22 Slices
Medium 9788131808153

Ch_3_(69-130).pdf

Dr. R.K. Bansal Laxmi Publications PDF

3

CHAPTER

3.1

HYDROSTATIC FORCES

ON SURFACES

INTRODUCTION

This chapter deals with the fluids (i.e., liquids and gases) at rest. This means that there will be no relative motion between adjacent or neighbouring fluid layers. The velocity gradient, which is equal to the change of velocity between two adjacent fluid layers divided by the distance between the layers, du

∂u

= 0. The shear stress which is equal to m will also be zero. Then the forces acting will be zero or dy

∂y on the fluid particles will be :

1. due to pressure of fluid normal to the surface,

2. due to gravity (or self-weight of fluid particles).

3.2 TOTAL PRESSURE AND CENTRE OF PRESSURE

Total pressure is defined as the force exerted by a static fluid on a surface either plane or curved when the fluid comes in contact with the surfaces. This force always acts normal to the surface.

Centre of pressure is defined as the point of application of the total pressure on the surface. There are four cases of submerged surfaces on which the total pressure force and centre of pressure is to be determined. The submerged surfaces may be :

See All Chapters
Medium 9788131808153

Ch_21_(1041_1061).pdf

Dr. R.K. Bansal Laxmi Publications PDF

21

FLUID SYSTEM

CHAPTER

21.1

INTRODUCTION

Fluid system is defined as the device in which power is transmitted with the help of a fluid which may be liquid (water or oil) or a gas (air) under pressure. Most of these devices are based on the principles of fluid statics and fluid kinematics. In this chapter, the following devices will be discussed:

1. The hydraulic press,

2. The hydraulic accumulator,

3. The hydraulic intensifier,

4. The hydraulic ram,

5. The hydraulic lift,

6. The hydraulic crane,

7. The fluid or hydraulic coupling,

8. The fluid or hydraulic torque converter,

9. The air lift pump, and

10. The gear-wheel pump.

21.2

THE HYDRAULIC PRESS

The hydraulic press is a device used for lifting heavy weights by the application of a much smaller force. It is based on Pascal’s law, which states that the intensity of pressure in a static fluid is transmitted equally in all directions.

The hydraulic press consists of two cylinders of different diameters. One of the cylinder is of large diameter and contains a ram, while the other cylinder is of smaller diameter and contains a plunger as shown in Fig. 21.1. The two cylinders are connected by a pipe. The cylinders and pipe contain a liquid through which pressure is transmitted.

See All Chapters
Medium 9788131808153

Ch_10_(433-464).pdf

Dr. R.K. Bansal Laxmi Publications PDF

10

TURBULENT FLOW

CHAPTER

10.1

INTRODUCTION

The laminar flow has been discussed in chapter 9. In laminar flow the fluid particles move along straight parallel path in layers or laminae, such that the paths of individual fluid particles do not cross those of neighbouring particles. Laminar flow is possible only at low velocities and when the fluid is highly viscous. But when the velocity is increased or fluid is less viscous, the fluid particles do not move in straight paths. The fluid particles move in random manner resulting in general mixing of the particles. This type of flow is called turbulent flow.

A laminar flow changes to turbulent flow when (i) velocity is increased or (ii) diameter of a pipe is increased or (iii) the viscosity of fluid is decreased. O. Reynold was first to demonstrate that the rVD

. transition from laminar to turbulent depends not only on the mean velocity but on the quantity m rVD

This quantity is a dimensionless quantity and is called Reynolds number (Re). In case of circular m pipe if Re < 2000 the flow is said to be laminar and if Re > 4000, the flow is said to be turbulent. If

See All Chapters
Medium 9788131808153

Ch_2_(34-68).pdf

Dr. R.K. Bansal Laxmi Publications PDF

2

CHAPTER

2.1

PRESSURE AND ITS

MEASUREMENT

FLUID PRESSURE AT A POINT

Consider a small area dA in large mass of fluid. If the fluid is stationary, then the force exerted by the surrounding fluid on the area dA will always be perpendicular to the surface dA. Let dF is the force dF is known as the intensity of acting on the area dA in the normal direction. Then the ratio of dA pressure or simply pressure and this ratio is represented by p. Hence mathematically the pressure at a point in a fluid at rest is dF

. dA

If the force (F) is uniformly distributed over the area (A), then pressure at any point is given by

p =

F

Force

=

.

A

Area

\ Force or pressure force, F = p ¥ A.

The units of pressure are : (i) kgf/m2 and kgf/cm 2 in MKS units, (ii) Newton/m 2 or N/m 2 and

N/mm2 in SI units. N/m2 is known as Pascal and is represented by Pa. Other commonly used units of pressure are : kPa = kilo pascal = 1000 N/m2 bar = 100 kPa = 105 N/m2.

p =

2.2 PASCAL'S LAW

It states that the pressure or intensity of pressure at a point in a static fluid is equal in all directions. This is proved as :

See All Chapters
Medium 9788131808153

Ch_5_(163-258).pdf

Dr. R.K. Bansal Laxmi Publications PDF

5

CHAPTER

KINEMATICS OF FLOW

AND IDEAL FLOW

A. KINEMATICS OF FLOW

5.1

INTRODUCTION

Kinematics is defined as that branch of science which deals with motion of particles without considering the forces causing the motion. The velocity at any point in a flow field at any time is studied in this branch of fluid mechanics. Once the velocity is known, then the pressure distribution and hence forces acting on the fluid can be determined. In this chapter, the methods of determining velocity and acceleration are discussed.

5.2 METHODS OF DESCRIBING FLUID MOTION

The fluid motion is described by two methods. They are —(i) Lagrangian Method, and (ii) Eulerian

Method. In the Lagrangian method, a single fluid particle is followed during its motion and its velocity, acceleration, density, etc., are described. In case of Eulerian method, the velocity, acceleration, pressure, density etc., are described at a point in flow field. The Eulerian method is commonly used in fluid mechanics.

5.3

TYPES OF FLUID FLOW

The fluid flow is classified as :

See All Chapters

See All Slices