Pumps, Turbines, and Fluid Machinery

Introduction and Context

Fluid machinery transfers energy between a fluid and a mechanical device. Pumps add energy to liquids, usually to overcome elevation differences, pressure requirements, and friction losses. Turbines extract energy from flowing fluids and convert it into mechanical power. Fans, blowers, compressors, hydraulic motors, and mixers are related machines, although their operating fluids and pressure ranges differ.

Fluid machinery is central to construction and building services. Water-supply systems, dewatering installations, fire-protection networks, chilled-water systems, sewage plants, irrigation systems, hydropower facilities, and temporary construction pumping all depend on correct equipment selection and operation. A pump that is too small cannot satisfy the required flow and pressure; one that is too large wastes energy, operates away from its best-efficiency point, and may suffer vibration and premature failure.

This chapter develops the relationships between pump or turbine performance, the piping system, efficiency, operating point, cavitation, net positive suction head, control, maintenance, and energy optimization.

Learning Objectives

By the end of this chapter, you should be able to:

1. Explain how pumps and turbines exchange energy with a fluid.
2. Use head, power, efficiency, and system-curve concepts to interpret performance.
3. Determine an operating point from pump and system characteristics.
4. Apply affinity laws within their assumptions and limitations.
5. Diagnose cavitation using suction conditions and NPSH.
6. Select, control, maintain, and evaluate pumps and turbines for practical projects.
7. Identify opportunities for energy savings and reliable operation.

1. Energy Transfer in Fluid Machinery

For steady, incompressible flow, the mechanical-energy equation between sections 1 and 2 is

where p is pressure, ρ is fluid density, g is gravitational acceleration, z is elevation, V is mean velocity, α is the kinetic-energy correction factor, h_p is pump head added, h_t is turbine head extracted, and h_L is head loss. All head terms have units of metres of fluid. The equation assumes steady flow and a single-phase fluid; heat transfer and compressibility effects are neglected.

For many engineering calculations, α is approximated as 1. The total head added by a pump is the increase in the fluid’s mechanical energy, including losses between the pump suction and discharge reference sections. A turbine head is the mechanical energy removed from the fluid.

The hydraulic power transferred is

where P_h is hydraulic power in watts, Q is volumetric flow rate in m³/s, and H is the relevant head in metres. For a pump, H is pump head added; for a turbine, H is the usable head extracted. Dimensional checking gives (kg/m³)(m/s²)(m³/s)(m) = kg·m²/s³ = W.

Pump input power and efficiency are related by

where η_p is overall pump efficiency and P_in is shaft or electrical input power, depending on the stated measurement boundary. If motor efficiency η_m is considered separately, electrical input power is

This expression assumes that η_p describes shaft-to-fluid efficiency and η_m describes electrical-to-shaft efficiency. Efficiencies must be expressed as decimals in calculations.

For a turbine,

where P_shaft is mechanical shaft output. Generator efficiency must be included separately when electrical output is required.

2. Pumps: Types and Operating Principles

A pump converts shaft power into hydraulic energy. The two broad categories are dynamic pumps and positive-displacement pumps.

2.1 Dynamic pumps

Centrifugal pumps are the most common dynamic pumps in construction services. An impeller accelerates the fluid radially or axially, and the casing converts part of the velocity increase into pressure. They are suited to continuous flow and moderate-to-high flow rates.

Common centrifugal configurations include:

• End-suction pumps: compact and widely used for water services.
• Split-case pumps: suitable for large flow rates and easier maintenance of major components.
• Vertical turbine pumps: used where the suction source is below the pump, such as wells or reservoirs.
• Multistage pumps: use several impellers in series to produce high head.
• Mixed-flow and axial-flow pumps: provide high flow at relatively low head.

The pump’s developed head depends on flow rate. In general, centrifugal-pump head decreases as flow increases, although the exact curve depends on impeller geometry and speed.

2.2 Positive-displacement pumps

Positive-displacement pumps trap a volume of fluid and force it into the discharge line. Reciprocating piston and diaphragm pumps provide high pressure and accurate dosing at comparatively low flow. Rotary gear, screw, and lobe pumps handle viscous fluids effectively. Their flow is approximately proportional to speed, but a pressure-relief device is essential because blocking the discharge can create dangerously high pressure.

A positive-displacement pump should not normally be controlled by throttling alone. Speed control, bypass flow, or a properly set relief system is generally more appropriate.

3. Pump Performance Curves

Manufacturers provide pump curves based on tests under stated conditions. The principal curves are:

• Head–flow curve, H–Q: pump head as a function of flow.
• Efficiency curve: often shown as contours or a curve over the operating range.
• Power curve: shaft or input power versus flow.
• NPSH required curve: minimum suction head required to avoid unacceptable cavitation under the test criterion.

The best-efficiency point (BEP) is the flow at which pump efficiency is greatest for a specified speed, impeller diameter, and fluid. Continuous operation near BEP usually reduces vibration, radial hydraulic forces, recirculation, and bearing or seal loading. The acceptable operating range around BEP is called the preferred or allowable operating region, depending on the manufacturer’s terminology.

A pump curve is not a universal property independent of installation. It applies to a specified speed, impeller, fluid, and test standard. Changing fluid viscosity, speed, impeller diameter, or configuration changes performance.

Pump head from a system calculation

For a pumping system, the required head can be written as

Here Δz = z₂ − z₁, Δp = p₂ − p₁, and h_L represents all relevant pipe, fitting, valve, and equipment losses. If both reservoirs are open to the atmosphere and their surface velocities are negligible, this simplifies to

For turbulent flow in a constant-diameter pipe, a common estimate of friction loss is the Darcy–Weisbach equation:

where f is the Darcy friction factor, L is pipe length, D is internal diameter, and V is mean velocity. Minor losses may be represented by

where K is a dimensionless loss coefficient. These equations require consistent units and an appropriate friction factor; f depends on Reynolds number and relative roughness.

Because friction loss varies approximately with Q² in a fixed system, the system curve often has the form

where H_static is the elevation and pressure difference independent of flow, and k is a system-resistance coefficient. This is an approximation valid when the flow regime and system configuration remain sufficiently similar.

4. Operating Point and System Curves

The operating point is the intersection of the pump curve and system curve. At that point, the head the pump can produce equals the head required by the system at the actual flow. The pump does not independently impose both flow and head; the piping system and pump interact to determine both.

If a valve is throttled, resistance increases. The system curve becomes steeper, the operating flow decreases, and the pump head generally increases along its pump curve. If a parallel pipe is opened, resistance decreases and flow increases. Increasing static elevation shifts the system curve upward and normally reduces flow.

A useful design procedure is:

1. Define design and minimum/maximum flow requirements.
2. Establish elevations, pressure requirements, pipe sizes, fittings, valves, and equipment losses.
3. Construct or calculate the system curve.
4. Superimpose candidate pump curves.
5. Check that the operating point lies near the preferred operating region.
6. Verify efficiency, power, NPSH margin, materials, controls, and transient behavior.

5. Worked Example: Pump Selection and Power

An open tank supplies water to a higher open tank. The water-surface elevation difference is 18 m. At the required flow of 0.040 m³/s, pipe and fitting losses are 7 m. Select the required pump head and estimate electrical power if pump efficiency is 78% and motor efficiency is 92%.

For open tanks, pressure terms cancel and surface velocities are negligible. Therefore,

The hydraulic power is

Using ρ = 1000 kg/m³ and g = 9.81 m/s²,

The required electrical power is

A practical selection would use a motor rating above this calculated demand, with allowance for operating range, starting conditions, service factor, and applicable electrical standards. The selected pump curve should provide approximately 25 m at 0.040 m³/s without operating at the extreme end of its curve.

6. Affinity Laws

For a geometrically similar centrifugal pump operating with the same fluid and approximately similar efficiency, the affinity laws provide first estimates of the effect of speed N:

For the same pump at different impeller diameters D, approximate relationships are

The diameter relationships are less exact than the speed relationships and depend on trimming limits and pump geometry. The laws do not guarantee identical efficiency, Reynolds number, or hydraulic similarity. They should support preliminary estimation, not replace manufacturer data.

Variable-speed control can be highly effective because, approximately, power varies with the cube of speed. For example, reducing speed to 80% can reduce idealized power demand to about 0.80³ = 0.512, or 51.2%, when the system and operating conditions permit. Static-head-dominated systems achieve less saving than friction-dominated systems because the pump must still overcome the static component.

7. Turbines and Their Performance

A turbine extracts energy from a fluid. Hydraulic turbines are commonly classified as:

• Impulse turbines: the available head is largely converted into jet velocity before striking the runner. Pelton turbines are typical for high head and low flow.
• Reaction turbines: pressure changes occur through the runner. Francis turbines suit medium head and flow, while Kaplan turbines suit low head and high flow.

The hydraulic power available is ρgQH, but actual shaft power is lower because of hydraulic, mechanical, and leakage losses. Turbine selection considers head range, flow variation, speed, cavitation risk, sediment, governing requirements, and grid or generator characteristics.

Turbine characteristic curves show efficiency, power, discharge, and sometimes cavitation performance over operating conditions. A turbine should be operated near its design or best-efficiency region where practical. Part-load operation may increase hydraulic instability, vibration, and fatigue.

The Euler turbomachinery relationship expresses ideal specific work in terms of velocity triangles:

where w is specific work transferred, u is blade peripheral speed, and V_u is the tangential component of absolute fluid velocity. The sign and station convention depend on whether the machine is a pump or turbine. The equation is based on conservation of angular momentum and assumes a steady, one-dimensional representation at the selected stations.

8. Cavitation and Net Positive Suction Head

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

For a pump, the available net positive suction head is commonly defined at the pump suction reference as

where p_{s,abs} is absolute suction pressure, V_s is suction velocity, and p_v is liquid vapour pressure at the operating temperature. If the suction pressure is calculated from a reservoir, atmospheric pressure, elevation, and suction losses must be included. Gauge pressure must not be used directly as absolute pressure.

The manufacturer supplies NPSH required, NPSH_R, determined using a specified test criterion. A basic operating requirement is

A practical margin is required because NPSH_R is not a guarantee of completely bubble-free operation and because temperature, flow, altitude, measurement uncertainty, and transients may vary. The required margin should follow manufacturer guidance, project standards, and applicable codes.

Ways to increase NPSH_A include lowering the pump, raising the liquid level, reducing suction-pipe losses, increasing suction-pipe diameter, reducing fluid temperature, and avoiding blocked strainers or excessive fittings. Increasing NPSH_A is usually preferable to simply accepting a small calculated margin.

9. Pump Control and System Operation

Throttling

A discharge valve increases resistance and shifts the operating point to lower flow. It is simple and useful for commissioning or limited control, but throttling dissipates energy as heat and may move the pump away from BEP.

Bypass control

A bypass returns part of the flow to the source or suction vessel. It can protect a positive-displacement pump or maintain minimum flow through a centrifugal pump, but it wastes energy unless required for protection or process reasons.

Variable-speed drives

A variable-frequency drive changes motor speed and can closely match demand. It may reduce energy use and improve control, but it requires correct motor compatibility, minimum-speed limits, harmonic assessment where relevant, cooling consideration, and protection against rapid transients.

Parallel and series operation

Pumps in parallel add flow at approximately common head; their combined curve is formed by adding flows at each head. Pumps in series add head at approximately common flow. Pumps must be compatible, and check valves, controls, minimum-flow protection, and transient analysis are essential.

10. Maintenance, Reliability, and Safety

A maintenance program should combine inspection, condition monitoring, preventive tasks, and corrective action. Important observations include:

• vibration and bearing temperature;
• mechanical-seal leakage;
• motor current and abnormal heating;
• suction and discharge pressure;
• flow and operating point;
• noise, especially gravel-like cavitation noise;
• coupling alignment and soft-foot condition;
• foundation bolts, pipe strain, and support condition;
• strainer, filter, and valve condition.

Lubrication must follow the manufacturer’s type, quantity, and interval. Over-lubrication can be as harmful as under-lubrication. Alignment should be checked after installation, pipe connection, thermal changes, and major maintenance. Pumps should not be run dry unless specifically designed for it.

Before maintenance, isolate, lock out, tag out, depressurize, drain, and verify zero energy. Electrical, hydraulic, pneumatic, thermal, and stored mechanical energy must be considered. Guards must remain installed during operation. Applicable occupational-safety, electrical, pressure-equipment, environmental, and water-quality regulations govern the installation.

11. Energy Optimization and Sustainable Practice

Energy optimization begins with reducing unnecessary system resistance and avoiding excessive design margins. Important measures include:

1. Select pipe diameters using life-cycle cost, not only initial cost.
2. Choose a pump whose BEP is near the normal duty point.
3. Avoid permanent throttling when speed control or system redesign is practical.
4. Repair leaks and malfunctioning control valves.
5. Clean blocked strainers and fouled heat exchangers.
6. Use automatic sequencing for multiple pumps.
7. Measure flow, head, power, and efficiency periodically.
8. Match operating schedules to actual demand.
9. Use high-efficiency motors and properly sized drives.
10. Include embodied energy, maintenance, replacement, and disposal in life-cycle decisions.

Pump efficiency can be estimated from field measurements using ρgQH/P_in, but uncertainty in flow, pressure, density, and measurement location must be reported. A measured efficiency decrease should trigger investigation rather than immediate replacement; wear, impeller damage, air entrainment, incorrect rotation, valve position, and instrumentation error may all be causes.

12. Illustrative Case: Construction-Site Dewatering

Background

A basement excavation is 12 m below the surrounding ground level. During wet weather, groundwater enters the excavation at an estimated 0.025 m³/s. Water must be discharged to a settling tank whose water surface is 6 m above the excavation sump. The temporary pipeline has an estimated loss of 9 m at the target flow.

Problem

The contractor initially proposes a pump rated at 0.025 m³/s and 15 m head. The pump repeatedly trips, delivers less flow than expected, and produces a rattling sound.

Analysis

The required static head is approximately 12 + 6 = 18 m. Therefore, the required total head is approximately

The proposed pump cannot reliably provide the target flow at 27 m. The rattling sound suggests possible cavitation or air ingestion. The suction hose is long, undersized, and partially blocked by a damaged strainer. The pump is also placed on uneven ground, causing poor suction conditions and coupling misalignment.

Approach and solution

The project team should:

• select a pump whose curve provides 0.025 m³/s near its preferred operating region at about 27 m;
• enlarge and shorten the suction line where possible;
• install a properly sized, clean strainer and avoid vortex formation;
• place the pump close to and below the minimum expected sump water level when feasible;
• verify NPSH_A at the highest expected water temperature;
• provide a level-controlled standby pump;
• use a settling tank and comply with discharge-quality requirements;
• monitor flow, suction pressure, discharge pressure, and motor current.

Outcome

After correction, the system operates near the intended duty point, cavitation noise disappears, and the excavation remains dry. The standby pump reduces risk during rainfall, while measurements allow the contractor to identify blocked strainers before pump failure.

Learning points

The case illustrates that a nominal flow rating is insufficient for selection. Static head, friction losses, operating-point intersection, suction design, NPSH, reliability, and environmental controls must be evaluated together.

13. Limitations and Contemporary Developments

Performance curves are usually based on controlled tests, whereas construction sites contain air, sediment, fluctuating levels, variable voltage, temporary pipework, and uncertain measurements. A calculated system curve may therefore differ from field behavior. Transient events such as rapid valve closure, pump trips, and check-valve slam can create pressure surges not represented by a steady-state calculation.

Modern installations increasingly use sensors, remote monitoring, digital motor controls, and condition-based maintenance. Data analytics can detect deviations in head, flow, power, and vibration. Artificial intelligence can assist anomaly detection and remaining-life estimation, but it does not replace sound hydraulic models, calibrated sensors, manufacturer limits, or engineering accountability. Poor-quality data can produce confident but incorrect recommendations.

Chapter Summary

Pumps add mechanical energy to fluids, while turbines extract it. The mechanical-energy equation connects pressure, elevation, velocity, losses, pump head, and turbine head. Pump and turbine power depend on density, gravitational acceleration, flow, head, and efficiency. A pump’s actual flow and head are determined by the intersection of its performance curve and the system curve.

System resistance commonly varies approximately with Q², while centrifugal-pump affinity laws relate flow, head, and power to speed or, approximately, impeller diameter. These laws are useful for estimation but do not replace manufacturer data. Cavitation is controlled by ensuring adequate NPSH available relative to NPSH required, with a practical margin. Good selection places normal operation near the best-efficiency region and considers power, controls, materials, maintenance, safety, transients, and life-cycle cost. Energy optimization depends on correct sizing, efficient control, low system resistance, measurement, and reliable maintenance.

Key Terms

Pump: Machine that adds energy to a fluid.

Turbine: Machine that extracts energy from a fluid.

Pump head: Mechanical energy added per unit weight of fluid.

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

Operating point: Intersection of pump and system curves.

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

Hydraulic power: Rate of useful energy transferred to or from the fluid.

Overall efficiency: Useful output divided by input at the selected system boundary.

Centrifugal pump: Dynamic pump using an impeller to increase fluid energy.

Positive-displacement pump: Pump that displaces trapped fluid volumes.

Affinity laws: Approximate scaling relationships for speed or impeller changes.

Cavitation: Formation and collapse of vapour bubbles due to low absolute pressure.

NPSH available: Suction energy above liquid vapour-pressure head.

NPSH required: Manufacturer-specified suction requirement for a stated test condition.

Impulse turbine: Turbine using a high-velocity jet with little runner pressure change.

Reaction turbine: Turbine in which pressure changes occur through the runner.

Throttling: Flow control by increasing valve resistance.

Variable-speed drive: Device that controls motor speed electronically.

Darcy friction factor: Dimensionless factor used to calculate pipe friction loss.

Life-cycle cost: Total ownership cost including energy, maintenance, and replacement.

Review Questions

Short Answer Questions

1. What is the operating point of a pump and piping system?
2. Distinguish between NPSH available and NPSH required.
3. State the three centrifugal-pump affinity laws involving speed.
4. Why is operation near the best-efficiency point generally preferred?
5. Name two common causes of cavitation.

Long Answer Questions

1. Explain how a pump curve and system curve are developed and used for equipment selection.
2. Compare centrifugal and positive-displacement pumps, including suitable applications and control methods.
3. Explain the mechanical-energy equation and the meaning of each head term.
4. Discuss pump maintenance practices that improve reliability and safety.
5. Explain how variable-speed control can reduce energy consumption and identify its limitations.

Analytical / Application Questions

1. A pump delivers 0.030 m³/s against a head of 32 m at an overall efficiency of 75%. Calculate the required input power using water density of 1000 kg/m³ and g = 9.81 m/s².
2. A system has a static head of 14 m and a friction-loss coefficient such that losses are 6 m at 0.020 m³/s. Explain how the operating point would change if a valve increased the losses at that flow to 10 m.
3. A pump produces cavitation during hot-weather operation although it was satisfactory in winter. Identify the relevant physical change and propose three corrective actions.

Multiple Choice Questions with Answers

Question 1

Which condition defines the operating point of a pump system?

A. The maximum flow on the pump curve

B. The intersection of the pump curve and system curve

C. The point of zero system resistance

D. The motor nameplate speed only

Correct Answer: B. The intersection of the pump curve and system curve

Question 2

A pump delivers water at Q = 0.020 m³/s and H = 30 m. With ρ = 1000 kg/m³ and g = 9.81 m/s², what is the hydraulic power?

A. 0.5886 kW

B. 5.886 kW

C. 58.86 kW

D. 588.6 kW

Correct Answer: B. 5.886 kW

Question 3

For geometrically similar centrifugal-pump operation with unchanged fluid and approximate efficiency, how does head vary with speed?

A. H is proportional to N

B. H is proportional to N²

C. H is proportional to 1/N

D. H is independent of N

Correct Answer: B. H is proportional to N²

Question 4

Which action directly increases NPSH available?

A. Increasing suction-pipe friction

B. Lowering the liquid level

C. Reducing suction losses

D. Increasing liquid temperature

Correct Answer: C. Reducing suction losses

Question 5

What is the principal physical cause of cavitation?

A. Absolute pressure falling to or below vapour pressure

B. Excessively high motor voltage only

C. Pressure exceeding the pipe rating

D. A pump operating at zero elevation difference

Correct Answer: A. Absolute pressure falling to or below vapour pressure

Question 6

In a fixed piping system, friction loss is commonly approximated as proportional to which quantity?

A. Q

B. √Q

C. Q²

D. 1/Q²

Correct Answer: C. Q²

Question 7

Which pump type is generally suitable for accurate dosing at high pressure and relatively low flow?

A. Axial-flow pump

B. Positive-displacement pump

C. Open impeller circulation fan

D. Mixed-flow turbine

Correct Answer: B. Positive-displacement pump

Question 8

If a centrifugal pump speed is reduced to 80% of its original value, the idealized power ratio from the speed affinity law is approximately:

A. 0. vinte

B. 0.512

C. 0.800

D. 1.250

Correct Answer: B. 0.512

Question 9

What is the principal effect of closing a discharge valve on a centrifugal-pump system?

A. System resistance decreases and flow increases

B. System resistance increases and flow generally decreases

C. Pump speed automatically doubles

D. NPSH required becomes zero

Correct Answer: B. System resistance increases and flow generally decreases

Question 10

Which turbine classification describes a machine in which pressure changes occur through the runner?

A. Reaction turbine

B. Impulse-only turbine

C. Positive-displacement turbine

D. Reciprocating turbine

Correct Answer: A. Reaction turbine