💧Fluid Mechanics Unit 11 – Pumps and Turbomachinery

Key Concepts and Definitions

• Pumps convert mechanical energy into hydraulic energy to transport fluids from one location to another
• Turbomachines extract energy from a fluid to produce mechanical work and include both pumps and turbines
• Head ($H$) represents the energy imparted to the fluid by the pump, expressed in terms of equivalent height of the fluid column
• Flow rate ($Q$) quantifies the volume of fluid passing through the pump per unit time, typically expressed in units such as gallons per minute (gpm) or cubic meters per second (m³/s)
• Specific speed ($N_s$) is a dimensionless parameter that characterizes the geometry and performance of a pump or turbine, allowing for comparison between different designs
  • Calculated using the formula: $N_s = \frac{N\sqrt{Q}}{H^{3/4}}$, where $N$ is the rotational speed, $Q$ is the flow rate, and $H$ is the head
• Net positive suction head (NPSH) represents the pressure available at the pump inlet to prevent cavitation, which can cause damage to the pump components
• Efficiency ($\eta$) measures the ratio of the useful hydraulic power output to the mechanical power input, expressed as a percentage

Types of Pumps and Turbomachines

• Centrifugal pumps use an impeller to impart kinetic energy to the fluid, which is then converted to pressure energy in the volute or diffuser
  • Suitable for high flow rates and moderate heads, commonly used in water supply systems, irrigation, and industrial processes
• Positive displacement pumps (reciprocating pumps, gear pumps, screw pumps) move a fixed volume of fluid with each cycle or revolution, providing a constant flow rate regardless of the system pressure
• Axial flow pumps (propeller pumps) move fluid along the axis of rotation, suitable for high flow rates and low heads, often used in flood control and large-scale water transfer projects
• Turbines convert the energy of a moving fluid (water, steam, or gas) into mechanical work, driving generators for electricity production or powering other machinery
  • Impulse turbines (Pelton wheel) utilize the kinetic energy of a high-velocity fluid jet to drive the turbine blades
  • Reaction turbines (Francis, Kaplan) rely on both pressure and velocity changes in the fluid as it passes through the turbine runner
• Jet pumps (ejectors) use a high-velocity jet of fluid to entrain and compress a secondary fluid, often used in vacuum systems and condensers

Fundamental Principles of Operation

• Conservation of mass (continuity equation) states that the mass flow rate entering a pump or turbomachine must equal the mass flow rate exiting, assuming no accumulation or leakage
  • For incompressible fluids: $Q_1 = Q_2$, where $Q_1$ and $Q_2$ are the flow rates at the inlet and outlet, respectively
• Conservation of energy (Bernoulli's equation) describes the relationship between pressure, velocity, and elevation in a fluid system, neglecting losses
  • $\frac{p_1}{\rho g} + \frac{v_1^2}{2g} + z_1 = \frac{p_2}{\rho g} + \frac{v_2^2}{2g} + z_2 + H_p$, where $p$ is pressure, $\rho$ is fluid density, $g$ is gravitational acceleration, $v$ is velocity, $z$ is elevation, and $H_p$ is the head added by the pump
• Euler's pump and turbine equations relate the change in angular momentum of the fluid to the torque and energy transfer in a turbomachine
  • For pumps: $H_p = \frac{1}{g}(u_2v_{u2} - u_1v_{u1})$, where $u$ is the blade speed and $v_u$ is the tangential component of the fluid velocity
• Velocity triangles represent the relationship between the fluid velocity, blade velocity, and relative velocity at the inlet and outlet of a pump or turbine impeller
• Cavitation occurs when the local pressure in a fluid falls below the vapor pressure, leading to the formation and collapse of vapor bubbles, which can cause damage to pump components and reduce performance

Performance Characteristics and Curves

• Head-capacity (H-Q) curve represents the relationship between the head developed by the pump and the flow rate, typically showing a decreasing trend with increasing flow rate
  • Shutoff head is the maximum head developed by the pump at zero flow rate
  • Best efficiency point (BEP) is the flow rate at which the pump operates with the highest efficiency
• Power-capacity (P-Q) curve shows the relationship between the input power required by the pump and the flow rate, generally increasing with increasing flow rate
• Efficiency-capacity (η-Q) curve depicts the variation of pump efficiency with flow rate, with the peak efficiency occurring at the BEP
• Net positive suction head required (NPSHR) curve represents the minimum NPSH needed at the pump inlet to prevent cavitation at different flow rates
  • NPSH available (NPSHA) must be greater than NPSHR to ensure proper pump operation without cavitation
• Specific speed-efficiency (Ns-η) curve is used to compare the performance of different pump designs and select the most suitable type for a given application

Design and Selection Criteria

• Flow rate and head requirements are determined based on the specific application and system characteristics, such as pipe size, length, and elevation changes
• Fluid properties, including viscosity, density, and temperature, influence pump selection and performance
  • Viscous fluids may require positive displacement pumps or specially designed centrifugal pumps
  • High-temperature fluids may necessitate the use of materials with appropriate thermal properties
• System layout and space constraints affect the choice of pump type, size, and orientation
  • Submersible pumps are used in applications where the pump must be located below the fluid level
  • Vertical turbine pumps are suitable for deep well and borehole applications
• Material compatibility ensures that the pump components can withstand the chemical and physical properties of the pumped fluid without corrosion, erosion, or degradation
• Cost considerations include initial capital investment, operating costs (energy consumption), and maintenance requirements
  • Life cycle cost analysis helps in selecting the most economical pump option over its entire service life

Efficiency and Energy Considerations

• Pump efficiency is crucial for minimizing energy consumption and operating costs in fluid transport systems
  • Hydraulic efficiency ($\eta_h$) represents the ratio of the fluid power output to the mechanical power input, accounting for losses in the impeller and volute
  • Mechanical efficiency ($\eta_m$) accounts for losses in bearings, seals, and other mechanical components
  • Overall efficiency ($\eta_o$) is the product of hydraulic and mechanical efficiencies: $\eta_o = \eta_h \times \eta_m$
• Energy optimization strategies include selecting pumps with high efficiencies, operating pumps near their BEP, and using variable speed drives to match pump output to system demands
• Proper sizing and selection of pumps and motors can significantly reduce energy consumption and improve system performance
  • Oversized pumps operate inefficiently and may require throttling valves, leading to additional energy losses
  • Undersized pumps may not meet the required flow rate and head, leading to inadequate system performance
• Regular maintenance, such as impeller trimming, bearing lubrication, and seal replacement, helps maintain pump efficiency and prevent energy losses over time

Applications in Industry

• Water supply and distribution systems rely on pumps to transport water from sources (wells, reservoirs) to treatment plants and end-users
  • Booster pumps maintain pressure in distribution networks to ensure adequate flow and pressure at all points
• Wastewater treatment plants use pumps to move sewage and effluent through various treatment stages, including screening, sedimentation, and biological treatment
• Oil and gas industry employs pumps for extraction (downhole pumps), transportation (pipeline pumps), and processing (refinery pumps) of hydrocarbons
  • Multiphase pumps can handle a mixture of oil, gas, and water, eliminating the need for separate separation equipment
• Chemical processing plants use pumps to transfer raw materials, intermediates, and finished products between storage tanks, reactors, and separation units
  • Sealless pumps, such as magnetic drive or canned motor pumps, are used for handling hazardous or toxic chemicals to minimize leakage risk
• Power generation facilities use pumps in various applications, such as boiler feed water, condensate return, and cooling water circulation
  • High-pressure pumps are critical for boiler feed water systems in thermal power plants to maintain proper boiler operation and efficiency

Troubleshooting and Maintenance

• Cavitation can cause damage to pump components, vibration, and noise, often resulting from insufficient NPSHA or excessive suction lift
  • Symptoms include reduced flow rate, increased power consumption, and pitting or erosion of impeller and volute surfaces
  • Remedies involve increasing NPSHA (raising suction tank level, reducing suction line losses) or reducing NPSHR (trimming impeller, using inducer)
• Mechanical seal failure can lead to leakage, contamination, and reduced pump performance
  • Causes include improper installation, misalignment, lack of lubrication, or chemical incompatibility
  • Regular inspection, replacement of worn seals, and proper alignment during installation can prevent seal failures
• Bearing wear and failure can cause increased vibration, noise, and heat generation, potentially leading to catastrophic pump damage
  • Lubrication issues, misalignment, and excessive loads are common causes of bearing problems
  • Implementing a proper lubrication schedule, using appropriate lubricants, and monitoring bearing temperature and vibration can help extend bearing life
• Performance deterioration over time may result from wear, fouling, or changes in system conditions
  • Regular testing and comparison of pump curves with baseline data can help identify performance issues early
  • Cleaning, adjustment, or replacement of worn components (impeller, wear rings) can restore pump performance
• Preventive maintenance programs, including regular inspections, lubrication, and parts replacement, can minimize unplanned downtime and extend the service life of pumps and turbomachinery
  • Predictive maintenance techniques, such as vibration analysis, thermography, and oil analysis, can help detect potential issues before failure occurs