Hydraulic Machinery

Pumps add energy to a fluid system, primarily to increase the pressure head, overcome friction, or lift the fluid to a higher elevation. The added energy enables the fluid to move from a region of lower potential energy to a region of higher potential energy.

The most common classifications based on the direction of fluid flow relative to the impeller are:

• Centrifugal (Radial Flow) Pumps: Fluid enters axially and exits radially. Ideal for high head and low flow rate applications.
• Axial Flow Pumps (Propeller Pumps): Fluid flows parallel to the axis of rotation. Ideal for low head and high flow rate applications.
• Mixed Flow Pumps: Fluid exits at an angle between radial and axial. They balance head and flow rate requirements.

Hydraulic pump power is analyzed to determine the efficiency of the energy transfer and to size the motor correctly. The difference between the Brake Power and the Water Power represents the energy lost as heat and friction within the pump casing.

In a hydroelectric setup, potential energy from a reservoir is converted into kinetic energy as water flows down a penstock. The turbine captures this kinetic energy. Depending on how they harness the energy, turbines are categorized as:

• Impulse Turbines (e.g., Pelton Wheel): The fluid's pressure is converted entirely to kinetic energy before hitting the turbine blades in the form of a high-speed jet. The turbine operates in the air.
• Reaction Turbines (e.g., Francis, Kaplan): The fluid completely fills the casing, and the rotor is driven by both the fluid's pressure and its kinetic energy.

Unlike pumps where efficiency divides the useful power to find the required input, for turbines, efficiency multiplies the available fluid power to find the actual mechanical output. The mechanical power extracted is what drives the generators in hydroelectric dams.

Specific speed is arguably the most important parameter in hydraulic machinery selection. It characterizes the shape and design of the impeller or runner. Machines with the same specific speed will have similar geometric proportions, regardless of their actual physical size.

Pump specific speed ($N_s$) is theoretically defined as the rotational speed in RPM at which a geometrically similar pump would deliver 1 unit of flow rate at 1 unit of head. It depends entirely on the design shape of the impeller.

Impeller classification based on $N_s$ ranges:

• Low $N_s$: Radial Flow (Centrifugal). Designed for high head and low flow applications. The flow exits radially.
• Medium $N_s$: Mixed Flow. Designed for moderate head and moderate flow.
• High $N_s$: Axial Flow (Propeller). Designed for low head and very high flow applications.

For turbines, specific speed ($N_s$) is defined based on the design power output ($P$) rather than discharge ($Q$), because generating power is the primary objective of a turbine.

Turbine classification based on $N_s$ ranges:

• Low $N_s$: Pelton Wheel (Impulse turbine). Used for very high head installations ($> 200\text{ m}$) with low flow rates.
• Medium $N_s$: Francis Turbine (Reaction turbine). Used for medium head installations ($40\text{ m} - 400\text{ m}$) with medium flow rates.
• High $N_s$: Kaplan Turbine (Reaction turbine, axial flow). Used for low head installations ($< 40\text{ m}$) with high flow rates.

Characteristic curves are essential for pump selection and system design. They show how a pump will behave under varying flow conditions:

• Head-Discharge Curve (H-Q): Shows that as flow rate ($Q$) increases, the head ($H$) the pump can deliver typically decreases.
• Efficiency Curve: Starts at zero when flow is zero, rises to a maximum point called the Best Efficiency Point (BEP), and then declines as flow increases further. Pumps should be operated as close to the BEP as possible to minimize energy costs and wear.
• Power Curve: Shows the brake power required. For radial flow pumps, power typically increases as flow increases.

The most common application of affinity laws involves calculating performance changes for a single, specific pump (where the impeller diameter $D$ is fixed) when driven by a Variable Frequency Drive (VFD) to change its rotational speed.

These scaling laws assume that the hydraulic efficiency remains constant between the different speeds. The relationships demonstrate how sensitive power consumption is to speed changes:

• Discharge ($Q$): Scales linearly. Doubling the speed doubles the flow.
• Head ($H$): Scales quadratically. Doubling the speed quadruples the head.
• Power ($P$): Scales cubically. Doubling the speed requires eight times the power. This cubic relationship makes VFDs highly economical for reducing flow compared to throttling with a valve.

In pumps, cavitation typically occurs at the suction eye of the impeller where the pressure is lowest. The collapsing bubbles generate microscopic shockwaves that relentlessly pit and erode the metal impeller. Cavitation causes severe vibration, distinct noise (often sounding like marbles rattling in the casing), a sharp drop in pump efficiency, and eventual mechanical failure.

To prevent cavitation, the system designer must ensure that the pressure at the pump inlet is sufficiently high to keep the fluid from vaporizing. This is evaluated by comparing the available head provided by the system against the required head dictated by the pump's physical design.