# UNIT I FLUID AND CONTINUUM in Fluid Mechanics Important Question with solution

This resource contains key questions and answers for Unit I – Fluid and Continuum in Fluid Mechanics, a topic covered in the B.Tech AKTU program. This section covers topics including fluid properties, fluid types, and fluid continuum. The provided questions and answers may help students prepare for exams and improve their understanding of the subject.

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Important Questions For Fluid Mechanics:
*Unit-01     *Unit-02
*Unit-03    *Unit-04
*Unit-05    *Short-Q/Ans
*Question-Paper with solution 21-22 ```

## Q1. Discuss physical properties of fluids in brief.

Ans. Physical Properties of Fluid :

Some physical properties of fluids are as follows:

A. Density:

1. It can be characterised as the mass per unit volume at a constant pressure and temperature. It is sometimes referred to as particular mass or mass density.

2. The unit of p is kg/m3

B. Weight Density:

1. It can be characterised as the mass per unit volume at standard pressure and temperature. It also goes by the name “specific weight.”

2. The unit of w is N/m3

C. Specific Volume:

1. It is defined as the volume per unit mass of fluid.

D. Specific Gravity:

1. It is the ratio of the specific weight of the given fluid to the specific weight of a standard fluid.

2. For liquids, standard fluid is pure water at 4 °C and pressure at 101 kN/ m2. Air is standard fluid, for gases.

## Q2. Discuss the concept of continuum in brief.

Ans. Continuum:

• 1. A fluid is made up of molecules, which, particularly in the gas phase, may be widely spread apart. However, it is more practical to ignore the fluid’s atomic structure and consider it to be a continuous, homogenous mass without any holes, or a continuum.
• 2. We can treat characteristics as point functions and assume that they change continuously in space without leap discontinuities thanks to the continuum idealisation.
• 3. This idealization is accurate as long as the system we’re dealing with is sizable in comparison to the distance between molecules.
• 4. High density gases and liquid applications are constrained by the continuum.

## Q3. State and derive the Newton’s law of viscosity. Give its applications.

Ans. A. Newton’s Law of Viscosity:

1. This law states that the shear stress (τ) acting on a fluid element layer is directly proportional to the rate of shear strain.

B. Derivation:

• 1. From Fig., when two layers of fluid, at a distance dy apart, move one over the other at different velocities u and u + du.
• 2. Shear tension acting between fluid layers is caused by viscosity and relative velocity.
• 3.This shear stress is proportional to the rate of change of velocity with respect to y. It is denoted by τ.

C. Applications:

• 1 Lubrication in bearings.
• 2. Relative movement between two plates.
• 3. Low viscosity oil is used in car engines whereas high viscosity liquids are employed in hydraulic brakes.

## Q4. What is capillarity ? What is its significance in fluid flow problems?

Ans. A. Capillarity:

• 1. Capillarity is a phenomena when a liquid rises beyond or below its normal level inside a thin glass tube.
• 2. This resulted from the interaction of liquid particle cohesion and adhesion.
• 3. The Fig. shows the phenomenon of rising water in the tube of smaller diameter.

B. Significance:

1. Water rises in the tube of smaller diameters above or below its level.

## Q5. Draw and explain the Rheological diagram.

Ans. 1. Rheology is the study of deformation of flowing fluids

Explanation of Rheological Diagram:

• 1. Non-Newtonian fluids are those whose shear stress and shear strain rate do not relate linearly.
• 2. A fluid that returns (either entirely or partially) to its previous shape after the applied stress is relaxed is known as viscoelastic. This trait is present in some non-Newtonian fluids. For these kinds of fluids, the shear stress is influenced by both the history of the fluid and the local strain rate.
• 3. Because non-Newtonian fluids grow less viscous the more they are sheared, they are sometimes referred to as shear thinning fluids or pseudoplastic fluids.
• 4. Fluids with a strong shear thinning effect are known as plastic fluids.
• 5. Some fluids, known as Bingham plastic fluids, require a finite stress called the yield stress before they can even start to flow. For illustration, consider toothpaste.
• 6. The fluids if sheared more, the more viscous it becomes are known as shear thickening fluids or dilatant fluids. Example : a thick mixture of sand and water.

## Q6. Define the following terms:

• a. Buoyancy.
• b. Centre of buoyancy.
• c Metacentre.
• d. Metacentric height.

Ans. A. Buoyancy:

• 1. A fluid exerts an upward force on a body when the body is submerged in it.
• 2. The term “force of buoyancy” or “buoyancy” refers to this upward force, which is equivalent to the weight of the fluid that the body has displaced.

B. Centre of Buoyancy:

• 1. It is defined as the point, through which the force of buoyancy is supposed act.
• 2. The centre of buoyancy will be the centre of gravity of the fluid displaced if the force of buoyancy is a vertical force and equal to the weight of the fluid displaced by the body.

C. Metacentre:

• 1. It is described as the location at which a body begins to oscillate when tilted at a slight angle.
• 2. When the body is given a slight angular displacement, the line of action of the buoyancy force will intersect the normal axis of the body at the metacentre.

D. Metacentric Height:

1. Metacentric height is the separation between a body’s centre of gravity and its metacentre when it is floating.