight, Specific Volume and Specific Gravity
Units and Dimensions :
Units are arbitrary names and magnitudes assigned to the primary dimensions adopted as standards for measurements. There are basically three systems of units namely SI (System International of Units), BG (British Gravitational Units) and EE (English Engineering Units). The units for fundamental quantities in each system of units are shown in Table 1.
Fundamental Quantities & Dimensions:
Physical quantities which are independent of each other and those that cannot be further resolved into any other physical quantities are Fundamental Quantities. They have specific dimensions which are specified in Table 2. From the seven fundamental quantities & dimensions, the first four are extensively used in our fluid mechanics study.
Derived Quantities & Dimensions:
Physical quantities which depend upon fundamental quantities or which can be derived from the fundamental quantities are known as derived quantities. The Table 3 shows some of the derived quantities which are used in our study of the fluid mechanics.
Properties of Fluids :
Density: Density is the mass of a substance per unit volume. It is measured in kilograms per cubic meter (kg/m^3). The density of a fluid can be determined by dividing its mass by its volume.
Classroom Demonstration of Density Measurement
Is the density of a fluid is Constant?
Is the density of a fluid is Constant?
The density of a fluid is not constant. It can change depending on the temperature, pressure, and composition of the fluid.
Temperature: As the temperature of a fluid increases, its density decreases. This is because the molecules of the fluid move faster and take up more space.
Pressure: As the pressure of a fluid increases, its density increases. This is because the molecules of the fluid are squeezed closer together.
Composition: The density of a fluid can also change depending on the composition of the fluid. For example, salt water is denser than fresh water.
An incompressible fluid is a fluid whose density is constant. This means that the density of the fluid does not change with changes in temperature, pressure, or composition. Incompressible fluids are an idealized concept, and no real fluid is perfectly incompressible. However, many fluids, such as liquids, can be considered incompressible for practical purposes.
Specific Weight: Specific weight is the weight of a substance per unit volume. It is measured in newtons per cubic meter (N/m^3). The specific weight of a fluid can be determined by multiplying its density by the acceleration due to gravity.
Specific Volume: Specific volume is the volume of a substance per unit mass. It is measured in cubic meters per kilogram (m^3/kg). The specific volume of a fluid can be determined by dividing its volume by its mass.
Specific Gravity: Specific gravity is the ratio of the density of a substance to the density of a reference substance. The reference substance is usually water. Specific gravity is a dimensionless quantity.
Significance of Density in Engineering Applications
Significance of Density in Engineering Applications
Buoyancy: Buoyancy is the force that pushes an object upwards in a fluid. The buoyant force is equal to the weight of the fluid that the object displaces. The density of the fluid is one of the factors that determine the buoyant force.
The density of water is used to calculate the buoyancy of ships and other marine vessels. Buoyancy is the force that pushes a floating object up against the force of gravity. The greater the density of the fluid, the greater the buoyancy force.
Fluid flow: The density of a fluid affects its flow rate. The higher the density, the slower the flow rate. This is because a denser fluid has more mass and therefore more inertia.
The density of water is used to calculate the buoyancy of ships and other marine vessels. Buoyancy is the force that pushes a floating object up against the force of gravity. The greater the density of the fluid, the greater the buoyancy force.
Heat transfer: The density of a fluid affects its ability to transfer heat. The higher the density, the better the fluid can transfer heat. This is because a denser fluid has more molecules and therefore more collisions between molecules.
The density of fluids is used to calculate the heat transfer rate in engines and other heat transfer devices. Heat transfer is the movement of heat from one object to another. The greater the density of the fluid, the greater the heat transfer rate.
Pressure: The density of a fluid affects its pressure. The higher the density, the higher the pressure. This is because a denser fluid has more mass and therefore more weight.
The density of water is used to calculate the force of water on dams and other hydraulic structures. The force of water on a structure is called hydrostatic pressure. Hydrostatic pressure is equal to the density of water multiplied by the depth of the water.
Aerodynamics: Aerodynamics is the study of the motion of fluids, such as air, around objects. The density of the fluid is one of the factors that determine the aerodynamic forces acting on an object.
The density of air is used to calculate the lift and drag forces on aircraft and other aerospace vehicles. Lift is the force that pushes an aircraft up against the force of gravity. Drag is the force that opposes the motion of an aircraft. The greater the density of air, the greater the lift and drag forces.
Hydraulics: Hydraulics is the study of the use of fluids to transmit power. The density of a fluid is one of the factors that determines the force that can be transmitted by a hydraulic system.
Lecture 03: (23 Aug 2022)
Demonstrative Tutorial on Density, Specific Weight, Specific Volume and Specific Gravity
Demonstrative Tutorial on Density, Specific Weight, Specific Volume and Specific Gravity
Problem-Solving Tutorial on Density, Specific Weight, Specific Volume and Specific Gravity
Problem-Solving Tutorial on Density, Specific Weight, Specific Volume and Specific Gravity
A 100-liter tank is filled with gasoline. The mass of the gasoline is 74 kg. What is the density of the gasoline?
Answer: 740 kg/cu.m
2. A helium balloon has a volume of 10 cubic meters. The density of helium is 0.18 kg/cubic meter. What is the mass of the helium in the balloon?
Answer: 1.8 kg
3. A cylindrical tank has a radius of 5 meters and a height of 10 meters. It is filled with water to a height of 8 meters. What is the mass of the water in the tank?
Answer: 6,28,310 kg (or) 628 Tones
4. If the density of Aviation Turbine Fuel (ATF) is 775 kg/cu.m. Calculate the height of fuel tank to carry 100 kg of fuel. Provided the length of tank is 1 m and breadth is 0.75 m.
Solution: height = 0.1720 m (or) 17.2 cm
5. The density of two liquids (A and B) is given as 1000 kg/m3 and 600 kg/m3, respectively. The two liquids are mixed in a certain proportion and the density of the resulting liquid is 850 kg/m3. How much of liquid B (in grams) does 1 kg of the mixture contain? Assume the volume of the two liquids is additive when mixed.
Answer: 1 kg of the mixture contains 250 - 270 grams of liquid B
6. A container has a volume of 10 liters and is filled with a mixture of water and oil. The mass of the mixture is 15 kg. If the density of water is 1000 kg/liter and the density of oil is 900 kg/liter, what is the volume of water in the mixture?
Answer: The volume of water in the mixture is 5 liters.
Lecture 04: ( 25 Aug 2023)
Viscosity, Newton's Law of Viscosity, Newtonian & Non-Newtonian Fluids,
Viscosity, Newton's Law of Viscosity, Newtonian & Non-Newtonian Fluids,
Coefficient of Dynamic and Kinematic Viscosity
Coefficient of Dynamic and Kinematic Viscosity
Viscosity - Viscosity is the property of a fluid, due to cohesion and interaction between molecules, which offers resistance to shear deformation. Different fluids deform at different rates under the same shear stress.
The viscosity of a fluid is important in many applications, such as:
Engine oil: The viscosity of engine oil is important for lubrication and cooling.
Blood: The viscosity of blood is important for blood flow.
Paint: The viscosity of paint is important for application and drying.
Food: The viscosity of food is important for texture and taste.
Consider the behavior of a fluid element between two infinite plates as shown in the Figure 1. The rectangular fluid element is initially at rest at time t. Let us now apply a constant force δFx to the upper plate so that it moves across the fluid at a constant velocity δu. The relative shearing action of the infinite plates produces a shear stress τyx, which acts on the fluid element is given by
Where δAy is the area of the contact of the fluid element with the plate and δFx is the force exerted by the plate on that element. The above Figure 1 shows the deformation of the fluid element from position MNOP at time t, to M’NOP’ at time t+δt, to M’’NOP’’ at time t+2δt due to the imposed shear stress.
Now let us focus at the time interval δt , the deformation of the fluid element is given by
We want to express dα/dt in terms of readily measurable quantities. The distance δl is measured between M and M’ is given by,
From the above expression we can understand that a fluid subjected to shear stress experiences a rate of deformation which is given by du/dy.
“Fluids in the shear stress is proportional to the rate of deformation”
Newton’s Law of Viscosity -
The fluids which obey the above newton’s law of viscosity are described as the Newtonian Fluids. In Newtonian Fluids in the shear stress is directly proportional to the rate of deformation”. They have the linear relationship between the shear stress and rate of shear deformation.
The constant of proportionality is the absolute (or) dynamic viscosity denoted by μ.
Kinematic Viscosity -The ratio of the dynamic viscosity, μ to the density ρ is called the kinematic viscosity, υ.
How to Measure Viscosity? - Viscometers
How to Measure Viscosity? - Viscometers
The viscosity of a fluid can be measured using a viscometer
Capillary viscometers:
These viscometers measure the time it takes for a fluid to flow through a narrow tube. The viscosity is inversely proportional to the flow rate, so the higher the viscosity, the longer it will take for the fluid to flow through the tube.
Capillary viscometers are the simplest type of viscometer and are often used to measure the viscosity of liquids. They are relatively inexpensive and easy to use, but they can be inaccurate for high-viscosity fluids.
The Redwood viscometer consists of a calibrated capillary tube, a reservoir for the liquid, and a stopwatch. The liquid is placed in the reservoir and the stopwatch is started. The time it takes for the liquid to flow through the capillary tube is measured. The viscosity of the liquid is then calculated using the following equation:
where:
A, B is a constant that depends on the type of viscometer
t is the time it takes for the liquid to flow through the capillary tube
A Redwood viscometer is a device used to measure the kinematic viscosity of liquids. It is a type of capillary viscometer that uses the time it takes for a liquid to flow through a calibrated capillary tube to determine its viscosity.
There are two types of Redwood viscometers: Redwood No. 1 and Redwood No. 2.
Redwood No. 1 is used to measure the viscosity of liquids with viscosities in the range of 1 to 100 centistokes (cSt), while
Redwood No. 2 is used to measure the viscosity of liquids with viscosities in the range of 100 to 1000 cSt.
Rotational viscometers:
These viscometers measure the torque required to rotate a spindle or bob in a fluid. The viscosity is proportional to the torque, so the higher the viscosity, the more torque will be required to rotate the spindle.
Rotational viscometers are more accurate than capillary viscometers and can be used to measure the viscosity of liquids and gases. They are also more versatile and can be used to measure the viscosity of fluids under different shear rates.
A Brookfield viscometer is a type of rotational viscometer that uses a rotating spindle to measure the viscosity of a liquid. It is a versatile instrument that can be used to measure the viscosity of a wide range of liquids, including oils, paints, lubricants, and food products.
The Brookfield viscometer consists of a spindle, a torque sensor, and a housing. The spindle is immersed in the liquid and rotated at a constant speed. The torque sensor measures the force required to rotate the spindle. The viscosity of the liquid is then calculated from the torque reading.
There are many different types of Brookfield viscometers available, each with its own spindle and range of measurement. The most common types are the DV series, the LV series, and the RV series.
The DV series is used to measure the viscosity of low-viscosity liquids,
the LV series is used to measure the viscosity of high-viscosity liquids, and
the RV series is used to measure the viscosity of very high-viscosity liquids.
Laboratory Demonstration of Viscosity Measurement
Spindle Number for Brookfield viscometer
Falling ball viscometers:
These viscometers measure the time it takes for a ball to fall through a fluid. The viscosity is inversely proportional to the square of the ball's velocity, so the higher the viscosity, the slower the ball will fall.
Falling ball viscometers are used to measure the viscosity of highly viscous fluids, such as paints and lubricants. They are relatively inexpensive and easy to use, but they can be inaccurate for low-viscosity fluids.
Rheometers:
Rheometers are a more advanced type of viscometer that can measure the viscosity of a fluid under different shear rates. Shear rate is the rate at which the fluid is deformed, and it is measured in units of 1/s.
Rheometers are a versatile type of viscometer that can measure the viscosity of fluids under different shear rates. They are used in a wide variety of applications, including the food, pharmaceutical, and oil and gas industries.
Pulsed-field gradient viscometers:
These viscometers measure the diffusion of tracer particles in a fluid. The viscosity is inversely proportional to the diffusion coefficient, so the higher the viscosity, the slower the tracer particles will diffuse.
Pulsed-field gradient viscometers are the most accurate type of viscometer and are used to measure the viscosity of complex fluids, such as suspensions and emulsions. They are also used to measure the viscosity of fluids under extreme conditions, such as high temperatures and pressures.
Stokes and Poise
Stokes and Poise
Stokes and poise are both units of viscosity.
Stokes (St) is the unit of kinematic viscosity in the CGS (centimeter–gram–second) system. It is named after George Gabriel Stokes, an Irish mathematician and physicist.
Poise (P) is the unit of dynamic viscosity in the CGS (centimeter–gram–second) system. It is named after Jean Louis Poiseuille, a French physicist.
The stokes is more commonly used in fluid mechanics than the poise.
This is because the stokes is dimensionless, while the poise has units of grams per centimeter per second.
One stoke is equivalent to one poise divided by the density of the fluid in g/cm3.
Viscosity of Common Fluids :
Viscosity of Common Fluids :
Lecture 05: (28 Aug 2023)
Effect of Temperature on Viscosity, Viscosity Measuring Instruments, Engine Oils and Viscosity
Effect of Temperature on Viscosity, Viscosity Measuring Instruments, Engine Oils and Viscosity
Variation of Viscosity with Temperature -
The origin of the viscosity is due to cohesion and intermolecular momentum transfer across the fluid layers. These two factors contribute to providing resistance to the shearing force.
The interesting factor is that the viscosity of the liquids drops with the temperature as the viscosity of the gases increases with the temperature. This is due to the fact that in liquids the cohesive force is predominant due to the closely packed molecules and as the temperature rises the cohesive force decreases which in turn decreases viscosity. The following expression describes the variation of viscosity for liquids with temperature,
Where
μo, α and β are constants for liquids
T is temperature in Celsius scale
Where
μo, α and β are constants for gases
T is temperature in Celsius scale
In gases cohesive forces are small and the molecular momentum transfer predominates which increases as the temperature increases it in turn increases the viscosity of the gases. The following expression describes the variation of viscosity of the gases with the temperature.
Non-Newtonian Fluids
Fluids in which shear stress is not directly proportional to deformation rate are termed as the Non-Newtonian Fluid. The power law model for one-dimensional (or) unidirectional flows are given by,
Where the exponent n is called the flow behavior index and k is the consistency index.
The below Figure shows the relationship between the rate of shear deformation with the shear stress acting on them,
Below are brief descriptions of the physical properties of the several categories:
1. Plastic: Shear stress must reach a certain minimum before flow commences.
2. Bingham plastic: As with the plastic above a minimum shear stress must be achieved.
3. Pseudo-plastic: No minimum shear stress necessary and the viscosity decreases with rate of shear, e.g. colloidal substances like clay, milk and cement.
4. Dilatant substances: Viscosity increases with rate of shear e.g. quicksand.
5. Thixotropic substances: Viscosity decreases with length of time shear force is applied e.g. thixotropic jelly paints.
6. Rheopectic substances: Viscosity increases with length of time shear force is applied
7. Viscoelastic materials: Similar to Newtonian but if there is a sudden large change in shear they behave like plastic.
Engine Oils and Viscosity
Engine Oils and Viscosity
Engine oil is a lubricant used in internal combustion engines to reduce friction between moving parts and to prevent wear. It also helps to cool the engine, remove contaminants, and seal the pistons and cylinders.
The best type of engine oil for your bike/car will depend on the make, model, and year of your bike/car, as well as your driving conditions. The owner's manual will specify the recommended type of engine oil for your bike/car.
Here are some of the factors to consider when choosing an engine oil:
Viscosity: The viscosity of an engine oil is a measure of its thickness. A higher-viscosity oil is thicker and will provide more lubrication, but it will also be more difficult to pump. A lower-viscosity oil is thinner and will flow more easily, but it may not provide as much lubrication.
Additives: Engine oils contain additives that help to improve their performance. Some common additives include antioxidants, detergents, and dispersants. Antioxidants help to prevent the oil from breaking down. Detergents help to keep the engine clean by removing contaminants. Dispersants help to keep the contaminants suspended in the oil so that they do not settle and form deposits.
Engine oil viscosity is a measure of its resistance to flow. The higher the viscosity, the thicker the oil and the more difficult it is to flow. Engine oil viscosity is important for several reasons:
It helps to lubricate the engine's moving parts, preventing them from rubbing against each other and causing wear.
It helps to cool the engine by carrying away heat from the moving parts.
It helps to seal the engine, preventing leaks.
It helps to clean the engine by picking up dirt and debris and carrying it away.
The viscosity of engine oil is affected by temperature. As the temperature decreases, the viscosity of the oil increases. This is why it is important to use the correct viscosity of oil for the climate in which you live. In cold climates, a lower-viscosity oil is used because it will flow more easily at low temperatures. In hot climates, a higher-viscosity oil is used because it will not thin out as much at high temperatures.
Engine oils are classified by their viscosity using the SAE (Society of Automotive Engineers) viscosity rating system. The SAE viscosity rating system uses two numbers, separated by a "W". The first number is the viscosity of the oil at a cold temperature (0°F or -17.8°C). The second number is the viscosity of the oil at a hot temperature (210°F or 99°C).
For example, an oil with a viscosity rating of 5W-30 has a low viscosity at cold temperatures (5) and a high viscosity at hot temperatures (30).
The most common viscosity ratings for engine oils are:
0W-20: This is a low-viscosity oil that is designed for use in cold climates.
5W-30: This is a mid-range viscosity oil that is suitable for most climates.
10W-40: This is a high-viscosity oil that is designed for use in hot climates.
The SAE 5W-30 viscosity rating indicates the viscosity of the oil at two different temperatures:
5W: This is the viscosity of the oil at a cold temperature of 0°F (-17.8°C).
30: This is the viscosity of the oil at a hot temperature of 210°F (99°C).
The lower the number before the "W", the thinner the oil will be at a cold temperature. The higher the number after the "W", the thicker the oil will be at a hot temperature.
So, an SAE 5W-30 oil is a thin oil that will flow easily at a cold temperature but will still provide adequate lubrication at a hot temperature.
The viscosity readings for SAE 5W-30 oil are as follows:
Kinematic viscosity at 100°C (212°F): 9.3 mm²/s
Kinematic viscosity at 40°C (104°F): 60.7 mm²/s
Viscosity index: 159
The viscosity index is a measure of how much the viscosity of the oil changes with temperature. A higher viscosity index indicates that the oil will change less with temperature.
The SAE 5W-30 viscosity rating is a common viscosity rating for many car engines. It is a good choice for most climates and driving conditions.
Lecture 06: (30 Aug 2023)
Tutorial on Solving Numerical Problems based on Viscosity
Tutorial on Solving Numerical Problems based on Viscosity
1. A body weighing 1000 N slides down at a uniform speed of 1 m/s along a lubricated inclined plane making 30 degree angle with the horizontal.
The viscosity of lubricant is 0.1 kg/ms and contact area of the body is 0.25 sq.m. Determine the lubricant thickness assuming the linear velocity distribution
Answer: 0.041 m (or) 41 mm
2. A uniform film of oil 0.13 mm thick separated two discs, each of 200 mm diameter, mounted coaxially. Ignoring the edge effects, calculate the torque necessary to rotate one disc relative to other at a speed of 7 rev/s, if the oil has viscosity of 0.14 Pas.
Answer: 0.0615 N-m
Lecture 07: (01 Sep 2023)
Surface Tension, Capillarity, Vapour Pressure, Compressibility, and Speed of Sound
Surface Tension, Capillarity, Vapour Pressure, Compressibility, and Speed of Sound
Surface Tension -
Surface tension is caused by the force of cohesion at the free surface. Cohesion means intermolecular attraction between molecules of the same liquid. It enables a liquid to resist small amount of tensile stress. The below figure depicts the surface tension.
Surface tension is responsible for many phenomena, such as:
The formation of droplets and bubbles.
The ability of insects to walk on water.
The ability of water to climb up a thin tube.
The formation of soap bubbles.
The spreading of a liquid on a solid surface.
The surface tension of a liquid can be measured using a variety of methods, such as the capillary rise method and the Wilhelmy plate method.
The capillary rise method is based on the fact that a liquid will rise up a narrow tube against the force of gravity. The height of the rise is related to the surface tension of the liquid.
The Wilhelmy plate method is based on the fact that a force is required to pull a plate out of a liquid. The force is related to the surface tension of the liquid.
The surface tension of a liquid is affected by a number of factors, such as:
The temperature of the liquid.
The presence of impurities in the liquid.
The surface area of the liquid.
The shape of the container holding the liquid.
The surface tension of a liquid decreases with increasing temperature. This is because the kinetic energy of the molecules increases with increasing temperature, which makes it easier for the molecules to break away from the surface of the liquid.
The presence of impurities in a liquid can also affect its surface tension. Impurities can weaken the cohesive forces between the molecules of the liquid, which can decrease the surface tension.
The surface area of a liquid can also affect its surface tension. The larger the surface area, the greater the force required to hold the molecules together at the surface, which can increase the surface tension.
The shape of the container holding a liquid can also affect its surface tension. For example, a liquid will have a higher surface tension in a narrow tube than in a wide dish. This is because the molecules of the liquid are more attracted to each other at the edges of the tube, which creates a stronger surface tension.
Engineering Applications of Surface Tension
Engineering Applications of Surface Tension
Ink-jet printing: Ink-jet printers use surface tension to create tiny droplets of ink. The ink is held in a reservoir and then forced through a tiny nozzle. The surface tension of the ink causes the droplets to form and break away from the nozzle.
Microfluidics: Microfluidics is the study of the behavior of fluids at very small scales. Surface tension is an important factor in microfluidics, as it affects the flow of fluids through small channels.
Capillarity - is a phenomenon when a liquid is in contact with thin solid tubes changes in the level above or below depending on its specific weight. The features of this effect are,
1. The contact angle, θ
2. The magnitude of the surface tension, σ (N/m)
This depends upon the type of liquid and the type of solid surface. The capillary action is due to both cohesion and adhesion of liquid particles.
The above figure shows the phenomenon of rising water in the tube of smaller diameters. Let,
d = Diameter of the capillary tube
θ = Angle of contact of the water surface
σ = Surface tension force for unit length
w = specific weight (ρg)
(Upward surface tension force) = (Weight of the water column in the tube –Gravity force)
Vapour Pressure - All liquids have a tendency to vaporize i.e. the molecules are continuously ejected from free surface to the atmosphere. These ejected molecules are in gaseous state and exerts their own partial pressure on liquid. This pressure is known as Vapour pressure.
Since the molecules of a liquid are in constant motion, some of the molecules in the surface layer having sufficient energy will escape from the liquid surface, and then changes from liquid state to gas state. If the space above the liquid is confined and the number of the molecules of the liquid striking the liquid surface and condensing is equal to the number of liquid molecules at any time interval becomes equal, equilibrium exists. These molecules exerts of partial pressure on the liquid surface known as Vapour pressure of the liquid, because degree of molecular activity increases with increasing temperature. The Vapour pressure increases with temperature. Boiling occurs when the pressure above a liquid becomes equal to or less then the Vapour pressure of the liquid. It means that boiling of water may occur at room temperature if the pressure is reduced sufficiently.
Compressibility
Compressible fluid is a type of fluid whose density changes with the variation of applied pressure. Compressible flow is the type of flow in which the density does not remain same. Compressibility is defined as the relative change in fluid volume for the applied pressure change. The bulk modulus of elasticity (K) which is defined as the ratio of compressive stress to the volumetric strain.
Speed of sound, a - An important consequence of compressibility of the fluid is that the disturbances introduced at some point in the fluid propagate at finite velocity. The velocity at which these disturbances propagate is known as “acoustic velocity/speed of sound”.
Mathematically, it is represented as below,
Properties of Common Fluids at Standard Temperature and Pressure (STP)
Lecture 08: (04 Sep 2023)
Tutorial on Solving Numerical Problems based on Surface Tension, Capillarity,
Tutorial on Solving Numerical Problems based on Surface Tension, Capillarity,
Vapour Pressure, & Compressibility
Vapour Pressure, & Compressibility
1. Calculate the capillary depression of mercury at 20 degree Celsius with contact angle θ = 140 degrees to be expected in a 2.5 mm diameter tube. The surface tension of mercury at 20 degree Celsius is 0.4541 N/m.
Answer: 4.2 mm
2. A capillary tube of internal diameter 0.21 mm is dipped into a liquid whose density is 790 kg/cu.m. The liquid rises in this capillary to a height of 6.30 cm. Calculate the surface tension of the liquid.
Answer: 0.0256 N/m
In-Semester Evaluation : Activity Based Assessment
In-Semester Evaluation : Activity Based Assessment
Activity 1: "Calculate the Density, Specific Weight, Specific Volume and Specific Gravity of the Coconut Oil, Honey, & Bike Engine Oil."
Due Date: 31 Aug 2023 (Thursday)
Chose Three different fluids such as Coconut Oil, Honey and Engine - Using the weighing scale and measuring beaker measure the Density, Specific Weight, Specific Volume and Specific Gravity of the chosen fluid and Tabulate the results.
Assessment Parameters:
Explanation of Density, Specific Weight, Specific Volume and Specific Gravity
Procedure of carrying out the experiment
Data Presentation, Tabulation and Inference
Activity 2: "Measuring Viscosity of a given fluid using Viscometer"
Due Date: 06 Sep 2023 (Wednesday)
Select an Engine Oil of your choice and measure the viscosity of the engine oil using any of the viscometer available in the Institute
Assessment Parameters:
Explanation of Viscosity, Coefficient of Dynamic and Kinematic Viscosity
Procedure of carrying out the experiment
Data Presentation, Analysis and Inference
Activity 3: "Prepare a Neat Chart of Fluid Properties"
Due Date: 08 Sep 2023 (Friday)
Prepare a Neat Chart of Fluid Properties, their definition, units, dimensions and their significance on a Chart Paper
Assessment Parameters:
Explanation of Fluid Properties
Data Presentation
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