Formula Sheets: Hydraulic Machines: Turbines & Pumps | Fluid Mechanics for Civil Engineering - Civil Engineering (CE) PDF Download

 Page 1


Hydr aulic Machines: Turbines & Pumps
F ormula Sheet for GA TE Civil Engineering
Fluid Mechanics: Hydr aulic Machines (Turbines &
Pumps)
1. Turbines: Basic Concepts
• Power Output :
P =?gQH?
whereP = power (W),? = density of water , g = gr avitational acceler ation, Q =
discharge,H = net head,? = o ver all efficiency .
• Efficiencies :
– Hydr aulic efficiency ( ?
h
): ?
h
=
Power delivered to runner
?gQH
– Mechanical efficiency ( ?
m
): ?
m
=
Power output
Power delivered to runner
– Over all efficiency ( ? ): ? =?
h
·?
m
2. Classification of Turbines
• Impulse Turbines (e.g., Pelton):
Power =?Q(V
1
-u)(1+ cosß)u
whereV
1
= jet velocity ,u = blade speed,ß = blade angle.
• Reaction Turbines (e.g., Fr ancis, Kaplan):
Power =?Q(V
w1
u
1
-V
w2
u
2
)
whereV
w1
,V
w2
= whirl components of velocity at inlet and outlet,u
1
,u
2
= blade
speeds.
1
Page 2


Hydr aulic Machines: Turbines & Pumps
F ormula Sheet for GA TE Civil Engineering
Fluid Mechanics: Hydr aulic Machines (Turbines &
Pumps)
1. Turbines: Basic Concepts
• Power Output :
P =?gQH?
whereP = power (W),? = density of water , g = gr avitational acceler ation, Q =
discharge,H = net head,? = o ver all efficiency .
• Efficiencies :
– Hydr aulic efficiency ( ?
h
): ?
h
=
Power delivered to runner
?gQH
– Mechanical efficiency ( ?
m
): ?
m
=
Power output
Power delivered to runner
– Over all efficiency ( ? ): ? =?
h
·?
m
2. Classification of Turbines
• Impulse Turbines (e.g., Pelton):
Power =?Q(V
1
-u)(1+ cosß)u
whereV
1
= jet velocity ,u = blade speed,ß = blade angle.
• Reaction Turbines (e.g., Fr ancis, Kaplan):
Power =?Q(V
w1
u
1
-V
w2
u
2
)
whereV
w1
,V
w2
= whirl components of velocity at inlet and outlet,u
1
,u
2
= blade
speeds.
1
3. Specific Speed of Turbines
• Specific Speed ( N
s
) : Dimensionless par ameter to select turbine type.
N
s
=
N
v
P
v
gH
5/4
whereN = rotational speed (rpm),P = power (kW),H = head (m).
• Typical r anges:
– Pelton: N
s
= 10-50
– Fr ancis: N
s
= 50-250
– Kaplan: N
s
= 250-1000
4. Pumps: Basic Concepts
• Power Input :
P =
?gQH
?
whereH = total dynamic head,? = pump efficiency .
• T otal Dynamic Head :
H =h
s
+h
d
+h
f
+
V
2
2g
whereh
s
= suction head,h
d
= delivery head,h
f
= friction head loss,V = velocity .
5. Specific Speed of Pumps
• Specific Speed ( N
s
) :
N
s
=
N
v
Q
H
3/4
whereN = rotational speed (rpm),Q = discharge (m
3
/s),H = head (m).
• Typical r anges:
– Centrifugal pumps: N
s
= 10-80
– Mixed flow pumps: N
s
= 80-160
– Axial flow pumps: N
s
= 160-400
6. Pump Performance
• Head-Discharge Relationship : Obtained from pump char acteristic curves.
• Efficiency ( ? ) :
? =
W ater power output
Power input
=
?gQH
P
2
Page 3


Hydr aulic Machines: Turbines & Pumps
F ormula Sheet for GA TE Civil Engineering
Fluid Mechanics: Hydr aulic Machines (Turbines &
Pumps)
1. Turbines: Basic Concepts
• Power Output :
P =?gQH?
whereP = power (W),? = density of water , g = gr avitational acceler ation, Q =
discharge,H = net head,? = o ver all efficiency .
• Efficiencies :
– Hydr aulic efficiency ( ?
h
): ?
h
=
Power delivered to runner
?gQH
– Mechanical efficiency ( ?
m
): ?
m
=
Power output
Power delivered to runner
– Over all efficiency ( ? ): ? =?
h
·?
m
2. Classification of Turbines
• Impulse Turbines (e.g., Pelton):
Power =?Q(V
1
-u)(1+ cosß)u
whereV
1
= jet velocity ,u = blade speed,ß = blade angle.
• Reaction Turbines (e.g., Fr ancis, Kaplan):
Power =?Q(V
w1
u
1
-V
w2
u
2
)
whereV
w1
,V
w2
= whirl components of velocity at inlet and outlet,u
1
,u
2
= blade
speeds.
1
3. Specific Speed of Turbines
• Specific Speed ( N
s
) : Dimensionless par ameter to select turbine type.
N
s
=
N
v
P
v
gH
5/4
whereN = rotational speed (rpm),P = power (kW),H = head (m).
• Typical r anges:
– Pelton: N
s
= 10-50
– Fr ancis: N
s
= 50-250
– Kaplan: N
s
= 250-1000
4. Pumps: Basic Concepts
• Power Input :
P =
?gQH
?
whereH = total dynamic head,? = pump efficiency .
• T otal Dynamic Head :
H =h
s
+h
d
+h
f
+
V
2
2g
whereh
s
= suction head,h
d
= delivery head,h
f
= friction head loss,V = velocity .
5. Specific Speed of Pumps
• Specific Speed ( N
s
) :
N
s
=
N
v
Q
H
3/4
whereN = rotational speed (rpm),Q = discharge (m
3
/s),H = head (m).
• Typical r anges:
– Centrifugal pumps: N
s
= 10-80
– Mixed flow pumps: N
s
= 80-160
– Axial flow pumps: N
s
= 160-400
6. Pump Performance
• Head-Discharge Relationship : Obtained from pump char acteristic curves.
• Efficiency ( ? ) :
? =
W ater power output
Power input
=
?gQH
P
2
• Net Positive Suction Head (NPSH) :
NPSH =
p
a
?g
+h
s
-
p
v
?g
-h
f
wherep
a
= atmospheric pressure, p
v
= vapor pressure, h
s
= suction head, h
f
=
friction loss in suction pipe.
7. Cavitation
• Occurs when NPSH< NPSH
required
.
• Thoma’ s Cavitation F actor (s ) :
s =
NPSH
H
Criticals varies with specific speed.
8. Pump S ystems
• Pumps in Series : T otal head adds up, discharge remains same.
H
total
=H
1
+H
2
• Pumps in Par allel : Discharge adds up, head remains same.
Q
total
=Q
1
+Q
2
9. Unit Quantities (Turbines and Pumps)
• Unit Speed (N
u
) :
N
u
=
N
v
D
v
H
• Unit Discharge (Q
u
) :
Q
u
=
Q
D
2
v
H
• Unit Power (P
u
) :
P
u
=
P
D
2
H
3/2
whereD = runner or impeller diameter .
3