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Wednesday, 15 May 2019

May 15, 2019

HYDRAULIC TURBINES AND THEIR CLASSIFICATION

We were discussing a new topic, in the subject of fluid mechanics and hydraulics machine, i.e. an introduction to hydraulic machine in our recent posts. 

Now we will focus here to understand the basics of hydraulic turbines and classification of hydraulic turbines with the help of this post. Further we will find out, in our next post, some important terminologies associated with a hydraulic turbine such as Gross head, Net head and efficiencies of a hydraulic turbine. 

So let us start here with the basics and classification of hydraulic turbines. 

Hydraulic turbines 

Hydraulic turbines are basically defined as the hydraulic machines which convert hydraulic energy in to mechanical energy and this mechanical energy will be given to a generator to produce electric energy.

Now there will be one question that how this mechanical energy will be given to electric generator. Electric generator will be directly coupled with the hydraulic turbine and therefore mechanical energy, developed by hydraulic turbines, will be transmitted to electric generator and hence mechanical energy will be converted in to electrical energy. 

Electric power developed from hydraulic energy will be considered as hydroelectric power. We have used here term i.e. hydraulic energy that indicates the energy of water. 

Classifications of hydraulic turbines 

Hydraulic turbines will be classified on the basis of the type of energy available at the inlet of the hydraulic turbine, direction of flow through the vanes, head at the inlet of the hydraulic turbine and specific speed of the hydraulic turbine. 

Let us find out here a brief classification of hydraulic turbines as mentioned here. 

According to the type of energy at the inlet of the turbine

  1. Impulse turbine
  2. Reaction turbine

Impulse turbine:

If the energy available at the inlet of the hydraulic turbine is only kinetic energy, the hydraulic turbine will be considered as Impulse turbine.

Reaction turbine:

If the energy available at the inlet of the hydraulic turbine is kinetic energy and pressure energy, the hydraulic turbine will be considered as Reaction turbine. 

According to the direction of flow through runner

  1. Tangential flow turbine
  2. Radial flow turbine
  3. Axial flow turbine
  4. Mixed flow turbine 

Tangential flow turbine:

If the water flows along the tangent of the runner, the hydraulic turbine will be considered as Tangential flow turbine.

Radial flow turbine:

If the water flows in radial direction through the runner, the hydraulic turbine will be considered as Radial flow turbine. 

If the water flows in radial direction through the runner from outwards to inwards, the hydraulic turbine will be considered as inward radial flow turbine. 

If the water flows in radial direction through the runner from inwards to outwards, the hydraulic turbine will be considered as outward radial flow turbine. 

Axial flow turbine:

If the water flows through the runner along the direction parallel to the axis of rotation of the runner, the hydraulic turbine will be considered as axial flow turbine. 

Mixed flow turbine:

If the water flows through the runner in the radial direction but leaves in the direction parallel to the axis of rotation of the runner, the hydraulic turbine will be considered as mixed flow turbine. 

According to the head at the inlet of the turbine

  1. High head turbine
  2. Medium head turbine
  3. Low head turbine 

According to the specific speed of the turbine

  1. Low specific speed turbine
  2. Medium specific speed turbine
  3. High specific speed turbine 

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

Further we will find out, in our next post, some important terminologies associated with a hydraulic turbine such as Gross head, Net head and efficiencies of a hydraulic turbine. 

Reference: 

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

Also read  

Tuesday, 14 May 2019

May 14, 2019

INTRODUCTION TO HYDRAULIC MACHINES

We have seen various topics such as  force exerted by a jet on vertical flat plate,  force exerted by a jet on stationary inclined flat plateforce exerted by a jet on stationary curved plateforce exerted by a jet on a hinged plate,  force exerted by a jet on a curved plateforce exerted by a jet of water on a series of vanes,  force exerted by a jet of water on a series of radial curved vanes and basics of jet propulsion of ships in our recent posts. 

Now we will start here a new topic i.e. Hydraulic Machine with the help of this post. 

An introduction to hydraulic machine 

Let us first understand here the fundamental meaning of hydraulic machine. 

Hydraulic machines are basically defined as those machines which convert either hydraulic energy in to mechanical energy which will be further converted in to electrical energy or mechanical energy in to hydraulic energy. 

We can classify the hydraulic machines broadly in following two types as mentioned here

Hydraulic Turbine
Hydraulic Pump 

Hydraulic machines which convert hydraulic energy in to mechanical energy will be termed as hydraulic turbines. 

Let us see here Francis turbine as displayed here in following figure. 

Hydraulic machines which convert mechanical energy in to hydraulic energy will be termed as hydraulic pumps. 

Let us see here centrifugal pump as displayed here in following figure. 

Now we will be focused here and in our next post basically on the study of hydraulic turbines and hydraulic pumps. 

We will discuss hydraulic turbines in detail and further we will also find out the various types of hydraulic turbine such as Pelton turbine, Francis turbine and Kaplan turbine. 

Similarly, we will discuss hydraulic pumps in detail and further we will also find out the various types of hydraulic pumps such as reciprocating pumps and centrifugal pumps. 

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

Further, we will see hydraulic turbine and their classification, in the subject of fluid mechanics, with the help of our next post. 

Reference: 

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

Also read  

Monday, 13 May 2019

May 13, 2019

JET PROPULSION OF SHIPS

We have seen various topics such as  force exerted by a jet on vertical flat plate,  force exerted by a jet on stationary inclined flat plateforce exerted by a jet on stationary curved plateforce exerted by a jet on a hinged plate,  force exerted by a jet on a curved plateforce exerted by a jet of water on a series of vanes and force exerted by a jet of water on a series of radial curved vanes in our recent posts.  

Now we will see here the basics of jet propulsion of ships with the help of this post. Before going to study the basics of jet propulsion of ships, we must have information about the principle of jet propulsion

We have already discussed the principle of jet propulsion, in our previous post, where we have discussed the following terms as mentioned here.  
  • Jet Propulsion definition 
  • Jet propulsion of a tank with an orifice 
  • Condition for maximum efficiency 
  • Equation for maximum efficiency 

Now it’s time to discuss the basics of jet propulsion of ships, so let us take one cup of coffee and read this post. 

Jet propulsion of ships 

As we know that Jet propulsion means the propulsion or movement of the bodies such as ships, aircraft, rocket etc., with the help of jet. The reaction of the jet, coming out from the orifice provided in the bodies, is used to move the bodies. 

We will be interested here to study the movement of ships with the help of jet. A ship will be driven through water on the basis of principle and application of jet propulsion. 

A jet of water, which is discharged at the back of ship, will exert a propulsive force on the ship. Ship will have centrifugal pumps which will withdraw water from the surrounding area from sea. This water will be discharged through the orifice, provided at the back of ship, in the form of jet. 

Hence the reaction of jet, coming out at the back of the ship, will propel the ship in the opposite direction of the jet. 

There will be two way through which centrifugal pump will take water from surrounding sea 

Through inlet orifices, orifices which are at right angles to the direction of motion of the ship
Through inlet orifices, orifices which are facing the direction of motion of the ship

Case I –
Jet propulsion of the ship when inlet orifices are at right angles to the direction of motion of the ship

Following figure, displayed here, indicates a ship which is having the inlet orifices at right angles to the direction of motion of the ship. 

Propulsive force exerted on the ship, F = ρ a (V + u) x V

Work done per second, W = ρ a (V + u) x V x u 


Where,
V = Absolute velocity of jet of water coming at the back of the ship
u = Velocity of the ship
Vr = Relative velocity of jet with respect to jet = (V + u)

Case II –
Jet propulsion of the ship when inlet orifices are facing the direction of motion of the ship

Following figure, displayed here, indicates a ship which is having the inlet orifices facing the direction of motion of the ship. 

In this case, the expression for propelling force and work done per second will be identical as we have seen in case I i.e. when orifices are at right angles to the direction of motion of the ship.
Energy supplied by the jet in case II will be different. 

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

We will see another topic i.e. Introduction to hydraulic machines, in the subject of fluid mechanics, with the help of our next post.  

Reference: 

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

Also read  

Thursday, 9 May 2019

May 09, 2019

JET PROPULSION IN FLUID MECHANICS

We have seen various topics such as  force exerted by a jet on vertical flat plate,  force exerted by a jet on stationary inclined flat plateforce exerted by a jet on stationary curved plateforce exerted by a jet on a hinged plate,  force exerted by a jet on a curved plate, force exerted by a jet of water on a series of vanes and force exerted by a jet of water on a series of radial curved vanes in our recent posts. 

Now we will see here the basics of jet propulsion with the help of this post. Further, we will also find out here the following points as mentioned here. 

Jet Propulsion definition 
Jet propulsion of a tank with an orifice 
Condition for maximum efficiency 
Equation for maximum efficiency 

Let us start here our discussion with definition part of jet propulsion. 

Jet propulsion 

Jet propulsion means the propulsion or movement of the bodies such as ships, aircrafts, rocket etc., with the help of jet. 

The reaction of the jet, coming out from the orifice provided in the bodies, is used to move the bodies. 

Confused????......  Okay, let me explain you. 

Let us consider that a jet of fluid, coming out from an orifice provided in the body, striking a plate. Jet of fluid will exert the force on the plate, when fluid jet will strike the plate. The magnitude of this force, exerted by the jet of fluid over the surface of plate, will be determined on the basis of condition and shape of the plate. 

Magnitude of this force will be dependent over the factor e.g. whether plate is moving or stationary, whether plate is curved, flat or inclined. 

This force, exerted by the jet of fluid over the surface of plate, will be termed as action of jet. Let us recall Newton’s third law i.e. every action will have one equal and opposite reaction. 

Therefore jet of fluid while coming out from an orifice, provided in the body, will exert a force on the orifice or body in opposite direction in which jet will be coming out. Magnitude of this force will be equivalent to the action of jet. This force, acting on the orifice or body in opposite direction, will be termed as reaction of jet. 

If the body, in which orifice is fixed, is free to move. Body will be started to move in the opposite direction of jet of fluid. 

Jet propulsion of a tank with an orifice 

Let us consider we have one large tank and one orifice is fixed with the tank to its one side as displayed here in following figure. 

Let us consider the following terms from above figure. 

H = Constant head of water in tank from the orifice center 
a = Area of orifice 
V = Velocity of jet of fluid 
CV = Co-efficient of the velocity of orifice 
V = CV x Square root of (2 g H) = CV x (2 g H) 1/2
u = Velocity of tank 

Force exerted on the tank

Force exerted on the tank will be given by following formula as displayed here. 

Work done on the moving tank by jet of fluid

Work done on the moving tank by jet of fluid per second will be given by following formula as mentioned here. 

Efficiency of propulsion will be determined as mentioned here

Efficiency of propulsion = Work done per second / Kinetic energy of the issuing jet per second 
 

Condition and expression for maximum efficiency 

For a given value of V, efficiency will be maximum when dη/du = 0.
After differentiating the efficiency with respect to the velocity of tank i.e. u, we will have one condition for maximum efficiency i.e. V = u 

Condition for maximum efficiency, V = u 

After putting the value of V = u in the equation of maximum efficiency, we will have one value of maximum efficiency and that is 50%. 

Maximum efficiency = 50% 

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

We will see another topic i.e. Jet propulsion of ships, in the subject of fluid mechanics, with the help of our next post.  

Reference: 

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

Also read  

Monday, 6 May 2019

May 06, 2019

FORCE EXERTED ON A SERIES OF RADIAL CURVED VANES

We have seen the fundamentals of impact of jets, force exerted by a jet on vertical flat plate,  force exerted by a jet on stationary inclined flat plateforce exerted by a jet on stationary curved plateforce exerted by a jet on a hinged plate,  force exerted by a jet on a curved plate and force exerted by a jet ofwater on a series of vanes in our recent posts. 

Now we will see here the derivation of expression of force exerted by a jet of water on a series of radial curved vanes with the help of this post. Let us first brief here the basic concept of impact of jets and after that we will derive the expression of force exerted by a jet of water on a series of radial curved vanes.  

Impact of jets  

Let us consider that we have one pipe through which liquid is flowing under pressure. Let us assume that a nozzle is fitted at outlet of pipe. Liquid which will come through the outlet of nozzle will be in the form of jet.  

If a plate, which may be moving or fixed, is placed in the path of jet, there will be one force which will be exerted by the jet over the surface of plate. The force which will be exerted by the jet over the surface of plate, which might be moving or fixed, will be termed as impact of jet.  

Force exerted by a jet of water on a series of radial curved vanes 

If we see practically, force exerted by a jet of water on a single moving plate will not be feasible. 
Therefore, we will see the practical case where large number of plates will be mounted on the circumference of a wheel at a fixed distance apart as displayed here in following figure.  

Jet will strike a plate and due to the force exerted by the jet on plate, wheel will be started to move and therefore second plate mounted on the circumference of wheel will be appeared before the jet and jet will again exert the force to the second plate. 

Let us see here the condition of impact of jet on a series of radial curved vanes mounted on a wheel as displayed here in following figure. 

For a radial curved vane, the radius of the vane at inlet and outlet will be different and therefore the tangential velocities of the radial vane at inlet and outlet will be different. 

Jet of water will strike the vanes and the wheel will start rotating at a constant angular speed. Let us consider the following terms as mentioned here. 

R1 = Radius of wheel at the inlet of vane
R2 = Radius of wheel at the outlet of vane
ω = Angular speed of the wheel 

Velocity triangles at the inlet and outlet are drawn here in above figure. 



Efficiency of the radial curved vane 


Work done per second on the wheel will be considered as the output of the system and initial kinetic energy per second of the jet will be taken as input of the system. 

We can conclude here the efficiency of the radial curved vane as mentioned here. 

If there is no loss of energy when water is flowing over the vanes, the work done on the wheel per second will be equal to the change in kinetic energy of the jet per second. 

Work done per second on the wheel = Change in kinetic energy of the jet per second 

From the above expression, we can say that for a given initial velocity of the jet i.e. V1, the efficiency will be maximum when V2 will be minimum. But same time we can also conclude that V2 could not be zero, as in that condition incoming jet will not move out of the vane. 

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

We will see another topic i.e. Jet propulsion, in the subject of fluid mechanics, with the help of our next post. 

Reference: 


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

Also read  

Thursday, 28 March 2019

March 28, 2019

FORCE EXERTED BY A JET OF WATER ON A SERIES OF VANES

We have seen the fundamentals of impact of jets, force exerted by a jet on vertical flat plate,  force exerted by a jet on stationary inclined flat plate, force exerted by a jet on stationary curved plate, force exerted by a jet on a hinged plate and  force exerted by a jet on a curved plate when the plate is moving in the direction of jet in our recent post. 

Now we will see here the derivation of expression of force exerted by a jet of water on a series of vanes with the help of this post. Let us first brief here the basic concept of impact of jets and after that we will derive the expression of force exerted by a jet of water on a series of vanes. 

Impact of jets  

Let us consider that we have one pipe through which liquid is flowing under pressure. Let us assume that a nozzle is fitted at outlet of pipe. Liquid which will come through the outlet of nozzle will be in the form of jet. 

If a plate, which may be moving or fixed, is placed in the path of jet, there will be one force which will be exerted by the jet over the surface of plate. The force which will be exerted by the jet over the surface of plate, which might be moving or fixed, will be termed as impact of jet. 

Force exerted by a jet of water on a series of vanes 

If we see practically, force exerted by a jet of water on a single moving plate will not be feasible. Therefore, we will see the practical case where large number of plates will be mounted on the circumference of a wheel at a fixed distance apart as displayed here in following figure. 

Jet will strike a plate and due to the force exerted by the jet on plate, wheel will be started to move and therefore second plate mounted on the circumference of wheel will be appeared before the jet and jet will again exert the force to the second plate. 

Therefore, each plate will be appeared successively before the jet and jet will strike each plate or jet will exert force to each plate. Therefore, wheel will be rotated with a constant speed. 

Let us consider the following terms as mentioned here
V = Velocity of jet
d = Diameter of jet
a = Cross-sectional area of jet = (π/4) x d2
u = Velocity of vane 

Mass of water striking the series of plate per second = ρaV 

Jet strikes the plate with a velocity = V-u 

After striking, jet will move tangential to the plate and therefore velocity component in the direction of motion of plate will be zero. 

Force exerted by the jet in the direction of motion of plate
FX = Mass striking the series of plate per second x [Initial velocity – final velocity]
FX = ρaV [(V-u)-0] = ρaV (V-u) 

Work done by the jet on the series of plate per second = Force x Distance per second in the direction of force 

Work done by the jet on the series of plate per second = FX x u = ρaV (V-u) x u 

Kinetic energy of the jet per second = (1/2) x mV2
Kinetic energy of the jet per second = (1/2) x ρaV V2
Kinetic energy of the jet per second = (1/2) x ρaV

Efficiency = Work done per second / Kinetic energy per second 
Efficiency = ρaV (V-u) x u / (1/2) x ρaV3
Efficiency = 2 u (V-u)/V2

Maximum efficiency will be 50 % and it will be when u = V/2 

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

We will see another topic i.e. Force exerted on a series of radial curved vanes in the subject of fluid mechanics with the help of our next post. 

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

Also read