Pumps and Other Hydraulic Machines

Introduction

Hydraulic machines transfer energy between a fluid and a mechanical device. A pump converts mechanical energy supplied by a motor or engine into hydraulic energy, increasing the pressure, velocity, or elevation head of a liquid. A turbine performs the reverse function: it extracts energy from flowing liquid and converts it into mechanical power. Pumps are essential in water supply, irrigation, drainage, chemical processing, refrigeration, power generation, mining, and manufacturing.

The correct selection and operation of a pump require more than matching a nominal flow rate. The engineer must evaluate the system head, losses, efficiency, power, speed, suction conditions, cavitation risk, control method, and the pump’s characteristic curves. This chapter develops these principles for centrifugal, axial-flow, mixed-flow, reciprocating, and other positive-displacement pumps.

Learning Objectives

After studying this chapter, the reader should be able to:

• distinguish dynamic pumps from positive-displacement pumps;
• apply the energy equation to pump systems;
• calculate pump head, hydraulic power, shaft power, and efficiency;
• explain priming, cavitation, NPSH, and pump characteristic curves;
• analyze pumps in series and parallel;
• use affinity laws and specific speed for preliminary selection;
• compare centrifugal, axial, mixed-flow, reciprocating, and rotary pumps;
• determine an operating point from pump and system curves; and
• select and operate pumps safely and efficiently.

1. Classification and Operating Principle

Pumps are commonly classified as follows:

In a centrifugal pump, liquid enters near the impeller eye and is accelerated radially outward. The casing or diffuser converts part of the velocity head into pressure head. An axial-flow pump moves liquid mainly parallel to the shaft, while a mixed-flow pump has both radial and axial components.

A positive-displacement pump does not continuously accelerate the fluid in the same way. It encloses a volume and forces that volume into the discharge line. A relief valve is therefore normally required, because closing the discharge valve can produce dangerously high pressure.

2. Energy Transfer and Pump Head

For steady incompressible flow between a suction section 1 and a delivery section 2, the pump head added to the liquid is obtained from the mechanical energy equation:

Here, H_p is pump head in metres of liquid; p₁ and p₂ are pressures; ρ is liquid density in kg/m³; g is gravitational acceleration in m/s²; V₁ and V₂ are mean velocities; z₁ and z₂ are elevations; and h_L is the head loss between the selected sections. The equation assumes steady flow and uses mean velocities at sections where pressure and velocity can be represented adequately.

If both pressure measurements are atmospheric and the reservoir velocities are negligible, the pump head required between two reservoirs becomes:

The pump adds energy per unit weight of liquid. The hydraulic power delivered to the liquid is:

where Q is volume flow rate in m³/s and P_h is in watts. The shaft power required is greater because of losses:

where η_o is overall pump efficiency. Overall efficiency may be represented as the product of hydraulic, volumetric, and mechanical efficiencies:

The hydraulic efficiency accounts for fluid-flow losses, volumetric efficiency accounts for leakage or slip, and mechanical efficiency accounts for bearing, seal, disk-friction, and transmission losses.

Worked Example 1: Pump Power

A pump delivers water at Q=0.08 m³/s against a head of 32 m. Its overall efficiency is 78%. Take ρ=1000 kg/m³ and g=9.81 m/s². Determine hydraulic and shaft power.

Thus, the liquid receives approximately 25.1 kW, while the motor must supply approximately 32.2 kW, excluding additional motor and drive losses.

3. Centrifugal Pumps

Construction and Flow Path

The principal components of a centrifugal pump are the impeller, casing, shaft, bearings, wear rings, shaft seal, suction nozzle, and discharge nozzle. Impellers may be open, semi-open, or closed. Closed impellers are efficient for relatively clean liquids; open and semi-open types tolerate suspended solids better.

The casing may be volute or diffuser type. A volute gradually collects fluid leaving the impeller. A diffuser uses stationary vanes to reduce velocity and increase static pressure. Multistage pumps contain several impellers in series and are used when high head is required.

Euler Pump Equation

The theoretical energy transfer is described by the Euler equation for turbomachines:

Here, u is blade speed, V_w is the tangential or whirl component of absolute velocity, and subscripts 1 and 2 denote impeller inlet and outlet. The equation follows from angular momentum and assumes one-dimensional mean-flow analysis. For radial entry with no prewhirl, V_w1=0, so:

The actual pump head is less than the theoretical value because of hydraulic losses, leakage, and mechanical losses. Velocity triangles are used to determine whirl components and blade angles. Backward-curved blades generally provide stable power characteristics and good efficiency, while radial blades are suitable for some high-head applications.

Priming

A centrifugal pump normally cannot pump air effectively. Before starting, the casing and suction pipe must be filled with liquid; this operation is called priming. Priming methods include manual filling, a foot valve, an ejector, a vacuum pump, or an automatically controlled priming system. A pump installed above the liquid level is especially vulnerable to loss of prime. A foot valve must have low resistance and must seal reliably, since leakage allows the suction line to drain.

4. Axial-Flow and Mixed-Flow Pumps

An axial-flow pump has a propeller-like impeller. The fluid enters and leaves approximately parallel to the shaft. It produces high flow at relatively low head and is used for flood control, irrigation, cooling-water circulation, and drainage.

A mixed-flow pump produces both axial and radial velocity components. It occupies an intermediate position between centrifugal and axial-flow pumps and is often used for medium head and medium-to-high flow.

The choice among these pumps is governed primarily by required head and discharge. Radial centrifugal pumps are appropriate for high head and lower flow, axial pumps for low head and high flow, and mixed-flow pumps for intermediate conditions. Actual selection must also consider liquid properties, solids, temperature, speed, efficiency, and control requirements.

5. Pump Characteristic Curves and the Operating Point

Manufacturers provide curves showing head, efficiency, power, and often NPSH required as functions of flow at a specified speed and impeller diameter. A centrifugal pump usually has decreasing head as flow increases. Efficiency rises to a maximum near the best-efficiency point (BEP) and decreases on either side.

The system curve represents the head required by the piping system:

where H_static is the elevation and pressure head independent of flow, and K_sysQ² represents friction and minor losses for turbulent flow in a fixed system. More generally, losses should be calculated from pipe friction and fittings rather than assuming a single constant over all flow regimes.

The operating point is the intersection of the pump curve and system curve. At this point, the pump head equals the head demanded by the system. If the operating point is far from the BEP, vibration, recirculation, overheating, seal damage, and poor efficiency may result.

Affinity Laws

For geometrically similar operation, approximately constant fluid properties, and unchanged impeller geometry, the affinity laws are:

For changes in impeller diameter at constant speed, approximate relationships are:

These relations are most reliable for moderate changes and similar operating regions. They should not replace manufacturer test data for large diameter reductions, highly viscous liquids, or strongly altered hydraulic geometry.

Specific Speed

Specific speed is a nondimensional or customary index used to compare pump geometries. One common SI nondimensional form is:

where N is rotational speed in rad/s, Q is m³/s, and H is m. Other industries use a dimensional specific-speed convention based on rpm, flow in selected units, and head in metres. The numerical value therefore has meaning only when the convention is stated. Low specific speed generally indicates radial-flow geometry; high specific speed indicates axial-flow geometry; mixed-flow pumps occupy the intermediate range.

6. Pumps in Series and Parallel

Pumps connected in series discharge through one another. At a given flow, their heads are added:

Series operation is used when a high head is required, such as in multistage pumping or long-distance water transmission. The casing, seals, and downstream pipework must withstand the resulting pressure.

Pumps connected in parallel operate between common suction and discharge headers. At a given head, their flow rates are added:

Parallel operation increases capacity and can improve turndown by switching pumps on or off. The pumps should have compatible curves and check valves are normally installed to prevent reverse flow through an idle pump. The combined curve must be intersected with the system curve; simply adding rated flow values is not sufficient.

7. NPSH and Cavitation

Cavitation occurs when local absolute pressure falls to or below the liquid vapour pressure. Vapour bubbles then form and collapse as pressure recovers. Consequences include noise, vibration, pitting, reduced head, loss of capacity, seal damage, and possible impeller failure.

The available net positive suction head is defined at the pump suction reference section as:

where p_s,abs is absolute suction pressure, V_s is suction velocity, and p_v is vapour pressure at operating temperature. For a reservoir supplying the pump, atmospheric pressure, elevation, and suction losses can be used to calculate the suction absolute head. The manufacturer specifies NPSH required, NPSH_R, based on a stated test criterion.

A safe design requires:

The required margin depends on standards, pump type, liquid, operating variability, and consequences of cavitation. It should not be selected arbitrarily.

NPSH is an absolute-pressure concept. Gauge pressure must be converted to absolute pressure before use. Increasing liquid temperature raises vapour pressure and reduces NPSH available. Lowering the pump, enlarging the suction pipe, reducing suction losses, reducing speed, or lowering liquid temperature can improve suction conditions.

8. Reciprocating and Positive-Displacement Pumps

A reciprocating pump uses a piston or plunger in a cylinder. Suction and delivery valves open because of pressure differences. A single-acting pump delivers during one stroke per cycle; a double-acting pump delivers during both directions of piston movement.

For a single-acting pump with cylinder area A, stroke length L, and speed N rpm, the theoretical discharge is:

For a double-acting pump, neglecting piston-rod area, the theoretical discharge is approximately:

Actual discharge is lower or may vary because of leakage, valve timing, compressibility, and air entrainment. Volumetric efficiency is:

A reciprocating pump can generate high pressure at low flow and is well suited to metering, boiler feed, hydraulic testing, and chemical injection. Air vessels reduce acceleration head and discharge pulsation. Relief protection is essential because positive-displacement pumps continue attempting to deliver flow when the discharge is blocked.

Rotary positive-displacement pumps include gear, screw, vane, lobe, and progressive-cavity pumps. They are useful for viscous fluids, fuels, oils, polymers, and slurries, although each design has limits concerning solids, shear sensitivity, leakage, and allowable pressure.

9. Pump Selection and Control

A sound selection procedure is:

1. Define required flow range, static head, pressure, temperature, viscosity, solids concentration, corrosiveness, and operating schedule.
2. Establish the complete system curve, including pipe friction, fittings, valves, filters, heat exchangers, and elevation.
3. Select pump type according to flow, head, fluid, and control requirements.
4. Compare manufacturer curves at the actual speed and impeller diameter.
5. Check BEP proximity, efficiency, motor power, starting conditions, NPSH margin, materials, seals, and minimum continuous stable flow.
6. Evaluate life-cycle cost, not only purchase price.
7. Confirm standards, installation requirements, maintenance access, and spare-parts availability.

Flow may be controlled by throttling, variable-speed drive, impeller trimming, bypassing, or switching pumps. Throttling changes system resistance and wastes energy in the valve. A variable-speed drive can reduce energy consumption, but motor cooling, minimum speed, resonance, control stability, and harmonic effects must be considered. Bypass control is sometimes necessary for minimum-flow protection but is generally inefficient.

10. Illustrative Case: Irrigation Pump Station

Background

An illustrative irrigation station must deliver 0.12 m³/s from a low-level reservoir to an elevated distribution tank. The static elevation difference is 24 m. At the design flow, pipe and fitting losses are estimated as 11 m. The water temperature may reach 30 °C.

Problem

Select a suitable pump arrangement and estimate the required shaft power. The station must also operate efficiently at half flow during part-load irrigation.

Analysis

The required design head is:

Suppose a selected centrifugal pump provides 0.12 m³/s at 35 m head with an overall efficiency of 82%.

A motor rated above this calculated value is selected after considering service factor, starting method, ambient conditions, and applicable motor standards.

Because the suction reservoir is open, the available NPSH is found from atmospheric pressure head, static suction elevation, suction losses, velocity head, and vapour-pressure head. At 30 °C, vapour pressure is substantially higher than at room temperature; therefore the NPSH margin must be checked using the worst credible temperature and lowest reservoir level.

Approach and Solution

Two identical pumps in parallel are considered. Parallel operation permits one pump to operate during low demand and both to operate at high demand. The combined pump curve, rather than twice the rated flow, must be intersected with the system curve. Each pump should have a check valve, and the station should include low-level protection, a suction strainer designed for low loss, pressure gauges, flow measurement, vibration monitoring, and a variable-speed drive if the operating range justifies it.

Outcome

The final choice should be based on the manufacturer’s tested curves. If one pump operates far to the left of its BEP during half-flow operation, cycling or speed control may be preferable to continuous throttling. The design should include a minimum-flow requirement and an emergency shutdown for loss of suction or excessive vibration.

Learning Points

The case demonstrates that pump selection is a system problem. Static head alone is insufficient; friction, operating range, NPSH, efficiency, control strategy, and maintainability determine the practical solution.

11. Limitations, Safety, and Contemporary Practice

Pump curves are test-based and depend on liquid properties, speed, impeller diameter, and measurement uncertainty. Extrapolating beyond the tested range is unsafe. Viscosity correction is required when pumping liquids significantly more viscous than water. Air entrainment can invalidate ordinary performance assumptions.

Installation quality is as important as pump selection. Poor alignment, inadequate grouting, pipe strain, sharp suction elbows close to the inlet, and insufficient venting can cause vibration and unstable operation. Operators should never run a centrifugal pump dry unless specifically designed for it, and should not close a positive-displacement pump discharge without verified relief protection.

Modern installations use sensors for pressure, flow, vibration, motor current, bearing temperature, and seal leakage. Condition-monitoring systems can identify bearing wear, cavitation, imbalance, and operation away from the BEP. Artificial-intelligence methods may assist anomaly detection and predictive maintenance, but sensor quality, calibrated baselines, cybersecurity, and engineering verification remain necessary. Automated control must include independent protective trips for overspeed, low suction level, overpressure, and excessive temperature where applicable.

Energy efficiency is both an economic and environmental responsibility. Engineers should minimize unnecessary throttling, avoid oversized pumps, reduce suction and discharge losses, select efficient motors and drives, and evaluate life-cycle energy consumption. Designs must comply with relevant safety, pressure, electrical, environmental, and machinery regulations.

Chapter Summary

Pumps add energy to liquids, while hydraulic turbines extract energy. Dynamic pumps transfer energy continuously through rotating impellers; positive-displacement pumps trap and displace definite fluid volumes. Pump head follows from the mechanical energy equation, and hydraulic power is ρgQH. Shaft power is higher than hydraulic power because of efficiency losses.

Centrifugal pumps are selected using head-flow, efficiency, power, and NPSH curves. The operating point is the intersection of pump and system curves. Affinity laws estimate the effects of speed and impeller-diameter changes, while specific speed relates pump geometry to flow and head. Pumps in series add head at common flow; pumps in parallel add flow at common head.

Priming is necessary for most centrifugal pumps. Cavitation is prevented by ensuring adequate NPSH available relative to NPSH required. Reciprocating and rotary positive-displacement pumps are valuable for high pressure, metering, viscous fluids, and applications requiring nearly fixed displacement, but they require relief protection. Good selection considers the complete system, fluid properties, operating range, efficiency, safety, maintenance, and life-cycle cost.

Key Terms

Pump head: Energy added to liquid per unit weight, expressed as a head of liquid.

Hydraulic power: Rate of useful energy delivered to the liquid, ρgQH.

Overall efficiency: Ratio of hydraulic power to shaft power.

Centrifugal pump: Rotodynamic pump in which an impeller accelerates liquid outward.

Axial-flow pump: Pump in which liquid moves mainly parallel to the shaft.

Mixed-flow pump: Pump having both radial and axial flow components.

Positive-displacement pump: Pump that traps and displaces a definite volume per cycle.

Priming: Filling a centrifugal pump and suction line with liquid before operation.

Best-efficiency point: Operating condition at which pump efficiency is maximum.

System curve: Relationship between required system head and flow rate.

Operating point: Intersection of pump and system curves.

Affinity laws: Similarity relationships connecting speed, flow, head, and power.

Specific speed: Index relating pump speed, flow, and head for geometric comparison.

NPSH available: Absolute suction energy head above liquid vapour-pressure head.

NPSH required: Minimum suction head specified by the pump manufacturer for a test criterion.

Cavitation: Formation and collapse of vapour bubbles caused by low local pressure.

Volumetric efficiency: Ratio of actual displacement flow to theoretical displacement flow.

Air vessel: Vessel used with reciprocating pumps to reduce flow pulsation and acceleration effects.

Minimum continuous stable flow: Lowest flow at which a pump can operate reliably without damaging internal recirculation or instability.

Review Questions

Short Answer Questions

1. Why must most centrifugal pumps be primed before starting?
2. Define pump head and hydraulic power.
3. What is the difference between NPSH available and NPSH required?
4. State the practical difference between series and parallel pump operation.
5. Why is a relief valve essential in many positive-displacement pump installations?

Long Answer Questions

1. Explain the construction, operation, characteristic curves, and applications of a centrifugal pump.
2. Derive and interpret the pump-system operating point using pump and system curves.
3. Discuss cavitation, its causes, consequences, and methods of prevention.
4. Compare centrifugal, axial-flow, mixed-flow, reciprocating, and rotary positive-displacement pumps.
5. Explain the affinity laws and discuss their assumptions and limitations.

Analytical / Application Questions

1. A pump delivers 0.05 m³/s against 28 m head at 75% efficiency. Calculate the shaft power required for water using ρ=1000 kg/m³ and g=9.81 m/s².
2. Two identical pumps operate in parallel. Explain why the combined flow at a specified head cannot generally be found by simply doubling the rated flow, and describe the correct graphical procedure.
3. A pump experiences noise, vibration, and falling discharge during a hot afternoon. Identify the most probable hydraulic cause and propose at least four engineering remedies.

Multiple Choice Questions with Answers

Question 1

Which expression gives the hydraulic power delivered to an incompressible liquid?

A. ρgQH

B. ρQ/(gH)

C. QH/(ρg)

D. ρgH/Q

Correct Answer: A. ρgQH

Question 2

The operating point of a pump system is determined by the intersection of the:

A. Efficiency curve and power curve

B. Pump curve and system curve

C. NPSH curve and efficiency curve

D. Motor curve and valve curve

Correct Answer: B. Pump curve and system curve

Question 3

For geometrically similar pump operation at constant diameter, head varies approximately with:

A. N

B. 1/N

C. N²

D. N³

Correct Answer: C. N²

Question 4

Which pump generally provides high flow at relatively low head?

A. Axial-flow pump

B. High-pressure reciprocating pump

C. Gear pump

D. Radial centrifugal pump

Correct Answer: A. Axial-flow pump

Question 5

Cavitation begins when local absolute pressure approaches or falls below the liquid’s:

A. Atmospheric pressure

B. Discharge pressure

C. Vapour pressure

D. Critical pressure only

Correct Answer: C. Vapour pressure

Question 6

Two pumps in series primarily increase the total:

A. Flow at a given head

B. Head at a given flow

C. Liquid viscosity

D. NPSH required to zero

Correct Answer: B. Head at a given flow

Question 7

A positive-displacement pump discharge is accidentally closed. The most important immediate protection is a:

A. Foot valve

B. Diffuser

C. Relief valve

D. Priming funnel

Correct Answer: C. Relief valve

Question 8

A pump delivers water at 0.10 m³/s against 20 m head with 80% overall efficiency. Its shaft power is approximately:

A. 19.6 kW

B. 24.5 kW

C. 15.7 kW

D. 196 kW

Correct Answer: B. 24.5 kW

Question 9

The best-efficiency point is important because operation far from it can increase:

A. Vibration and recirculation

B. Atmospheric pressure

C. Liquid density to zero

D. Theoretical displacement only

Correct Answer: A. Vibration and recirculation

Question 10

Which action generally increases NPSH available?

A. Increasing suction-line losses

B. Raising liquid temperature

C. Lowering the pump relative to the source liquid

D. Reducing suction-pipe diameter

Correct Answer: C. Lowering the pump relative to the source liquid