Fluid Mechanics (Properties 1) 🧩

Warm greetings🤩 to all in the 11th post on #Day10 ! On this day, we will start to Fluid Mechanics 🧚🏻 and will give introduction to the main properties of fluids. Here we go 🤩😉,

Introduction🤹🏻‍♂️

In this series, we will distinguish a fluid property, defined to be a characteristic of the material structure of the fluid, from a flow property, whose value is determined in part by how the fluid is moving. The color of a fluid is purely a fluid property, while the velocity of a fluid is purely a flow property. The density, pressure, temperature, and viscosity of a fluid , which you may have thought of as fluid properties, are actually flow properties whose precise values depend on the nature of the fluid and type of flow. In reading this post, keep in mind then that all fluid properties are variables rather than constants, and assumed to be functions of position and time.

📌Note carefully that in fluid mechanics a few symbols are used to represent more than one property. This is unavoidable but usually creates no confusion because the context of a problem makes it clear to which property the symbol refers.

Mass, Weight, Density🧗🏻‍♀️

The mass of an object is defined as a measure of its resistance to acceleration, i.e., resistance to a change in velocity. For an object of fixed mass, the relationship between acceleration, a, force, F, and mass, M, is given by Newton’s second law

• F= M*a

The weight of an object, W, is the magnitude of the force acting on the object due to Earth’s gravity field. Thus, weight is defined by the previous equation. If the acceleration produced by gravity is g, the weight of a mass M is:

• W = M*g

📌Note: Properties of a fluid that depend on the amount of fluid in a system are termed extensive properties. The weight of a volume of fluid is an extensive property. If an extensive property is divided by the total mass in a system, the result is an intensive property, i.e., a property per unit mass. Extensive and intensive properties are both common in thermodynamics. In fluid mechanics, where the total mass of fluid is usually not relevant, we normally use intensive properties defined per unit volume.

🧩Fluids differ in their resistance to acceleration in proportion to their density. The density of a fluid, ρ, may be determined by dividing the mass of a sample of that fluid by its volume V:

• ρ =M/V

Density has dimensions of kg/m3, lbm/ft3, or slugs/ft3. The reciprocal of density is called specific volume, υ:

• υ =1/ρ

As a thermodynamic property of a fluid , density has a certain numerical value defined by the pressure and temperature of the fluid.

Specific Weight🧯

The specific weight γ of a fluid is defined as the weight of a fluid per unit volume in Earth’s gravity field. For a volume of fluid – V of mass M, the weight of the fluid is

• W = M*g,

which we can also write as

• W = ρ*V*g.

Thus the specific weight of a fluid is given by any of the following formulas

• γ =W/V

• γ =M*g/V

• 📌γ = ρ*g

Specific weight has dimensions of {F/L3} and typical units abbreviated as N/m3 or lbf/ft3. The value of a fluid specific weight depends on the specific physical conditions to which the fluid is exposed.

Specific Gravity🔌

If you work for an international corporation and your product list contains dozens of different fluids, you will have a significant number of density values at STP to deal with, and these may be given in a number of different units. Placed in this situation, you might want to use a dimensionless, and therefore unitless, measure of density. This fluid property, known as specific gravity, sg, is defined as the ratio of a fluid density to that of a standard reference fluid (water for liquids, air for gases) at STP. Thus, for gases, we define the specific gravity as

• sg (gas) = ρ (gas)/ρ (air)

while for liquids, we write

• sg (liquid) = ρ (liquid)/ ρ (water)

Pressure🤖

All fluids are composed of energetic molecules in motion. When these molecules collide with a surface, they exert a normal and tangential force on the surface due to the change in momentum of colliding molecules. Since the resulting surface forces are of critical importance in all fluid mechanics problems, it is important for engineers to be able to quantify them. Here we focus on the normal force exerted by a fluid on a surface. This normal force exists in fluids at rest and in motion, whereas tangential (shearing) forces exist only for fluid in motion. Liquids and gases are unable to exert tensile stresses. Thus the normal force exerted by a fluid on a surface is always compressive; i.e., it is directed into the surface. It is easiest to envision this force as being applied by a fluid to a real physical surface, but it is also important to realize that a normal force is applied by a fluid on every surface it contacts.

📌Note that on the imaginary interior surface shown, the fluid on one side of the surface exerts a normal force on the fluid on the other side and vice versa. The pressure p on a planar surface is defined as the compressive normal force applied by the fluid to the surface, Fn, divided by the area of that surface, A. Thus we write

• p =Fn/A

and apply the convention that pressure is a positive quantity. Note that equation defines an average pressure acting on the surface.

Pressure Measurement👾

Absolute pressure is defined and measured in reference to a perfect vacuum. The pressure employed in an equation of state is always an absolute pressure. Most pressure measurements, however, are made by comparing the unknown pressure to an ambient pressure. This results in a reading of what is referred to as the gauge pressure. The gauge then responds to the difference in the two pressures. A pressure reading made this way gives zero when the unknown pressure is equal to atmospheric pressure, and −14.7 psi when the unknown pressure is a perfect vacuum. A gauge pressure is therefore specified with reference to atmospheric or ambient pressure and can range from minus atmospheric pressure to large positive values. The figure below shows a common pressure gauge. Note that the pressure indicated by the device represents the difference between the unknown pressure source and the ambient pressure.

The relationship between gauge and absolute pressure is given by

• P(gauge) = P(absolute)− P(ambient)

Manometer Readings 🧮

A manometer is a liquid-filled device used to measure pressure. As shown in the picture below, in a simple water filled U-tube manometer, an unknown pressure can be compared to atmospheric pressure by using equation above to estimate the pressure difference. By changing the liquid from water to mercury, a manometer of reasonable size may be used to read higher pressures.

Buoyancy Principle🖌

The increase in hydrostatic pressure with depth in a fluid creates a net force on an immersed object. The net vertical force acting on an object due to hydrostatic pressure is called the buoyancy force. F (buoyancy), acts in the direction opposite to that of the gravitational force, F (gravity), and has a magnitude equal to the weight of the displaced fluid . Figure below indicates that the buoyancy force arises because the increase in hydrostatic pressure with depth creates a net upward hydrostatic force on the surface of the object. Since the gravitational force on the object is equal to its weight, the net force F (net) on a submerged object is the difference between its weight W (object) and the weight of the displaced fluid W (fluid). That is, we can write the net force as

• F (net) = F (gravity) − F (buoyancy) = W (obj) −W (fluid)

📌Note that a positive value of F (net) represents a net force in the direction of the gravitational field. A negative value implies that the object is being pushed upward in the opposite direction. This principle may be used to estimate the buoyancy force acting on a heated volume of fluid immersed in similar fluid. In this case, the buoyancy force is the difference in the weight of the volume of hot fluid and the weight of an equal volume of the surrounding colder fluid.

Thermal Properties 🔥

The temperature T of a fluid is a thermodynamic state variable that provides a measure of the internal energy of the fluid. For a fluid in equilibrium, the temperature is proportional to the mean kinetic energy of the random motion of the molecules. Temperature is a base dimension in all unit systems and is often expressed in units of ◦C or◦F. The relationships between the Celsius and Fahrenheit temperature scales and their corresponding absolute temperature scales are:

• K=◦C+273.16 and

• ◦R=◦F+459.69

where K (no degree symbol) is the temperature unit in the Kelvin scale, and ◦R is the temperature unit in the Rankine scale. Remember that the temperature used in an equation of state and all other thermodynamic relationships is always an absolute temperature. As mentioned earlier, the density, pressure, and temperature of a fluid are related to one another by an equation of state. For many gases, the state equation is well approximated by the perfect gas law. Although all liquids also exhibit some dependence of density on pressure and temperature, the state equation of a liquid is usually replaced by the assumption that the liquid density is constant. This approximation should be examined before being applied to a specific flow problem. For example, if a constant density approximation is applied to a problem involving a liquid with an imposed temperature variation, the analysis cannot predict the tendency of warm, less dense liquid to rise in response to buoyancy forces. Despite these failings, we will see that the constant density assumption is appropriate for many of the liquid flows encountered in fluid mechanics, and also for gas flow at low speeds.

References 📖

1. Introduction to fluid mechanics/Edward J. Shaughnessy, Ira M. Katz, James P. Schaffer.

Additional Resources 🧪🔑

You can get deep insight about Process/Chemical Engineering from these sources😉:

1. https://t.me/ebookstorage/215- Industrial Separation Processes (book)

2. https://t.me/ebookstorage/214- Advanced Process Engineering Control (book)

3. https://t.me/OilAndGas- Information about Oil&Gas (mainly arabic lang)

4. https://t.me/chemical_worlds- Chemical Engineering Books, Quizzes and GATE Study Group

5. https://t.me/chemical_environmental- Discussion group related to Chemical Engineering Problems

6. https://t.me/chemicalengineeringworld_cew- Everything related to Chemical Engineering

7. https://t.me/ebookgate- Chemical Engineering E-books (Telegram Channel)

8. https://www.youtube.com/channel/UCqioh32NOJc8P7cPo3jHrbg- Piping Analysis

9. https://www.youtube.com/channel/UCQfMyugsjrVUWU0v_ZxQs2Q -Mechanics of engineered devices

10. http://chemicalengineeringguy.com/- suggests a wide range of courses in Chemical engineering (you can find free courses on topic of Aspen HYSYS, Aspen Plus)

11. https://www.youtube.com/user/LearnEngineeringTeam- suggests working principles of every engineered devices, equipment and etch.

12. https://www.youtube.com/channel/UCR0EfsRZIwA5TVDaQbTqwEQ- suggests great information about pumps, compressors with animation.

🔌Today we have already started to learn about Fluid Mechanics, mainly focused on Fluid Properties 1. Tomorrow, we will finish Fluid Properties with Surface Tension, Viscosity and Fluid Energy. Now, time to say goodbye👋🏻 until tomorrow and Stay tuned for more content 😉🌝✨!

✏️Note: If you need one of those books or links, you can contact me via my email or LinkedIn profile.

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