Performance of Centrifugal Pumps free study notes

1. What is performance of Centrifugal Pumps?

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

The performance characteristics of a centrifugal pump are represented by curves obtained from testing the pump at a constant speed. These curves show how the pump performs under different flow conditions.

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

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

• Shows variation of pump efficiency with flow rate.
• Efficiency increases with discharge, reaches a maximum, and then decreases.
• The point of maximum efficiency is called the Best Efficiency Point (BEP).

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

• Indicates the power required by the pump at different flow rates.
• Power consumption generally increases as discharge increases.
• 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

The losses occurring in a centrifugal pump reduce its overall efficiency. The main losses are:

1. Hydraulic Losses

These losses occur due to the flow of liquid through the pump.

• Friction Losses: Due to friction between the liquid and the impeller, casing, and passages.
• Shock or Eddy Losses: Caused when the liquid enters or leaves the impeller at an angle different from the vane angle.
• Circulation Losses: Due to recirculation of liquid within the impeller or casing.

2. Mechanical Losses

These losses occur due to moving parts of the pump.

• Bearing friction losses
• Shaft seal or gland friction losses
• Disc friction losses (friction between rotating impeller and liquid)

3. Volumetric Losses

These losses occur due to leakage of liquid.

• Leakage through the clearance between impeller and casing.
• Leakage through wear rings and shaft seals.

Total Losses

$$\text{Total Losses} = \text{Hydraulic Losses} + \text{Mechanical Losses} + \text{Volumetric Losses}$$

Efficiencies Related to Losses

• Hydraulic Efficiency (ηh): $$\eta_h = \frac{\text{Actual Head}}{\text{Theoretical Head}}$$
• Volumetric Efficiency (ηv): $$\eta_v = \frac{\text{Actual Discharge}}{\text{Discharge delivered by Impeller}}$$
• Mechanical Efficiency (ηm): $$\eta_m = \frac{\text{Power at Impeller}}{\text{Shaft Power}}$$
• Overall Efficiency (ηo): $$\eta_o = \eta_h \times \eta_v \times \eta_m$$

10. Factors Affecting Centrifugal Pump Performance

The performance of a centrifugal pump is influenced by several factors:

1. Pump Speed (N)

• Increasing speed increases discharge, head, and power requirement.
• Governed by the pump affinity laws:
  • $Q \propto N$
  • $H \propto N^2$
  • $P \propto N^3$

2. Impeller Diameter (D)

• Larger impeller diameter increases flow rate and head.
• Trimming the impeller reduces pump capacity and head.

3. Fluid Properties

• Density: Higher density increases power consumption.
• Viscosity: Higher viscosity increases friction losses and reduces efficiency.
• Temperature: Affects viscosity and vapor pressure.

4. Suction Conditions

• Insufficient NPSH can cause cavitation.
• Air leakage in the suction line reduces performance.

5. System Resistance

• Changes in pipe length, fittings, valves, and elevation affect the system head curve.
• Higher resistance reduces flow rate.

6. Cavitation

• Occurs when local pressure falls below the liquid’s vapor pressure.
• Causes noise, vibration, reduced capacity, and impeller damage.

7. Wear and Erosion

• Worn impellers, wear rings, and casings increase internal leakage and reduce efficiency.

8. Pump Installation

• Misalignment between pump and motor.
• Improper foundation causing vibration.
• Incorrect piping layout.

9. Entrained Air or Gas

• Air in the liquid can reduce discharge and head.
• May lead to loss of prime.

10. Operating Point

• Best performance occurs at the Best Efficiency Point (BEP).
• Operating too far from BEP increases vibration, recirculation, and energy consumption.

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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External References

• NPTEL open resources