Mechanics of Fluids

Pitot Tube

2011-11-15T09:30:00.001-08:00

Pitot Tube is a device used for measuring the velocity of flow at any point in a pipe or a channel. The Pitot tube was invented by the French Engineer Henri Pitot.

The principle of Pitot tube is based on the Bernoulli's equation, where each term can be interpreted as a form of pressure. If the velocity of flow at a point becomes zero, the pressure there is increased due to the conversion of kinetic energy into pressure energy.

The pitot tube is robust and simple to use. In its simplest form, it consists of a glass tube bent at right angles.

What is an Orifice?

2010-09-13T22:37:00.000-07:00

An orifice is a small opening provided on the side or bottom of a tank, through which a fluid is flowing. The opening can be of any shape or cross-section, like rectangular, triangular or circular. The orifices may discharge fluid into the atmosphere or from one tank to another.

Orifices are classified based on the shape or the cross-sectional area as:

Rectangular orifice
Circular orifice
Triangular orifice and
Square orifice

Orifices are classified based on the size of the orifice and the head of fluid above the orifice as:

Small orifice and
Large orifice

Depending on the shape of the upstream edge of the orifices, they are classified as:

Sharp-edged orifice and
Bell-mouthed orifice

They are also classified based on the nature of the discharge as:

Partially submerged or drowned orifice
Fully submerged or drowned orifice
Free discharging orifices

Displacement thickness

2009-05-28T20:01:00.000-07:00

Displacement thickness is a measure of boundary layer thickness. Displacement thickness is defined as the distance by which the boundary layer should be displaced to compensate for the reduction in flow rate on account of boundary layer formation. The concept of displacement thickness finds its application in the design of ducts and wind tunnels.

Momentum thickness

2009-05-27T19:49:00.000-07:00

Momentum thickness is a measure of the boundary layer thickness. Momentum thickness is defined as the distance by which the boundary should be displaced to compensate for the reduction in momentum of the flowing fluid on account of boundary layer formation.

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2009-04-09T01:57:00.000-07:00

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Define boundary layer

2009-03-31T22:39:00.000-07:00

A very thin layer of fluid, in the immediate vicinity of a solid boundary surface, where the velocity of the flowing fluid increases gradually from zero at the boundary surface to the velocity of the main stream is known as boundary layer.

It is to be noted that the higher the Reynolds number (or smaller the viscosity), the thinner is the boundary layer. Within the boundary layer, the flow can either be laminar or turbulent. The concept of boundary layer helps in significantly simplifying the theoretical treatment of flows with high Reynolds number.

Hydraulic Grade Line, Energy Gradient Line

2009-03-06T20:27:00.000-08:00

Hydraulic grade line
A line joining the piezometric levels at various points is known as hydraulic grade line or hydraulic gradient line.

Piezometric Head
The sum of the pressure head (p/w) and the potential head (Z) is known as piezometric head.

Total Head
Total head is given by the sum of piezometric head (p/w + Z) and the kinetic head (V²/2g)

Energy Gradient Line
Total energy at various points along the axis of the pipe is plotted and joined by a line, known as Energy Gradient Line.

Forces in Fluid Flow

2009-03-05T20:18:00.000-08:00

Name the different forces present in fluid flow.

* Inertia force
* Viscous force
* Gravity force
* Pressure force
* Surface tension force
* Elastic force

Reynolds Number

2009-03-04T22:37:00.000-08:00

Physical significance of Reynolds number:
* Reynolds number signifies the relative predominance of the inertia to viscous forces occurring in the flow system.
* Reynolds number is very useful in determining whether the flow is laminar or turbulent.

Moody's Chart
If the value of relative roughness k/D for the pipe and Reynolds number for the flow are known, the friction factor f can be determined using Moody’s chart.

Submarine is tested in the air tunnel. Identify the model law applicable.
Reynolds model law.

Distorted and Undistorted Models

2009-03-03T22:33:00.000-08:00

What is meant by undistorted models?
An undistorted model is one that is geometrically similar to its prototype.

Demerits of a distorted model:
* Pressure and velocity distributions are not truly reproduced
* Difficult to extrapolate and interpolate results obtained from distorted models
* The observer experiences an unfavourable psychological effect

Mach Model law

2009-03-02T22:28:00.000-08:00

In any fluid system, where the forces resulting from elastic compression alone are significant in addition to inertia force, the dynamic similarity between the model and the prototype may be achieved by equating the Mach numbers.

(M)_model = (M)_prototype

What is a Mach number?
Mach number is defined as the square root of the ratio of the inertia force and elastic force. It is a non-dimensional number.

Mach Number's field of use:
Aerodynamic testing and in phenomena involving velocities exceeding the speed of sound.

Dynamic Similarity in Fluid Flow

2009-03-01T22:26:00.000-08:00

In fluid flow, what does dynamic similarity mean?

Dynamic similarity means the similarity of forces between the model and the prototype.

What are the non-dimensional numbers associated with dynamic similarity?

Non-dimensional numbers associated with dynamic similarity:

# Reynolds number
# Froude’s number
# Euler’s number
# Weber number
# Mach number

Similitude involved in Model Analysis

2009-02-28T22:20:00.000-08:00

List the similitude involved in the model analysis.

* Geometric similarity
* Kinematic similarity
* Dynamic similarity

For the prototype and model to be geometrically similar, the ratio of all corresponding linear dimensions in the model and the prototype should be equal.

Kinematic similarity refers to the similarity of motion between model and prototype.

Dynamic similarity corresponds to the similarity of forces between model and prototype.

Meta Centre Definition

2009-02-27T03:42:00.000-08:00

Define Meta Centre

Metacentre is defined as the point about which a body starts oscillating when the body is tilted by a small angle.

Condition needed for the submerged body to be remaining in stable equilibrium
Centre of Gravity (G) is below the Centre of Buoyancy (B).

Laminar sub layer

2009-02-26T03:53:00.000-08:00

Define laminar sub layer

For a turbulent boundary layer, if the boundary is smooth, the roughness projections are covered by a very thin layer, which remains laminar. This thin layer is called laminar sub layer.

Bernoulli’s equation

2009-02-26T03:45:00.000-08:00

Bernoulli’s equation states that in a steady, irrotational flow of an incompressible fluid, the total energy per unit weight of the fluid remains constant.

p/w + V²/2g + Z = constant

Assumptions involved in Bernoulli’s equation:

1. The fluid is ideal
2. The flow is steady
3. The flow is irrotational
4. The flow is incompressible

Why is it necessary to assume that the flow is steady before integrating Euler’s equation to derive Bernoulli’s equation?

In steady flow, a fluid particle will move along a streamline. Thus, in describing the motion of a fluid particle, the distance along a streamline can be used in writing the equations of motion.

What is Dimensional Homogenity?

2009-02-03T21:17:00.000-08:00

Dimensional Homogenity

An equation is said to be dimensionally homogenous if the dimensions of the terms on its left hand side are same as the dimensions of the terms on its right hand side.

Dimensions of some of the physical quantities are given below for your use:

(a) Pressure - ML^-1T^-2
(b) Surface tension - MT^-2
(c) Dynamic viscosity - ML^-1T^-1
(d) Kinematic viscosity - L²T^-1

Simple Manometers: Piezometer

2009-01-09T21:10:00.000-08:00

Simple Manometers
A simple manometer is one which consists of a glass tube, whose one end is connected to a point where pressure is to be measured and the other end is open to atmosphere.

Piezometer
Piezometer is one of the simplest forms of manometers. It can be used for measuring moderate pressures of liquids. The setup of piezometer consists of a glass tube, inserted in the wall of a vessel or of a pipe. The tube extends vertically upward to such a height that liquid can freely rise in it without overflowing. The pressure at any point in the liquid is indicated by the height of the liquid in the tube above that point.

Pressure at point A can be computed by measuring the height to which the liquid rises in the glass tube. The pressure at point A is given by p = wh, where w is the specific weight of the liquid

Limitations of Piezometer
1. Piezometers can measure gauge pressures only. It is not suitable for measuring negative pressures.

2. Piezometers cannot be employed when large pressures in the lighter liquids are to be measured since this would require very long tubes, which cannot be handled conveniently.

3. Gas pressures cannot be measured with piezometers, because a gas forms no free surface.

Manometers

2009-01-08T17:06:00.000-08:00

What are Manometers?
Manometers are devices used for measuring the pressure at a point in a fluid, by balancing the column of fluid by the same or another column of fluid.

Types of Manometers
Manometers are classified as:

Simple manometers

Piezometer

U-tube manometer, and

Single column manometer

Vertical single column manometer

Inclined single column manometer

Differential manometers

U-tube differential manometer

Inverted U-tube differential manometer

Advantages of Manometers

Easy to fabricate and relatively inexpensive
Good accuracy
High Sensitivity
Requires little maintenance
Suitable for low pressure and low differential pressure

Flow Net

2009-01-07T20:57:00.000-08:00

What is a Flow Net?
A grid obtained by drawing a series of stream lines and equipotential lines is known as a flow net.

Equi-Potential Line is an imaginary line in a field of flow such that the total head is the same for all points on the line, and therefore the direction of flow is perpendicular to the line at all points.

Path line and Stream line

2009-01-06T20:54:00.000-08:00

Distinguish between stream line and path line
1. A stream line is an imaginary line drawn in a flow field such that a tangent drawn at any point on this line represents the direction of the velocity vector. Path line is the line traced by a single fluid particle as it moves over a period of time.

2. Stream line shows the direction of velocity of a number of fluid particles at the same instant of time. Path line shows the direction of velocity of the same fluid particle at successive instants of time.

Can the path line and a streamline cross each other at right angles?
A fluid particle always moves tangent to the streamline. In steady flow, the path lines and streamlines are identical. In unsteady flow, a fluid particle follows one stream line at one instant and another at the next instant and so on, so that the path line have no resemblance to any given instantaneous streamline.

Stream Line and Velocity Potential

2009-01-05T20:39:00.000-08:00

Define Stream line
A stream line is an imaginary line drawn in a flow field such that a tangent drawn at any point on this line represents the direction of the velocity vector.

In steady flow, a fluid particle will move along a streamline.

Equation of a stream line in a three-dimensional flow is given as
(dx/u) = (dy/v) = (dz/w)

Define Velocity Potential
Velocity Potential is defined as a scalar function of space and time such that its negative derivative with respect to any direction gives the fluid velocity in that direction.

Properties of a velocity potential function
1. If velocity potential exists, the flow should be irrotational
2. If velocity potential satisfies the Laplace equation, it represents the possible steady, incompressible, irrotational flow.

Cohesion, Adhesion, Surface Tension and Capillarity

2008-12-16T20:40:00.000-08:00

Cohesion means inter-molecular attraction between molecules of the same liquid.

Adhesion means attraction between the molecules of a liquid and the molecules of a solid boundary surface in contact with the liquid.

Surface tension is caused by the force of cohesion at the free surface.

Capillarity is defined as the phenomenon of rise or fall of a liquid surface in a small tube relative to the adjacent general level of liquid when the tube is held vertically in the liquid. Capillarity rise or fall is due to the combined effect of adhesion and cohesion.

Convective and Local Acceleration

2008-12-16T20:33:00.000-08:00

Convective acceleration is defined as the rate of change of velocity due to the change of position of fluid particles in a fluid flow.

Local acceleration or Temporal acceleration is defined as the rate of change of velocity with respect to time at a given point in a flow field.

Fluid Flows

2008-12-04T23:38:00.000-08:00

A flow is considered steady if the fluid characteristics like velocity, pressure, density, etc., at a point do not change with time.

Unsteady flow is defined as that type of flow in which the fluid characteristics like velocity, pressure, density change with respect to time. Eg. Flow of water in river.

A flow is said to be laminar when the various fluid particles move in layers (or laminae) with one layer of fluid sliding smoothly over an adjacent layer.

In a turbulent flow, the fluid particles move in an entirely haphazard or disorderly manner, that results in a rapid and continuous mixing of the fluid.

Compressible fluid is one in which the density changes from point to point.

Incompressible fluid is one in which the density is constant for the fluid flow.

When the velocity profile shape no longer changes with increasing distance, the flow is said to be fully developed.

Control Volume

2008-12-03T23:32:00.000-08:00

A control volume is an arbitrary volume in space through which fluid flows. The concept of control volume is used in fluid mechanics studies to understand the changes that take place in the fluid characteristics.

Viscosity

2008-12-03T16:53:00.000-08:00

Viscosity is a measure of the internal fluid friction that causes resistance to flow. It is defined as the shear stress required to produce unit rate of shear strain.

In SI units, viscosity is expressed in Ns/m².

Effect of Temperature on Viscosity of Water and Air
The viscosity of water decreases with the increase of temperature.
The viscosity of air increases with the increase of temperature.

Newtonian Fluids

2008-11-30T21:14:00.000-08:00

Newton’s law of Viscosity
Newton’s law of viscosity states that the shear stress on a fluid element layer is directly proportional to the rate of shear strain. The constant of proportionality used in Newton's equation is known as coefficient of viscosity.

What is a Newtonian Fluid?
Fluids that obey Newton’s law of viscosity are known as Newtonian fluids. In a Newtonian fluid, there is a linear relation between the magnitude of shear stress and the resulting rate of deformation.

Most of the common fluids follow Newton’s equation of viscosity. There are certain fluids which, however, do not follow Newton’s law of viscosity. Accordingly, fluids are classified as Newtonian fluids and non-Newtonian fluids.

Examples of Newtonian fluids
* Air
* Water
* Glycerine
* Kerosene

Examples of Non-Newtonian fluids
* Solutions or suspensions (slurries)
* Mud flows
* Polymer solutions
* Blood

Fluid Mechanics

2008-11-27T22:29:00.000-08:00

What is Fluid Mechanics?
Fluid Mechanics is the study of fluids at rest as well as in motion.

Applications of Fluid Mechanics
The applications of Fluid Mechanics are part and parcel of our day-to-day life. Wind mills, turbines, fans, pumps, airplanes, ships, pipe flow are some of the applications of fluid mechanics. Fluid Mechanics find applications in various fields like Civil Engineering, Mechanical Engineering, Aerospace Engineering, Chemical Engineering, Meteorology, Hydrology, Oceanography and the list continues. The varied and extensive amount of applications of Fluid Mechanics make it one of the fundamental and vital engineering studies.

Branches of Fluid Mechanics
The study of fluids can be broadly classified into three major branches:
1. Fluid Statics
2. Fluid Kinematics and
3. Fluid Dynamics

Ideal and Real Fluids

2008-11-27T21:21:00.000-08:00

Q: Distinguish between ideal and real fluids.

Ideal Fluids

Incompressible

It has zero viscosity

No resistance is encountered as the fluid moves

Real Fluids

Compressible

Viscous in nature

Certain amount of resistance is always offered by these fluids as they move

Real Fluids

2008-11-26T21:17:00.000-08:00

Q: What is a real fluid?

A: Real fluids are those fluids which are compressible and viscous in nature. A certain amount of resistance is always offered by these fluids when they are set in motion. Eg. Water.

Ideal Fluids

2008-11-25T21:01:00.000-08:00

Q: Define "Ideal Fluid".

A: An ideal fluid is one that is incompressible and has zero viscosity.

Fluid Mechanics Blog

2008-11-24T21:25:00.000-08:00

In this blog, I will share my knowledge about the subject of Fluid Mechanics or Mechanics of Fluids. It is an interesting subject and has a large number of practical applications.

I had a chance to study subjects like fluid mechanics, hydraulics, hydraulic machinery and hydrology during my undergraduate and postgraduate studies. I went on to teach these subjects for undergraduate students of Civil Engineering, Mechanical Engineering and Electrical and Electronics Engineering. Even though thats only for a short period of time, I have developed an interest for the subject and would like to put it down on this blog.

I do not claim any mastery over the subject of Fluid Mechanics. Rather, this blog is about my understanding of the concepts of Fluid mechanics and related subjects. Feel free to agree or disagree with my explanation of the concepts.