Short Notes: Head Losses in Pipes, Bends & Fittings | Short Notes for Mechanical Engineering PDF Download

 Page 1


Head Losses in Pipes, Bends and Fittings 
Energy loss is categorized as
Major Loss Minor Loss
I l
Due to friction Due to
• sudden expansion of pipe
• sudden contraction of pipe
• bend in pipe
• any obstruction in pipe
Major Loss: It is calculated by Darcy Weisbach formulas 
Loss of head due to friction
4 fLx 
d -2
where, L = Length of pipe, v = Mean velocity of flow 
d = Diameter of pipe, f = Coefficient of friction
or h f = -
d ig J J
friction factor
for laminar flow
frictional factor(4f)
64
Re
Coefficient of friction / = —
Page 2


Head Losses in Pipes, Bends and Fittings 
Energy loss is categorized as
Major Loss Minor Loss
I l
Due to friction Due to
• sudden expansion of pipe
• sudden contraction of pipe
• bend in pipe
• any obstruction in pipe
Major Loss: It is calculated by Darcy Weisbach formulas 
Loss of head due to friction
4 fLx 
d -2
where, L = Length of pipe, v = Mean velocity of flow 
d = Diameter of pipe, f = Coefficient of friction
or h f = -
d ig J J
friction factor
for laminar flow
frictional factor(4f)
64
Re
Coefficient of friction / = —
For turbulent flow, coefficient of friction
0.079
J
Re7
Chezy's Formula: In fluid dynamics, Chezy's formula describes the mean flow 
velocity of steady, turbulent open channel flow.
Chezy’s formula of steady flow
v= c-Jmi.c = Chezv constant =
j = Loss of head per unit length of pipe
_ hf
~ T
(hydraulic slope tan 0) 
m = Hydraulic mean depth 
Mean velocity of flow
Area (A)
TJ'etred perimetr(p)
Relation between Coefficient of Friction and Shear Stress
We get
where, f = Coefficient of friction 
t o = Shear stress
Minor Loss: The another type of head loss in minor loss is induced due to following 
reasons
Loss due to Sudden Enlargement 
Head loss
Loss due to Sudden Contraction
Page 3


Head Losses in Pipes, Bends and Fittings 
Energy loss is categorized as
Major Loss Minor Loss
I l
Due to friction Due to
• sudden expansion of pipe
• sudden contraction of pipe
• bend in pipe
• any obstruction in pipe
Major Loss: It is calculated by Darcy Weisbach formulas 
Loss of head due to friction
4 fLx 
d -2
where, L = Length of pipe, v = Mean velocity of flow 
d = Diameter of pipe, f = Coefficient of friction
or h f = -
d ig J J
friction factor
for laminar flow
frictional factor(4f)
64
Re
Coefficient of friction / = —
For turbulent flow, coefficient of friction
0.079
J
Re7
Chezy's Formula: In fluid dynamics, Chezy's formula describes the mean flow 
velocity of steady, turbulent open channel flow.
Chezy’s formula of steady flow
v= c-Jmi.c = Chezv constant =
j = Loss of head per unit length of pipe
_ hf
~ T
(hydraulic slope tan 0) 
m = Hydraulic mean depth 
Mean velocity of flow
Area (A)
TJ'etred perimetr(p)
Relation between Coefficient of Friction and Shear Stress
We get
where, f = Coefficient of friction 
t o = Shear stress
Minor Loss: The another type of head loss in minor loss is induced due to following 
reasons
Loss due to Sudden Enlargement 
Head loss
Loss due to Sudden Contraction
Head loss,
•5
Remember Vi is velocity at point which lies in contracted section. 
Loss of Head at Entrance to Pipe 
Head loss,
Loss at Exit from Pipe 
Head loss,
Note: In case 1 and 2, flow occurs between pipe to pipe, while in case 3 and 4, flow 
occurs between tank and pipe. We are taking entry or exit w.r.t. pipe. So, be careful. 
Combination of Pipes: Pipes may be connected in series, parallel or in both. Let see 
their combinations.
Pipe in Series: As pipes are in series, the discharge through each pipe will be same.
Q = A-|Vi = A2V 2 = A3V 3
Total loss of head = Major loss + Minor loss
H = h L + h k
Major loss = Head loss 
due to friction in each pipe
\ = hA+ h A + hA
= fA'i , fA 'i , f-A'i
d:.2g d:.2g dy 2g
While, minor loss = Entrance loss + Expansion loss + Contraction loss + Exit loss
h = OSvf _ (v ^ v ,)2 Q-5v; ±
k 2g 2g 2 g 2 g
If minor loss are neglected then,
H _ f iLt f , f A ' i ,
dv2g dy2g d..2g
n _ f\L \Q ' | A L z Q Z | fAQz
1 2 1 d{ ^ 12 -1^ ^ 12 1 d l
Page 4


Head Losses in Pipes, Bends and Fittings 
Energy loss is categorized as
Major Loss Minor Loss
I l
Due to friction Due to
• sudden expansion of pipe
• sudden contraction of pipe
• bend in pipe
• any obstruction in pipe
Major Loss: It is calculated by Darcy Weisbach formulas 
Loss of head due to friction
4 fLx 
d -2
where, L = Length of pipe, v = Mean velocity of flow 
d = Diameter of pipe, f = Coefficient of friction
or h f = -
d ig J J
friction factor
for laminar flow
frictional factor(4f)
64
Re
Coefficient of friction / = —
For turbulent flow, coefficient of friction
0.079
J
Re7
Chezy's Formula: In fluid dynamics, Chezy's formula describes the mean flow 
velocity of steady, turbulent open channel flow.
Chezy’s formula of steady flow
v= c-Jmi.c = Chezv constant =
j = Loss of head per unit length of pipe
_ hf
~ T
(hydraulic slope tan 0) 
m = Hydraulic mean depth 
Mean velocity of flow
Area (A)
TJ'etred perimetr(p)
Relation between Coefficient of Friction and Shear Stress
We get
where, f = Coefficient of friction 
t o = Shear stress
Minor Loss: The another type of head loss in minor loss is induced due to following 
reasons
Loss due to Sudden Enlargement 
Head loss
Loss due to Sudden Contraction
Head loss,
•5
Remember Vi is velocity at point which lies in contracted section. 
Loss of Head at Entrance to Pipe 
Head loss,
Loss at Exit from Pipe 
Head loss,
Note: In case 1 and 2, flow occurs between pipe to pipe, while in case 3 and 4, flow 
occurs between tank and pipe. We are taking entry or exit w.r.t. pipe. So, be careful. 
Combination of Pipes: Pipes may be connected in series, parallel or in both. Let see 
their combinations.
Pipe in Series: As pipes are in series, the discharge through each pipe will be same.
Q = A-|Vi = A2V 2 = A3V 3
Total loss of head = Major loss + Minor loss
H = h L + h k
Major loss = Head loss 
due to friction in each pipe
\ = hA+ h A + hA
= fA'i , fA 'i , f-A'i
d:.2g d:.2g dy 2g
While, minor loss = Entrance loss + Expansion loss + Contraction loss + Exit loss
h = OSvf _ (v ^ v ,)2 Q-5v; ±
k 2g 2g 2 g 2 g
If minor loss are neglected then,
H _ f iLt f , f A ' i ,
dv2g dy2g d..2g
n _ f\L \Q ' | A L z Q Z | fAQz
1 2 1 d{ ^ 12 -1^ ^ 12 1 d l
Pipes in Parallel: In this discharge in main pipe is equal to sum of discharge in 
each of parallel pipes.
Oi
Hence, Q = Qi + Q 2
Loss of head in each parallel pipe is same
K = K
or
d \ 2S ~ di 2g 1 2 ld! ~ 1 2 ldl 
where,
K
and
hf,
are head loss at 1 and 2 respectively.
Equivalent Pipe: A compound pipe which consists of several pipes of different 
lengths and diameters to be replaced by a pipe having uniform diameter and the 
same length as that of compound pipe is called as equivalent pipe.
K = hf +hf A hn
flQr fiLQ2 | fAQ1 fAQ2
12 Ad- 12.1 d{ 12.1 d[ 12.1 d\
(where, L = Li + L2 + L3 )
If f = fi =f2 = f3 
Then,
L _ L X L2 I 3 I _ I j Z, I,
d r ~~d[ 71 7 ! = ' 7 r ~ 7 F 7[ 7 !
1 2 1 2 3
Hydraulic Gradient Line (HGL) and Total Energy Line (TEL)
Page 5


Head Losses in Pipes, Bends and Fittings 
Energy loss is categorized as
Major Loss Minor Loss
I l
Due to friction Due to
• sudden expansion of pipe
• sudden contraction of pipe
• bend in pipe
• any obstruction in pipe
Major Loss: It is calculated by Darcy Weisbach formulas 
Loss of head due to friction
4 fLx 
d -2
where, L = Length of pipe, v = Mean velocity of flow 
d = Diameter of pipe, f = Coefficient of friction
or h f = -
d ig J J
friction factor
for laminar flow
frictional factor(4f)
64
Re
Coefficient of friction / = —
For turbulent flow, coefficient of friction
0.079
J
Re7
Chezy's Formula: In fluid dynamics, Chezy's formula describes the mean flow 
velocity of steady, turbulent open channel flow.
Chezy’s formula of steady flow
v= c-Jmi.c = Chezv constant =
j = Loss of head per unit length of pipe
_ hf
~ T
(hydraulic slope tan 0) 
m = Hydraulic mean depth 
Mean velocity of flow
Area (A)
TJ'etred perimetr(p)
Relation between Coefficient of Friction and Shear Stress
We get
where, f = Coefficient of friction 
t o = Shear stress
Minor Loss: The another type of head loss in minor loss is induced due to following 
reasons
Loss due to Sudden Enlargement 
Head loss
Loss due to Sudden Contraction
Head loss,
•5
Remember Vi is velocity at point which lies in contracted section. 
Loss of Head at Entrance to Pipe 
Head loss,
Loss at Exit from Pipe 
Head loss,
Note: In case 1 and 2, flow occurs between pipe to pipe, while in case 3 and 4, flow 
occurs between tank and pipe. We are taking entry or exit w.r.t. pipe. So, be careful. 
Combination of Pipes: Pipes may be connected in series, parallel or in both. Let see 
their combinations.
Pipe in Series: As pipes are in series, the discharge through each pipe will be same.
Q = A-|Vi = A2V 2 = A3V 3
Total loss of head = Major loss + Minor loss
H = h L + h k
Major loss = Head loss 
due to friction in each pipe
\ = hA+ h A + hA
= fA'i , fA 'i , f-A'i
d:.2g d:.2g dy 2g
While, minor loss = Entrance loss + Expansion loss + Contraction loss + Exit loss
h = OSvf _ (v ^ v ,)2 Q-5v; ±
k 2g 2g 2 g 2 g
If minor loss are neglected then,
H _ f iLt f , f A ' i ,
dv2g dy2g d..2g
n _ f\L \Q ' | A L z Q Z | fAQz
1 2 1 d{ ^ 12 -1^ ^ 12 1 d l
Pipes in Parallel: In this discharge in main pipe is equal to sum of discharge in 
each of parallel pipes.
Oi
Hence, Q = Qi + Q 2
Loss of head in each parallel pipe is same
K = K
or
d \ 2S ~ di 2g 1 2 ld! ~ 1 2 ldl 
where,
K
and
hf,
are head loss at 1 and 2 respectively.
Equivalent Pipe: A compound pipe which consists of several pipes of different 
lengths and diameters to be replaced by a pipe having uniform diameter and the 
same length as that of compound pipe is called as equivalent pipe.
K = hf +hf A hn
flQr fiLQ2 | fAQ1 fAQ2
12 Ad- 12.1 d{ 12.1 d[ 12.1 d\
(where, L = Li + L2 + L3 )
If f = fi =f2 = f3 
Then,
L _ L X L2 I 3 I _ I j Z, I,
d r ~~d[ 71 7 ! = ' 7 r ~ 7 F 7[ 7 !
1 2 1 2 3
Hydraulic Gradient Line (HGL) and Total Energy Line (TEL)
I *2
---- Datum
Equivalent pipe diagram
HGL —? It joins piezometric head
at various points.
TEL - ? It joins total energy head at various points
A + , + 1 1
PS -gj
Note: HGL is always parallel but lower than TEL. 
Power Transmission through Pipe (P)
Through pipe 
Wheel
= 0
Power transmission through pipe
P ^ = PSQH
= PgQ iH - hf ) 
h f = Head loss
H - hf
Efficiency rj = '
Power delivered by a given pipe line is maximum when the flow is such that one 
third of static head is consumed in pipe friction. Thus, efficiency is limited to only 
66.66%
Maximum efficiency,
_ H _
Water Hammer: When a liquid is flowing through a long pipe fitted with a vale at the 
end of the pipe and the valve is closed suddenly a pressure wave of high intensity 
is produced behind the valve. This pressure wave of high intensity is having the 
effect of hammering action on the walls of the pipe. This phenomenon is known as 
water hammer.
Intensity of pressure rise due to water hammer,
pLv
When valve is closed gradually when valve closed suddenly with rigid pipe