Hydraulic Machinery

Principles of pumps and turbines, power calculations, characteristic curves, and cavitation.

Concept Overview

Hydraulic machines convert fluid energy into mechanical energy (turbines) or mechanical energy into fluid energy (pumps).

Pumps

Concept Overview

Pumps increase the pressure head of a fluid. The most common types are centrifugal (radial flow) and axial flow pumps.

Pump Power

Water Power (PwP_w): The power delivered to the fluid.

Pump Power

Principles of pumps and turbines, power calculations, characteristic curves, and cavitation.

Pw=γQHP_w = \gamma Q H

Variables

SymbolDescriptionUnit
γ\gammaSpecific weight of fluid ($9.81 \text{ kN/m}^3$ for water).-
QQDischarge.-
HHTotal dynamic head (TDH).-
Brake Power (PbP_b): The power supplied to the pump shaft by the motor.
Pb=PwηP_b = \frac{P_w}{\eta}

Variables

SymbolDescriptionUnit
η\etaPump efficiency ($< 1$).-

Total Dynamic Head (TDH)

The total head against which the pump operates.

Total Dynamic Head (TDH)

H=hs+hd+hf+Vd22g−Vs22gH = h_s + h_d + h_f + \frac{V_d^2}{2g} - \frac{V_s^2}{2g}

Variables

SymbolDescriptionUnit
hsh_sStatic suction lift.-
hdh_dStatic discharge head.-
hfh_fFriction losses in suction and discharge pipes.-

Turbines

Concept Overview

Turbines extract energy from fluid flow to generate mechanical power (e.g., hydroelectric dams).

Turbine Power

Output Power (PP):

Turbine Power

P=γQHηP = \gamma Q H \eta
  • Here, η\eta accounts for hydraulic, volumetric, and mechanical losses.

Specific Speed

A dimensionless parameter used to classify and select the most efficient type of pump or turbine for a given application.

Pump Specific Speed (NsN_s)

It is defined as the speed in RPM at which a geometrically similar pump would deliver 1 unit of flow rate at 1 unit of head. It depends only on the design shape of the impeller, not its physical size or actual operating speed.

Pump Specific Speed ($N_s$)

A dimensionless parameter used to classify and select the most efficient type of pump or turbine for a given application.

Ns=NQH3/4N_s = \frac{N \sqrt{Q}}{H^{3/4}}

Variables

SymbolDescriptionUnit
NNPump rotational speedRPM
QQDischarge at Best Efficiency PointBEP
HHHead per stage at BEP-
Impeller Selection based on NsN_s:
  • Low NsN_s: Centrifugal (Radial flow). High head, low flow.
  • Medium NsN_s: Mixed flow.
  • High NsN_s: Axial flow (Propeller). Low head, very high flow.

Turbine Specific Speed (NsN_s)

For turbines, specific speed is defined based on power output (PP) rather than discharge (QQ), since generating power is the primary goal.

Turbine Specific Speed ($N_s$)

Ns=NPH5/4N_s = \frac{N \sqrt{P}}{H^{5/4}}

Variables

SymbolDescriptionUnit
PPPower output at design point-
Turbine Selection based on NsN_s:
  • Low NsN_s: Pelton Wheel (Impulse turbine). Very high head (>200m> 200m), low flow rate.
  • Medium NsN_s: Francis Turbine (Reaction turbine). Medium head (40m−400m40m - 400m), medium flow.
  • High NsN_s: Kaplan Turbine (Reaction turbine, axial flow). Low head (<40m< 40m), high flow.

Pump Characteristic Curves

Base elevation difference the pump must overcome.

Represents friction losses in pipes and fittings.

Operating Point

Discharge (Q_op):18.5 L/s
Head (H_op):37.1 m
Efficiency (η):84.5%
Brake Power (P_b):7981.4 kW
Q (L/s)Head (m)Pump CurveSystem Curve

Pump Characteristics

Characteristic Curves

Performance curves plot Head (HH), Power (PP), and Efficiency (η\eta) against Discharge (QQ) for a constant speed (NN).
  • Head-Discharge Curve (H-Q): Typically drops as QQ increases.
  • Efficiency Curve: Increases to a peak (Best Efficiency Point - BEP) and then drops.
  • Power Curve: Increases with QQ.

Affinity Laws

Scaling rules to predict pump or turbine performance under different operating conditions.

Pump Affinity Laws

When testing a single pump (diameter DD is constant) at a new rotational speed (N2N_2), the new performance parameters can be predicted from the original speed (N1N_1).
  • Discharge (QQ): Varies directly with speed.

    Pump Affinity Laws

    Scaling rules to predict pump or turbine performance under different operating conditions.

    Q1Q2=N1N2\frac{Q_1}{Q_2} = \frac{N_1}{N_2}
  • Head (HH): Varies with the square of the speed.
    H1H2=(N1N2)2\frac{H_1}{H_2} = \left(\frac{N_1}{N_2}\right)^2
  • Power (PP): Varies with the cube of the speed.
    P1P2=(N1N2)3\frac{P_1}{P_2} = \left(\frac{N_1}{N_2}\right)^3
These laws assume that efficiency remains constant between the two speeds, which is a reasonable assumption for small changes in NN.

Cavitation and NPSH

Cavitation occurs when the absolute pressure at the pump inlet drops below the vapor pressure (PvP_v) of the liquid. Bubbles form and collapse violently, causing damage.

Net Positive Suction Head (NPSH)

The absolute head at the pump inlet above the vapor pressure head. To prevent cavitation:

Net Positive Suction Head (NPSH)

NPSHavailable>NPSHrequiredNPSH_{available} > NPSH_{required}
NPSHA=Patmγ−hs−hfs−PvγNPSH_A = \frac{P_{atm}}{\gamma} - h_s - h_{fs} - \frac{P_v}{\gamma}

Variables

SymbolDescriptionUnit
hsh_sSuction lift (vertical distance from source to pump).-
hfsh_{fs}Friction loss in suction line.-
Key Takeaways
  • Pumps add energy to a fluid system, increasing its total dynamic head (TDH).
  • Affinity Laws: Predict performance changes when altering pump speed: Flow scales linearly, Head scales quadratically, Power scales cubically.
  • Water Power is the useful energy gained by the fluid, while Brake Power is the total energy that must be supplied by the motor. Brake power is always greater due to efficiency losses (η<1\eta < 1).
  • Turbines extract energy from a moving fluid and convert it into mechanical energy.
  • Unlike pumps where efficiency is in the denominator, for turbines, efficiency (η\eta) is in the numerator because the mechanical output power is always less than the available fluid power.
  • Pump performance is evaluated using characteristic curves supplied by the manufacturer.
  • The operating point of a pump in a specific system is found at the intersection of the pump's Head-Discharge (H-Q) curve and the system's curve.
  • Pumps should ideally operate near their Best Efficiency Point (BEP).
  • Cavitation is the highly destructive formation and collapse of vapor bubbles inside a pump when local pressure drops below the fluid's vapor pressure.
  • To prevent cavitation, the Net Positive Suction Head Available (NPSHANPSH_A) must strictly be greater than the NPSHNPSH required by the pump design.
  • Minimizing suction lift (hsh_s) and reducing friction in the suction line (hfsh_{fs}) are the primary ways to increase NPSHANPSH_A.
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