Load flow analysis, also known as power flow analysis, is a fundamental tool in power system engineering used to analyze and calculate the steady-state operating conditions of an electrical network. The primary goal of load flow analysis is to determine the voltage magnitude and phase angles at various buses in the system, as well as the real and reactive power flows on the transmission lines. Here are the basics of load flow analysis. It analyses the power system in normal steady state operation. Its Purpose is to calculate the voltages and once voltages are known for all buses, line flows and losses can be calculated. 1.2 Bus Types ➢ PQ Bus (P: Real Power, Q: Reactive Power): Represents a bus where both real and reactive powers are specified. ➢ PV Bus (P: Real Power, V: Voltage Magnitude): Specifies real power and voltage magnitude. ➢ Slack Bus (or Swing Bus): The reference bus where voltage magnitude and phase angle are specified. It serves as the reference point for the entire system 1.3 Significance of Power Flow studies Power flow studies are essential for understanding and optimizing the performance of electrical power systems. They provide valuable insights that support planning, operation, and decisionmaking processes, contributing to the overall reliability and efficiency of the power grid. They are Important in Planning future expansion of system and helps in determining the best operation of existing system 2 Methods of Power Flow Analysis 2.1 Power Flow Equations and their solution techniques • Formulation of network equations in nodal admittance results non-linear algebraic equations of node currents • For power systems, these are transformed to Power flow equations which can be solve by iterative techniques Load flow analysis, also known as power flow analysis, is a fundamental tool in power system engineering used to analyze and calculate the steady-state operating conditions of an electrical network. The primary goal of load flow analysis is to determine the voltage magnitude and phase angles at various buses in the system, as well as the real and reactive power flows on the transmission lines. Here are the basics of load flow analysis. It analyses the power system in normal steady state operation. Its Purpose is to calculate the voltages and once voltages are known for all buses, line flows and losses can be calculated. 1.2 Bus Types ➢ PQ Bus (P: Real Power, Q: Reactive Power): Represents a bus where both real and reactive powers are specified. ➢ PV Bus (P: Real Power, V: Voltage Magnitude): Specifies real power and voltage magnitude. ➢ Slack Bus (or Swing Bus): The reference bus where voltage magnitude and phase angle are specified. It serves as the reference point for the entire system 1.3 Significance of Power Flow studies Power flow studies are essential for understanding and optimizing the performance of electrical power systems. They provide valuable insights that support planning, operation, and dec

1. Lecture#4:
Centrifugal
Pumps
THE CENTRIFUGAL PUMP AND ITS
THEORETICAL CONSIDERATIONS

2. Prerequisites
 Chapter 12 of Book “Fundamentals of Fluid Mechanics Seventh Edition by Munson”
 Lecture 3
LECTURE#4 CENTRIFUGAL PUMPS BY SYED MUHAMMAD HARIS 2

3. Centrifugal Pumps
LECTURE#4 CENTRIFUGAL PUMPS BY SYED MUHAMMAD HARIS 3
One of the most common type of turbomachine is Centrifugal Pump

4. Impellers
LECTURE#4 CENTRIFUGAL PUMPS BY SYED MUHAMMAD HARIS 4
As the impeller rotates energy from shaft is transmitted to the fluid,
Double Suction Pump
Multistage Pump

5. Velocity
Triangles
LECTURE#4 CENTRIFUGAL PUMPS BY SYED MUHAMMAD HARIS 5
U1
V1
W1
β1
α1
U2
W2
V2
β2
α2
V=W+U

6. Derivation
LECTURE#4 CENTRIFUGAL PUMPS BY SYED MUHAMMAD HARIS 6
𝝉 =
𝒅𝑳
𝒅𝒕
= 𝒎 . 𝒓 ∆𝒗…….(1)

7. Total Energy of Fluid
LECTURE#4 CENTRIFUGAL PUMPS BY SYED MUHAMMAD HARIS 7
Potential Energy in Watts: 𝑚𝑔ℎ
Kinetic Energy in watts: ½𝑚𝑣2
Pressure Energy in watts: 𝑃𝐴𝑣
Per Unit Mass: gh
Per Unit Mass: ½ 𝑣2
Per Unit Mass:
𝑃
𝜌
Total Energy Per Unit Mass flow = 𝑔ℎ + ½ 𝑣2
+ 𝑃/𝜌
Divide by Gravitational Acceleration “g”
Head= ℎ +
1
2
𝑣2
𝑔
+
𝑃
𝜌𝑔

8. Derivation Continued
LECTURE#4 CENTRIFUGAL PUMPS BY SYED MUHAMMAD HARIS 8
= ℎ𝑖
ℎ𝑎

9. Relation Between Flowrate and Pump Ideal Head Rise
LECTURE#4 CENTRIFUGAL PUMPS BY SYED MUHAMMAD HARIS 9
If fluid enters radially, 𝑉𝜃1 = 0 , 𝛼1 = 90°

10. Thank You