**List of content**

**Physical properties of the fluid****Specific weight****Density****What is the requirement of indicating the density value of petrol and diesel?****What happens if the density of petrol or diesel will get change?****Specific gravity****Specific volume****Compressibility and Bulk modulus****Viscosity****Newton’s law of viscosity****Kinematic viscosity****Effect of temperature on viscosity****Questions & Answers****Multiple choice questions**

**Physical properties of fluids**

The properties can describe the physical condition of any fluid. It is essential to understand various properties of fluid before analyzing the fluid flow problem. The properties can be defined as the physical characteristic which indicates its state

Properties of fluid are broadly divided into two parts

Intensive property: it is a property whose magnitude is not dependent on mass. For example, pressure, temperature, mass density, etc.

Extensive property: it is a property whose magnitude is dependent on mass. For example, weight volume, mass, etc.

**Specific weight**

Specific weight is defined as weight per unit volume

W=w/v

Here **w** is the weight of the fluid,

**V** is the volume of fluid.

As we know, the body’s weight is the force of the body to center of the earth.

It is expressed as the multiplication of the mass of the body and gravitational acceleration. The value of g is measured at sea level 9.8 m/s^{2}

Weight is a force, so the unit of weight is Newton (N). The unit of volume is m^{3}

Hence, the unit of specific weight is N/m^{3}

The specific weight of water is 9810 N/m^{3} at standard pressure 760 mm of Mercury and temperature of 4°C.

Specificc weight of seawater is 10000 -10105 N/m^{3}.

The higher value of specific weight in seawater is due to dissolved salt and solid particulate matter. The specific weight of Mercury is 13 times greater than water. The air has specific weight around 11.9 N/m^{3} (at temperature 15°C and standard atmospheric pressure).

Since the specific weight is dependent on gravitational acceleration, its value changes with gravity.

**Density**

Density, the symbol of density, is rho (𝛒). The standard definition of density is mass per unit volume.

In other words, we can say that it is a matter (amount) of fluid storage in the given volume.

ρ=m/V

Here, m is mass of fluid, V indicates the volume of fluid,

We know that the unit of mass is in kg and the unit of volume is in m^{3}

So, The unit of density is taken in kg/m^{3}

The mass density of water 15.5°C is 1000 kg/m^{3}

The mass density of air is 1.24 kg/m^{3} at standard temperature 20°C and normal atmospheric pressure.

I have one practical question for you. You are frequently visiting the petrol pump filling petrol in your bike or car. You have noticed that the density of petrol or diesel is indicated on display. Now understand my question carefully,

**What is the requirement of indicating the density value of petrol and diesel? What happens if the density of petrol or diesel will get change?**

Think about it as an engineer and find an answer.

**Specific gravity**

Specific gravity is well-defined as the ratio of mass density or specific weight of the fluid to mass density or specific weight of the standard fluid.

Here, the standard fluid (sf) for liquid is water at 4°C and the standard fluid for gases is air at 0 °C.

As we can see, the specific gravity is the ratio of the same property, so the specific gravity is unitless.

There is no dimension of specific gravity..

The specific gravity of Mercury (Hg) is usually 13.6 times higher than water. It means that Mercury is 13.6 times heavier than water.

**Specific volume**

The specific volume is reciprocal of mass density

It can be defined as the ratio of volume and mass

v=V/m

Practically specific volume is a more useful incompressible fluid study.

The unit of specific volume is m^{3}/kg.

**Compressibility and bulk modulus**

The study of fluid mechanics includes compressible and incompressible fluid.

Compressible fluid means it will get a contract when pressure is applied, and removal of pressure it will get expand.

Compressibility is the an essential property of the fluid. It is the ability of fluid to get change volume under pressure. The equation of the Coefficient of compressibility is given as,

Here, the **dp** change in applied pressure and **dV** is a volume change.

Here, the -ve sign indicates an increase in pressure results reduction in volume.The Coefficient of compressibility is symbolized by **Β _{c}**.

Generally, In this measurement compressibility of fluid is represented by its bulk modulus of elasticity and the bulk modulus of elasticity is taken as reciprocal of the Coefficient of compressibility.

**Viscosity**

Viscosity can be defined as it is property of fluid by whic it exerts resistance to flow.

Practically if we take an example, fluid is flowing over any solid surface or planer surface. The velocity of the fluid is considered negligible (zero) at the solid surface boundary, and velocity is found increasing far away from the solid surface boundary. The fluid Layers offers resistance to each other. It is one type of friction between fluid layers.

Suppose we observe the velocity profile in the fluid layers. The velocity is found lesser near to the solid surface. The velocity is found greater at the outer layer, far from the solid surface boundary. This happens because of internal resistance, and it is known as viscous resistance. All real fluid possesses viscosity. As we know, that ideal fluid does not have viscosity. Some examples of highly viscous fluid are glycerine, tar, and molasses, etc.

The fluids with lower viscosity are air, water, petrol, etc.

**Newton’s law of viscosity**

Let’s, consider two adjacent layers at distance dy,

Layer 1 velocity is u,

Layer 2 velocity is u+du,

The top layer is flowing with velocity u+du. The top layer offers resistance to the lower layer with exerting force F. The lower layer also provides resistance to the top layer with equal and opposite force F. These two opposing forces generate shear resistance.

It is denoted by **τ** shear resistance. It is proportional to the velocity gradient.

If we remove the proportional limit, can we have to put one constant?

Here, the constant of proportionality or proportionality factor is **μ**

It is acknowledged as the Coefficient of viscosity. The value of Coefficient of viscosity is dependent on the type of surface and surface roughness.

This equation is widely known as Newton’s law of viscosity.

There is some observation based on this law. These observations are useful to study viscosity and velocity distribution.

Shear stress is the maximum velocity gradient is high.

When the velocity gradient is zero, the shear stress is also zero.

The value of shear stress is maximum at the boundary, and it will simultaneously decrease from the boundary.

The unit of viscosity can be formulated from Newton’s law of viscosity..

Here, N/m^{2} istaken as Pascal (Pa). Sometimes, the Coefficient of dynamic viscosity is taken in poise (P).

1 Poise = 0.1 Pa*s

Dynamic viscosity of water is 1 centipoise (cP)= 10^{-3} N s/m^{2}

Dynamic viscosity of air is 0.0181 centipoise =0.0181 *10^{-3} N s/m^{2}

Water is 55 times denser than air.

The given value is at standard temperature 20°C and atmospheric pressure.

**Kinematic viscosity**

The kinematics viscosity is well-defined as the ratio of dynamic viscosity and density.

The unit of kinematics viscosity is formulated as,

v=μ/ρ

As we know, that metric does not involve any force or energy, so the unit of kinematic viscosity only of length and time.

This unit is commonly known as stokes.

The kinematics viscosity of water is 10 raise to minus 6 meter square per second

The kinematic viscosity of air is 15

The value is at standard temperature of 20°C and atmospheric pressure.

The kinematics viscosity of air is 15 times higher than water.

**Effect of temperature on viscosity**

The effect of the temp. value of viscosity is different in liquid and gas.

If we consider the fluid is a liquid value of dynamic viscosity is decreasing with an increase in temperature

Suppose the fluid is gas; the value of viscosity is increasing with an increase in temperature.

Let’s see why

In liquid, the molecules are more closer as compare to gases.

Viscosity is act mainly due to molecular cohesion. The molecular cohesion is decreasing with increasing temperature.

Empirical relation is developed to explain the variation in viscosity due to temp.

For liquid:

Here, μ is the viscosity at the desired temperature t°C.

μ_{0} is the viscosity at 0°C

A, B are the constant, and their value is dependent on the used liquid.

For water μ_{0}= 0.0179 poise, A= 0.03368, B= 0.000221

For gases:

Here, μ_{t} is the viscosity at desired temperature t°C.

μ_{0} is the viscosity at 0°C

α,β are the constant and its value is dependent on used gas

For air. μ_{0}=1.7*10^{-5} Ns/m^{2}, α=0.56*10^{-7}, β= 0.1189*10^{-9}^{}

**Questions & Answers**

**What is an intensive property?**

It is the property of fluid whose magnitude is not dependent on mass or matter.

**What is the weight of the body? Is it one type of force?**

Yes, Weight is force. The weight of the body is the force of the body to the center of the earth.

**Why is specific gravity unitless?**

Specific gravity is the ratio of density of the fluid to density of the standard fluid. It means that ratio of the similar types. So there is no unit of specific gravity.

**Which type of study requires the use of specific volume?**

The study of compressible fluid requires the use of specific volume property.

**What is compressibility?**

Compressibility is the important property of fluid. It is ability of fluid to get change volume under pressure.

**What is meaning of negative sign in the equation of compressibility?**

The negative sign indicates increase in pressure results decrease in volume.

**Enlist the observation based on newton’s law of viscosity.**

Shear stress is maximum velocity gradient is high

When the velocity gradient is zero the shear stress is also zero

Value of shear stress is maximum at the boundary, and it will simultaneously decrease from the boundary.

**Define kinematic viscosity. Why is the unit only include length and time dimensions?**

The kinematics viscosity is represented as the ration of dynamic viscosity and density. We know that kinematic does not involve any force or energy, so the unit of kinematic viscosity only of length and time.

**What is the effect of temp. on gaseous fluid?**

If the fluid is gaseous, then the value of viscosity is increasing with an increase in temperature.

**Give some examples of highly viscous fluid.**

Examples of highly viscous fluid are glycerin, tar, and molasses, etc.

**What are the values of constants in correlation for “effect of temperature on viscosity of gases ?**

μ_{0} is the viscosity at 0°C

α,β are the constant and its value is dependent on used gas

For air. μ_{0}=1.7*10^{-5} Ns/m^{2}, α=0.56*10^{-7}, β= 0.1189*10^{-9}^{}

**Multiple Choice Questions**

## Which one of the following is extensive property?

a) Pressure b) Mass density c) Volume d) Temperature

Give the unit of specific weight.

a) N/m b) N/m^{2} c) N/m^{3} d) m/N

**What is the value of specific weight of seawater (at standard condition)?**

a) 10000 -10105 N/m^{3} b) 20000 -20105 N/m^{3} c) 1000 -1105 N/m^{3} d) None of above

**How many times is Mercury heavier than water?**

a) 11 b) 12 c) 13 d) 14

**What is the density of water at 15.5****°C in kg/m**^{3}

^{3}

a) 994 b) 1000 c) 1500 d) 846

**The specific gravity is ratio of mass density of fluid to mass density of_______**

a) Compressible fluid b) Incompressible fluid c) Standard fluid d) None

**The specific volume is reciprocal of__________**

a) Specific weight b) Viscosity c) Mass density d) Specific gravity

**The bulk modulus of elasticity is reciprocal of___________**

a) Coefficient of viscosity b) Coefficient of performance c) Coefficient of compressibility d) None

**Viscosity can be defined as resistance to ________**

a) Fluid flow b) Current flow c) Temperature flow d) Pressure

**What is the unit of kinematic viscosity?**

a) N/m b) m/s c) m^{3}/s d) m^{2}/s

**If fluid is liquid then the value of dynamic viscosity will ________ with increase in temperature of liquid**.

a) Increase b) Decrease c) be constant d) None of this

**The molecular cohesion is decreasing with________ temperature.**

a) Increase b) Decrease c) Remain constant d) None

**Conclusion**

This article is the concept of various properties and their relation. The properties like specific weight, mass density, specific gravity and specific volume are defined with the unit. The concept of viscosity and newton’s law of viscosity are described in detail with its equations. The most important phenomenon, the effect of temperature on the fluid’s viscosity, is discussed to make the concept easier to understand.

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