Performance of Centrifugal Pumps free study notes

1. Introduction

The performance of a centrifugal pump refers to its ability to convert mechanical energy into hydraulic energy efficiently. It is evaluated by studying parameters like head, discharge, power, and efficiency under different operating conditions.

2. Important Performance Parameters

(a) Discharge (Q)

• Volume of liquid delivered per unit time
• Unit: m³/s

(b) Head (H)

• Energy imparted to fluid per unit weight
• Types:
  • Static head
  • Manometric head
  • Total head

(c) Power

(i) Input Power (P₁)

Power supplied to the pump shaft.

(ii) Output Power (P₂)

$$P = \rho g Q H$$P=ρgQH

(d) Efficiency (η)

(i) Manometric Efficiency (ηₘₐₙ)

$$\eta_{man} = \frac{\text{Manometric head}}{\text{Theoretical head}}$$

(ii) Mechanical Efficiency (ηₘ)

$$\eta_m = \frac{\text{Output power}}{\text{Input power}}$$ηm​=Input powerOutput power​

(iii) Overall Efficiency (ηₒ)

$$\eta_o = \frac{\rho g Q H}{\text{Input power}}$$

3. Performance Characteristic Curves

Centrifugal pump performance is best understood using characteristic curves.

(a) Head vs Discharge Curve (H–Q Curve)

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• Head decreases as discharge increases
• Indicates operating range

(b) Efficiency vs Discharge Curve (η–Q Curve)

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• Efficiency increases with discharge up to a maximum
• Maximum efficiency point is called BEP (Best Efficiency Point)

(c) Power vs Discharge Curve (P–Q Curve)

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• Power generally increases with discharge
• Important for motor selection

4. Operating Point of Pump

• Intersection of pump curve and system curve
• Determines actual discharge and head
• Changes with system resistance

5. Specific Speed (Nₛ)

$$N_s = \frac{N \sqrt{Q}}{H^{3/4}}$$

Importance:

• Helps in pump design and selection
• Indicates type of impeller

Classification:

• Low Ns → Radial flow pump
• Medium Ns → Mixed flow pump
• High Ns → Axial flow pump

6. Unit Quantities

Used for comparing pumps under unit head.

• Unit speed:

$$N_1 = \frac{N}{\sqrt{H}}$$

• Unit discharge:

$$Q_1 = \frac{Q}{\sqrt{H}}$$

• Unit power:

$$P_1 = \frac{P}{H^{3/2}}$$

7. Cavitation in Pumps

Definition:

Formation of vapor bubbles when pressure falls below vapor pressure.

Effects:

• Noise and vibration
• Damage to impeller
• Loss of efficiency

Prevention:

• Maintain adequate suction head
• Reduce pump speed
• Use proper design

8. Net Positive Suction Head (NPSH)

(a) NPSH Available (NPSHₐ)

• Provided by system

(b) NPSH Required (NPSHᵣ)

• Required by pump

Condition to avoid cavitation:

$$NPSH_a > NPSH_r$$

9. Losses in Centrifugal Pumps

• Hydraulic losses (friction, turbulence)
• Mechanical losses (bearing, seal friction)
• Leakage losses

10. Factors Affecting Pump Performance

• Speed of pump
• Impeller diameter
• Fluid properties (viscosity, density)
• Suction conditions
• System resistance

11. Affinity Laws (Important for Exams)

For constant efficiency:

• Discharge:

$$Q \propto N$$

• Head:

$$H \propto N^2$$

• Power:

$$P \propto N^3$$

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