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Wednesday, 12 December 2018

December 12, 2018

MOMENTUM EQUATION FOR COMPRESSIBLE FLOW

We were discussing the basics of drag force &lift force and drag and lift coefficient in the subject of fluid mechanics, in our recent posts. 

We will discuss now a new topic i.e. compressible fluid flow, in the subject of fluid mechanics, with the help of this post. Before going in detail discussion about compressible flow, we must have basic knowledge about various equations associated with the compressible flow. 

Till now we were discussing the various concepts and equations such as continuity equation, Euler equation, Bernoulli’s equation and momentum equation for incompressible fluid flow. In same way we will have to discuss above equations for compressible fluid flow too. 

We have already seen the derivation of continuity equation and Bernoulli’s equation for compressible fluid flow in our previous post. We will start here our discussion about the compressible fluid flow with the basics of momentum equation for compressible fluid flow. 

Compressible flow is basically defined as the flow where fluid density could be changed during flow. 

Momentum equation for compressible fluid flow

The momentum per second of a flowing fluid will be equal to the product of mass per second and the velocity of flow. 

The momentum per second of a flowing fluid = Product of mass per second x Velocity of flow 

The momentum per second of a flowing fluid = ρ A V x V
ρ A V = Mass per second 

As we have already seen during discussion of continuity equation, term ρ A V will be constant at each section of flow. Therefore, the momentum per second of a flowing fluid will be equal to the product of mass per second which is a constant quantity and the velocity of flow. 

Therefore, we can say that momentum per second will not be affected due to compressible effect as term ρ A V is constant. In simple, we can say that momentum equation for incompressible and compressible fluid will be same. 

Momentum equation for compressible fluid for any direction will be given as mentioned here 

Momentum equation is based on the law of conservation of momentum or on the momentum principle. 

According to the law of conservation of momentum, net force acting on a fluid mass will be equivalent to the change in momentum of flow per unit time in that direction. 

Net force in a direction = Rate of change of momentum in same direction 
Net force in a direction = Mass per second x change of velocity 
Net force in a direction = ρ AV x [V2-V1

Further we will go ahead to find out the pressure wave and sound wave, in the subject of fluid mechanics, with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference: 
Fluid mechanics, By R. K. Bansal 
Image courtesy: Google 

Also read  

Monday, 10 December 2018

December 10, 2018

BERNOULLI’S EQUATION FOR COMPRESSIBLE FLUID FLOW

We were discussing the basics of drag force &lift force and drag and lift coefficient in the subject of fluid mechanics, in our recent posts. 

We will discuss now a new topic i.e. compressible fluid flow, in the subject of fluid mechanics, with the help of this post. Before going in detail discussion about compressible flow, we must have basic knowledge about various equations associated with the compressible flow. 

Till now we were discussing the various concepts and equations such as continuity equation Euler equation, Bernoulli’s equation and momentum equation for in-compressible fluid flow. In same way we will have to discuss above equations for compressible fluid flow too. 

We have already seen the derivation of continuity equation for compressible fluid flow in our previous post. We will start here our discussion about the compressible fluid flow with the derivation of Bernoulli’s equation for compressible fluid flow. 

Compressible flow is basically defined as the flow where fluid density could be changed during flow. 

Bernoulli’s equation for compressible fluid flow 

We will derive the Bernoulli’s equation for compressible fluid flow with the help of Euler’s equation. 

So, let us recall the Euler’s equation as mentioned here. 

In case of in-compressible fluid flow, the density of fluid will be constant and therefore the integral of dp/ρ will be equivalent to the P/ρ. 

We are interested here for compressible fluid flow and therefore the density of fluid will not be constant and therefore the integral of dp/ρ will not be equivalent to the P/ρ. 

In case of compressible fluid flow, the value of ρ will be changing and hence value of p will also be changing. Change in ρ and p will be dependent over the types of process during compressible fluid flow. 

We will now consider the various types of processes where pressure and temperature will be related with each other. We will secure the value of ρ in terms of p with the help of equations of these processes and we will use the value of ρ in above equation to secure the result of integral of dp/ρ. 

Bernoulli’s equation for isothermal process and for adiabatic process will be different. Let us first consider a basic process i.e. isothermal process. 

Bernoulli’s equation for compressible fluid for an isothermal process

We will secure here the value of ρ in terms of p with the help of following equation of isothermal process. 

PV = mRT, where temperature T will be constant
PV/m = RT = Constant
P/ ρ = Constant = C1
P/ ρ = C1
P / C1 = ρ

Above equation will be the Bernoulli’s equation for compressible fluid for an isothermal process. We can also write the Bernoulli’s equation for compressible fluid for an isothermal process for two points 1 and 2 as mentioned here. 

Bernoulli’s equation for compressible fluid for an adiabatic process 

We will secure here the value of ρ in terms of p with the help of following equation of adiabatic process. 

Above equation will be the Bernoulli’s equation for compressible fluid for an adiabatic process. We can also write the Bernoulli’s equation for compressible fluid for an adiabatic process for two points 1 and 2 as mentioned here. 

Further we will go ahead to find out the momentum equation for compressible fluid flow, in the subject of fluid mechanics, with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Image courtesy: Google  

Also read  

Friday, 7 December 2018

December 07, 2018

CONTINUITY EQUATION FOR COMPRESSIBLE FLUID FLOW

We were discussing the basics of Boundary layer theorylaminar boundary layerturbulent boundary layerboundary layer thickness, displacement thickness and momentum thicknessenergy thickness and drag force &lift force, in the subject of fluid mechanics, in our recent posts. 

After understanding the fundamentals of drag and lift coefficient, we will discuss now a new topic i.e. Compressible flow, in the subject of fluid mechanics, with the help of this post. Before going in detail discussion about compressible flow, we must have basic knowledge about various equations associated with the compressible flow. 

Till now we were discussing the various concepts and equations such as continuity equation Euler equation, Bernoulli’s equation and momentum equation for incompressible flow. In same way, we will start here our discussion about the compressible fluid flow with continuity equation. 

Compressible flow is basically defined as the flow where fluid density could be changed during flow. 

Continuity equation for compressible fluid flow 

As we know that continuity equation is based on the law of conservation of mass. 

According to the law of conservation of mass, matter could not be created and nor destroyed. In simple words, matter or mass will be constant. 

Therefore change in mass will be zero. Here, we will use this concept to find out the equation of continuity for compressible fluid flow. 

Let us write the equation now for conservation of mass for compressible fluid flow. Let us assume that fluid flow is one dimensional steady flow. 

Mass per second = Constant 
ρ AV = Constant 

Where, 
ρ = Density of fluid flow 
A = Area of cross-section 
V = Velocity of fluid flow 
Change of mass per second = 0 
d (ρ AV) = 0 
ρ d (AV) + AV dρ = 0 
ρ A dV +  ρ V dA + AV dρ = 0 

Now we will divide the above equation by term ρ A V 
Above equation is known as the continuity equation of compressible fluid flow. 

Further we will go ahead to find out the Bernoulli’s equation for compressible fluid flow, in the subject of fluid mechanics, with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Image courtesy: Google 

Also read  

Wednesday, 5 December 2018

December 05, 2018

DRAG AND LIFT COEFFICIENT IN FLUID MECHANICS

We were discussing the basics of Boundary layer theorylaminar boundary layerturbulent boundary layerboundary layer thickness, displacement thickness and momentum thicknessenergy thickness and drag force &lift force, in the subject of fluid mechanics, in our recent posts. 

After understanding the fundamentals of drag and lift force, we will see now drag and lift coefficient, with the help of this post. 

We have already discussed that drag and lift forces will be dependent over the various factors such as density of the fluid, upstream velocity, size, shape and orientation of the body. It will be quite easy to work with appropriate dimensionless numbers. 

These dimensionless numbers will represent the drag and lift characteristics of the body and these dimensionless numbers will be termed as drag coefficient and lift coefficient. 

Drag coefficient

Drag coefficient is basically defined as the ratio of drag force to the dynamic pressure. Drag coefficient could be determined with the help of following equation as mentioned here. Drag coefficient will be represented by CD

Lift coefficient

Lift coefficient is basically defined as the ratio of lift force to the dynamic pressure. Lift coefficient could be determined with the help of following equation as mentioned here. Lift coefficient will be represented by CL
Where, 
½ ρV2 = Dynamic pressure 
CD = Co-efficient of drag 
CL = Co-efficient of lift 
A = Area of the body which is projected area of the body perpendicular to the direction of flow 
FR = Resultant force on the body 
ρ = Density of the fluid 
V = Flow velocity relative to the object 

Further we will go ahead to start a new topic i.e.continuity equation for compressible fluid flow, in the subject of fluid mechanics, with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal 

Image courtesy: Google  

Also read  

Wednesday, 28 November 2018

November 28, 2018

PLUMBING TOOLS AND THEIR USES WITH PICTURES

We were discussing the various basic concepts of bearings such as Basic concept of bearings, Main functions of bearings, Bearing operating condition and various terminologies, Roller bearing basics and types, in the category of engineering practices or engineering maintenance, in our recent posts.  

Now we will go ahead to start a new topic in the field of engineering maintenance i.e. plumbing tools and their applications in our engineering life. 

Before going in detail, we should have one brief idea about the meaning of plumbing. Plumbing is basically the activities related with the laying of pipeline. 

Let us consider one example of leakage of water through a pipeline in your bathroom. The first question will be asked that how to arrest the water leakage. What you will do? 

You will start thinking about any plumber. But if we will have some basic knowledge about the plumbing tools and their applications, we can easily arrest such plumbing related issue. 

Therefore, let us find out here few basic plumbing tools and their applications in domestic and industrial areas. 

Classification of plumbing tools 

Pipe wrench 

A pipe wrench, as displayed here in following figure, is basically used for holding and turning the pipes. There are basically two types of pipe wrenches as mentioned here. 

Fixed wrenches 

Fixed wrenches are available with specific size and could not be adjusted. 

Adjustable wrenches 

Adjustable wrenches, as name indicates, could be adjusted within its given range. We can use an adjustable wrench for holding and turning the pipes of various sizes within the given range of the adjustable wrench. There will be one mechanism in adjustable wrench which will be rotated in order to move the jaw to secure the desired size. 
Fig: Pipe wrench

Pipe vice

Pipe vice, as displayed here in following figure, is basically used for gripping a pipe and preventing it from turning while cutting, threading, grinding and fitting of bends, couplings, nipples etc. 

Pipe vice will be fitted on the work bench. It will have one set of jaws, one jaw will be fixed and other jaw will be movable, to grip the pipe while doing the engineering activities such as cutting, threading, grinding etc. 
Fig: Pipe vice

Pipe cutter

Pipe cutter, as name indicates, is basically used for cutting pipes. Following figure shows a pipe cutter. A pipe cutter will have three wheels with hardened and sharp cutting edge along its periphery.
Out of three wheels of pipe cutter, one wheel will be adjustable to any desired distance for accommodating the various sizes of pipes. 

Once pipe will be adjusted at pipe cutter machine, cutter will be turned around the pipe and cutter wheel will cut the pipe along a circle. 
Fig: Pipe cutter

In current time, one modern pipe cutter is also available in market. In modern pipe cutter, there will be one electric motor and one cutting wheel. Cutting wheel will be driven via electric motor and it will be adjustable too for compensating the various diameters of pipes. 

There will be one set of jaws where pipe will be fixed to avoid any accident during cutting of pipe. Once pipe will be gripped properly, cutting wheel will be started and pressed along the pipes to cut the pipe. 
Fig: Pipe cutter

Hacksaw

Hacksaw is basically used for cutting pipes, fasteners, metal bar and rods. Workpiece will be fixed in vice and hacksaw will be used for cutting the workpiece at desired position. Hacksaw blade will be moved over the workpiece in forward and reverse direction for cutting the given workpiece. 

Cutting operation will only take place during forward stroke and hence forward stroke will also be termed as cutting stroke. While, reverse stroke will be termed as idle stroke as there will be no cutting operation during reverse direction motion of hacksaw. 

Following figure indicates the hacksaw and its various parts. 


Fig : hacksaw

Threading dies and taps

In order to provide the external threads over the surface of pipes, threading dies and taps are used. Threading dies and taps are displayed here in following figure. 

Threads will be developed in different shapes and sizes which will be used by fitting pipes inside a die handle. Length of thread will be dependent over the size of the pipe. 

Pipe will be fixed in vice and threads will be made with the help of die and die handle as displayed in following figure. 
Fig: Threading dies and taps

Files and rasps

Following figure indicates the files and rasps which is usually used in various assembly jobs, machining jobs in industrial areas. 

There will be sharp edge teeth over the surface of file and it will be used in order to remove the unwanted metal particle by rubbing file over the surface of workpiece. 
                                                                    Fig: Files and rasp

Rasp is basically used for securing the finishing surface of workpiece.

Plumb Bob

Plumb bob is a device which is used in alignment activity. Vertical alignment could be easily checked with the help of a plum bob. 

Material of casting for plum bob will be basically brass or steel. 
Fig: Plum bob
Further we will go ahead to start a new topic i.e. Pipes and fittings, in the subject of fluid mechanics, with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Image courtesy: Google  

Also read  

Monday, 26 November 2018

November 26, 2018

DRAG AND LIFT FORCE IN FLUID MECHANICS

We were discussing the basics of Boundary layer theorylaminar boundary layer, turbulent boundary layer, boundary layer thickness, displacement thickness and momentum thickness and energy thickness, in the subject of fluid mechanics, in our recent posts. 

After understanding the fundamentals of boundary layer, we will see here the concept of drag force, lift force and finally we will also find the expression for drag force and lift force with the help of this post. 

In fluid mechanics problems, it is very important to determine the forces that the fluid exerts on the body. Engineers usually apply the basics of such forces in order to quantify the efficiency and aerodynamic performance of the body. 

Before understanding the basics of lift force and drag force, we must understand here the forces acting on submerged bodies. 

There are basically two cases that we will see here. 

Case 1: Fluid is moving and body is stationary 

If a body is stationary and fluid is moving with a certain velocity, fluid will exert the force over the stationary submerged body. Force exerted by the moving air over the surface of a tree could be considered as one example of above case. 

Air is also a fluid and tree is submerged inside the air, now there will be one force which will be applied over the surface of tree by the moving fluid.    

Case 2: Fluid is stationary and body is moving 

If fluid is stationary and a body is moving with a certain velocity, there will be some force induced by the fluid on the body because moving body will cut the various layers of the fluid. 

Swimming through the water could be considered as one example of above case. Forces acting on submerged bodies will be divided in to drag force and lift force. 

Now we will go directly to the definition part of drag and lift forces. 


Drag Force  

Force exerted on the body in a direction parallel to the direction of motion when fluid is moving and body is stationary or body is moving and fluid is stationary. 

In simple we can say that force, which will be applied by the fluid over the body, in the direction of motion will be termed as drag force. 

Drag force will be represented by the symbol FD

Drag is basically an undesirable effect and we want to reduce the effect of drag because it takes power to overcome it. 

But in some cases, drag effect is good and beneficial such as in case of automobile brakes, parachutes. 


Lift force 

Lift force is basically defined as the force exerted on the body in a direction perpendicular to the direction of motion when fluid is moving and body is stationary or body is moving and fluid is stationary. 

Lift force will be represented by the symbol FL.

Where, 
CD = Co-efficient of drag 
CL = Co-efficient of lift 
A = Area of the body which is projected area of the body perpendicular to the direction of flow
FR = Resultant force on the body 
ρ = Density of the fluid 
V = Flow velocity relative to the object 

Further we will go ahead to start a new topic i.e. Drag and lift coefficient, in the subject of fluid mechanics, with the help of our next post. 

Do you have any suggestions? Please write in comment box.  

Reference: 

Fluid mechanics, By R. K. Bansal 

Image courtesy: Google  

Also read