Short Notes: Impulse and Reaction Principles | Short Notes for Mechanical Engineering PDF Download

 Page 1


Impulse and Reaction Principles
Turbo machines are classified as impulse and reaction machines depending on the 
relative proportions of the static and dynamic heads involved in the energy transfer. 
To aid this, we define a term referred to as degree of reaction Rd.
Degree of reaction Rd can be defined as the ratio of static head to the total head in 
the energy transfer.
R (u ^ - r ; - ( v fl- " -
(v i‘ - V j) + (uf - U j) - (v ( : -
Degree of reaction can be zero, positive or negative.
Rd=0, characterizes a close turbo machine for which a static head is equal to zero. 
In the most general case, this will happen if Ui = U2 and Vri = Vr2.
These classes of turbo machines are referred to as impulse machines. In most 
practical situations Vr2 may be less than Vr 1 even though r- i = r2.
This is generally due to frictional losses. Even then a machine is referred to as an 
axial flow turbines and pumps would have n = r2 and if Vri = Vr2 , then they become 
examples of pure impulse machines.
Pelton Wheel, tangential flow hydraulic machines is also example of impulse 
machine.
Velocity Triangles for impulse machine: Velocity triangle for axial flow impulse 
machine is shown in the following figure.
Page 2


Impulse and Reaction Principles
Turbo machines are classified as impulse and reaction machines depending on the 
relative proportions of the static and dynamic heads involved in the energy transfer. 
To aid this, we define a term referred to as degree of reaction Rd.
Degree of reaction Rd can be defined as the ratio of static head to the total head in 
the energy transfer.
R (u ^ - r ; - ( v fl- " -
(v i‘ - V j) + (uf - U j) - (v ( : -
Degree of reaction can be zero, positive or negative.
Rd=0, characterizes a close turbo machine for which a static head is equal to zero. 
In the most general case, this will happen if Ui = U2 and Vri = Vr2.
These classes of turbo machines are referred to as impulse machines. In most 
practical situations Vr2 may be less than Vr 1 even though r- i = r2.
This is generally due to frictional losses. Even then a machine is referred to as an 
axial flow turbines and pumps would have n = r2 and if Vri = Vr2 , then they become 
examples of pure impulse machines.
Pelton Wheel, tangential flow hydraulic machines is also example of impulse 
machine.
Velocity Triangles for impulse machine: Velocity triangle for axial flow impulse 
machine is shown in the following figure.
The velocity of whirl at exit is to be calculated by general expression,
v w, - U , - V ; C05 5 ,
If the value obtained is negative, then it suggests that
V rJ cos 5, > U ,
If Vw2 is positive, then OVT would appear as follows:
If V2=0, then the OVT would look like
U 2
Radial flow Pump and Compressors: 
General analysis:
Page 3


Impulse and Reaction Principles
Turbo machines are classified as impulse and reaction machines depending on the 
relative proportions of the static and dynamic heads involved in the energy transfer. 
To aid this, we define a term referred to as degree of reaction Rd.
Degree of reaction Rd can be defined as the ratio of static head to the total head in 
the energy transfer.
R (u ^ - r ; - ( v fl- " -
(v i‘ - V j) + (uf - U j) - (v ( : -
Degree of reaction can be zero, positive or negative.
Rd=0, characterizes a close turbo machine for which a static head is equal to zero. 
In the most general case, this will happen if Ui = U2 and Vri = Vr2.
These classes of turbo machines are referred to as impulse machines. In most 
practical situations Vr2 may be less than Vr 1 even though r- i = r2.
This is generally due to frictional losses. Even then a machine is referred to as an 
axial flow turbines and pumps would have n = r2 and if Vri = Vr2 , then they become 
examples of pure impulse machines.
Pelton Wheel, tangential flow hydraulic machines is also example of impulse 
machine.
Velocity Triangles for impulse machine: Velocity triangle for axial flow impulse 
machine is shown in the following figure.
The velocity of whirl at exit is to be calculated by general expression,
v w, - U , - V ; C05 5 ,
If the value obtained is negative, then it suggests that
V rJ cos 5, > U ,
If Vw2 is positive, then OVT would appear as follows:
If V2=0, then the OVT would look like
U 2
Radial flow Pump and Compressors: 
General analysis:
U1
I V T
0 V T (preferred)
1. ) Vr ,; U2 > v^ u ,
i_e. U ; > Uj or r: > r t flow is radially outward.
2. ) AxialentrvVj =
3 . ) P = “ v w,U,,\Vatt 
V ,u
H = — * —* - m of fluid, 
a
Most of the turbo machines belong to this class. In general, they have a restricted 
flow area for a given rotor diameter and have low to medium specific speed. 
Significant aspects:
1. Flow is outwards from the smaller to larger radius the Euler's turbine 
equation, i.e.,
p = ^ (\^ U 1- \ ^ l J2)
requires that
for pumps and compressors which are power absorbing machines. For this 
sake radial flow compressors and pumps generally have fluid entering at a 
smaller radius and leaving at a larger radius.
Page 4


Impulse and Reaction Principles
Turbo machines are classified as impulse and reaction machines depending on the 
relative proportions of the static and dynamic heads involved in the energy transfer. 
To aid this, we define a term referred to as degree of reaction Rd.
Degree of reaction Rd can be defined as the ratio of static head to the total head in 
the energy transfer.
R (u ^ - r ; - ( v fl- " -
(v i‘ - V j) + (uf - U j) - (v ( : -
Degree of reaction can be zero, positive or negative.
Rd=0, characterizes a close turbo machine for which a static head is equal to zero. 
In the most general case, this will happen if Ui = U2 and Vri = Vr2.
These classes of turbo machines are referred to as impulse machines. In most 
practical situations Vr2 may be less than Vr 1 even though r- i = r2.
This is generally due to frictional losses. Even then a machine is referred to as an 
axial flow turbines and pumps would have n = r2 and if Vri = Vr2 , then they become 
examples of pure impulse machines.
Pelton Wheel, tangential flow hydraulic machines is also example of impulse 
machine.
Velocity Triangles for impulse machine: Velocity triangle for axial flow impulse 
machine is shown in the following figure.
The velocity of whirl at exit is to be calculated by general expression,
v w, - U , - V ; C05 5 ,
If the value obtained is negative, then it suggests that
V rJ cos 5, > U ,
If Vw2 is positive, then OVT would appear as follows:
If V2=0, then the OVT would look like
U 2
Radial flow Pump and Compressors: 
General analysis:
U1
I V T
0 V T (preferred)
1. ) Vr ,; U2 > v^ u ,
i_e. U ; > Uj or r: > r t flow is radially outward.
2. ) AxialentrvVj =
3 . ) P = “ v w,U,,\Vatt 
V ,u
H = — * —* - m of fluid, 
a
Most of the turbo machines belong to this class. In general, they have a restricted 
flow area for a given rotor diameter and have low to medium specific speed. 
Significant aspects:
1. Flow is outwards from the smaller to larger radius the Euler's turbine 
equation, i.e.,
p = ^ (\^ U 1- \ ^ l J2)
requires that
for pumps and compressors which are power absorbing machines. For this 
sake radial flow compressors and pumps generally have fluid entering at a 
smaller radius and leaving at a larger radius.
2. The absolute velocity at inlet is oriented parallel to the axes of the shaft i.e., 
Vai = Vi and hence there is no whirl component at inlet i.e.,Vwi = 0.
3. Since Vwi = 0, the energy transferred is purely a function of exit condition i.e.
P = — V w , U , . \ V f l t t 
t * '
H = — m o f f l u i d 
9
Head-capacity relationship:
H = - i i
H = —M U . —V ,, cot 3,1
9 ' "
Q = , = A ,V „
H =
u ;
T 7
Q c o t 3 :
9 A ,
U * U , c o t 3 ;
g 9 A ,
H = K j — K , Q ( c o n s i d e r i n s r o t o r o p e r a t i n e f o r a g i v e n s p e e d . ) 
' ‘ ‘
9
3 < 9 0 '~
B a c k w a r d c u n -e d v a n e
3 = 9 C f 3 > 9 0 :
R a d i a l v a n e F o r w a r d c u r v e d v a n e
From the velocity triangles for the 3 types of vanes it may be noticed that the whirl 
component at exit is least for backward curved vane (j3<90° and most for a forward 
curved vane. When operating under similar condition of speed and cross section 
area. But from a practical view point a high value of exit velocity V2 is not 
desirable. This is because it becomes necessary to construct a diffuser of 
unreasonably large dimensions even for moderate sized rotors. Hence backward 
curved vane with 02 in the range of 20-25 degrees is preferred for radial flow pumps
Page 5


Impulse and Reaction Principles
Turbo machines are classified as impulse and reaction machines depending on the 
relative proportions of the static and dynamic heads involved in the energy transfer. 
To aid this, we define a term referred to as degree of reaction Rd.
Degree of reaction Rd can be defined as the ratio of static head to the total head in 
the energy transfer.
R (u ^ - r ; - ( v fl- " -
(v i‘ - V j) + (uf - U j) - (v ( : -
Degree of reaction can be zero, positive or negative.
Rd=0, characterizes a close turbo machine for which a static head is equal to zero. 
In the most general case, this will happen if Ui = U2 and Vri = Vr2.
These classes of turbo machines are referred to as impulse machines. In most 
practical situations Vr2 may be less than Vr 1 even though r- i = r2.
This is generally due to frictional losses. Even then a machine is referred to as an 
axial flow turbines and pumps would have n = r2 and if Vri = Vr2 , then they become 
examples of pure impulse machines.
Pelton Wheel, tangential flow hydraulic machines is also example of impulse 
machine.
Velocity Triangles for impulse machine: Velocity triangle for axial flow impulse 
machine is shown in the following figure.
The velocity of whirl at exit is to be calculated by general expression,
v w, - U , - V ; C05 5 ,
If the value obtained is negative, then it suggests that
V rJ cos 5, > U ,
If Vw2 is positive, then OVT would appear as follows:
If V2=0, then the OVT would look like
U 2
Radial flow Pump and Compressors: 
General analysis:
U1
I V T
0 V T (preferred)
1. ) Vr ,; U2 > v^ u ,
i_e. U ; > Uj or r: > r t flow is radially outward.
2. ) AxialentrvVj =
3 . ) P = “ v w,U,,\Vatt 
V ,u
H = — * —* - m of fluid, 
a
Most of the turbo machines belong to this class. In general, they have a restricted 
flow area for a given rotor diameter and have low to medium specific speed. 
Significant aspects:
1. Flow is outwards from the smaller to larger radius the Euler's turbine 
equation, i.e.,
p = ^ (\^ U 1- \ ^ l J2)
requires that
for pumps and compressors which are power absorbing machines. For this 
sake radial flow compressors and pumps generally have fluid entering at a 
smaller radius and leaving at a larger radius.
2. The absolute velocity at inlet is oriented parallel to the axes of the shaft i.e., 
Vai = Vi and hence there is no whirl component at inlet i.e.,Vwi = 0.
3. Since Vwi = 0, the energy transferred is purely a function of exit condition i.e.
P = — V w , U , . \ V f l t t 
t * '
H = — m o f f l u i d 
9
Head-capacity relationship:
H = - i i
H = —M U . —V ,, cot 3,1
9 ' "
Q = , = A ,V „
H =
u ;
T 7
Q c o t 3 :
9 A ,
U * U , c o t 3 ;
g 9 A ,
H = K j — K , Q ( c o n s i d e r i n s r o t o r o p e r a t i n e f o r a g i v e n s p e e d . ) 
' ‘ ‘
9
3 < 9 0 '~
B a c k w a r d c u n -e d v a n e
3 = 9 C f 3 > 9 0 :
R a d i a l v a n e F o r w a r d c u r v e d v a n e
From the velocity triangles for the 3 types of vanes it may be noticed that the whirl 
component at exit is least for backward curved vane (j3<90° and most for a forward 
curved vane. When operating under similar condition of speed and cross section 
area. But from a practical view point a high value of exit velocity V2 is not 
desirable. This is because it becomes necessary to construct a diffuser of 
unreasonably large dimensions even for moderate sized rotors. Hence backward 
curved vane with 02 in the range of 20-25 degrees is preferred for radial flow pumps
and compressors. Forward curved vanes are not preferred while radial vanes 
(j8=90°) are used in select applications requiring very high pressure.
Expression for Degree of reaction in terms of rotor velocity and rotor blade angles: 
We know that, Degree of reaction is given by,
ft--- £ • : ) - < - r ;..
( I- - V ;) + ( U ;- U ;) - ( J T :-V ^ )
Ki = Vl - (Va tan7lf = V' (1 - tan: 7l)
R =
*- =
Ki - Ki = K (tan; 7 , — tan: 7 )
For a pump it is generally acceptable to write degree of reaction as
V 'jta n 2 v2 - tan:
< y { - i\ :)- (y T \ - v r \)
We know that, Euler’s turbine equation for a pump may be written as
' ( K - v ; )
• >
[ \ - S s. - y j
Degree of reaction is the ratio of suction head to the total head. Which may be 
written as
{ v l i Y k
\ y
~Vl ) - ( V r2
R _ 7 > - 1 ,-ta n ;]
d 2UVJ\an yx - tan 7 , ]
„ re ta il 7 i + tan 7 ,]
A. —
2UV
a
R _ r ; [tan p + tan {3- ]
' 2U tan J tan /3,
General analysis of Turbines:
They are power generating turbo machines, which run on both incompressible 
fluids such as water as well as compressible fluids such as gases.
The efficiency of turbines may be defined as the ratio of actual work output to the 
fluid energy input.
This involves 2 types of efficiencies: