Pumps and Turbines

As civil engineers, we frequently encounter hydraulic systems where energy must be added to or extracted from flowing fluids. Understanding how pumps and turbines interact with the Bernoulli Energy Equation is fundamental to designing water supply systems, hydroelectric facilities, irrigation networks, and drainage infrastructure.

If you want to learn Bernoulli Energy Equation Fundamentals first you can click the link.

What you’ll learn

Understanding Pumps vs Turbines in Fluid Systems

Pumps

Pumps are mechanical devices that add energy to a fluid system. They work by converting mechanical energy (typically from an electric motor or engine) into hydraulic energy, which increases the total energy of the fluid.

This energy addition allows water to:

Flow uphill against gravity
Increase pressure in a system
Maintain flow rates

Turbines

Turbines perform the opposite function of pumps, they extract energy from flowing fluid and convert it into mechanical work, typically to generate electricity. The fluid does work on the turbine blades, causing rotation that drives a generator.

This energy is critical in:

renewable energy generation
pump storage facilities

The Bernoulli Energy Equation

The original equation was:

$\frac{P_1}{\gamma}+\frac{v^2_1}{2g}+z_1=\frac{P_2}{\gamma}+\frac{v_2^2}{2g}+z_2$

When a pump is present in a fluid system, we modify the standard Bernoulli equation to account for the energy added. The equation becomes:

$\frac{P_1}{\gamma}+\frac{v^2_1}{2g}+z_1+H_A=\frac{P_2}{\gamma}+\frac{v_2^2}{2g}+z_2$

When it is turbine,

$\frac{P_1}{\gamma}+\frac{v^2_1}{2g}+z_1-H_E=\frac{P_2}{\gamma}+\frac{v_2^2}{2g}+z_2$

Where:
P/γ = Pressure head
v²/2g = Velocity head
z = Elevation head
HA = Head added by the pump
HE = Head extracted by the turbine

Power

Power is different from energy.

Energy is the capacity to do work (measured in Joules or Newton-meters)
Power is the rate at which energy is transferred or work is done (measured in Watts or Joules per second)

In hydraulics, we express energy per unit weight, which gives us units of length (meters or feet). This is why pump and turbine performance is described in terms of “head” rather than total energy.

Power Units in Engineering

1 Watt = 1 Joule/second = 1 N·m/s
1 Horsepower (HP) = 746 Watts
1 HP = 0.746 kW
1 HP = 550 ft·lbf/s (US customary)

$P = \gamma QH$

Where:
P = Power
Q = Flow Rate
γ = Specific weight of fluid
H = Head added (H_A) or extracted (H_E) in meters

Efficiency

Not all machines are perfect. Some machines experiences friction in bearings and seals, turbulence, leakage, electrical losses, etc. That’s why we compute efficiency of the machine:

$Eff=\frac{P_{out}}{P_{in}} \times 100$

For Pumps

P_in = Electrical or mechanical power supplied to the pump
P_out = Hydraulic power delivered to the fluid
Typical efficiencies: 60-85% for centrifugal pumps, 70-90% for positive displacement pumps

For Turbines

P_in = Hydraulic power available from the flowing fluid
P_out = Mechanical/electrical power generated
Typical efficiencies: 85-95% for large hydro turbines

Engineering Applications

Pump Applications in Civil Engineering

Municipal water distribution systems
Wastewater treatment plant operations
Stormwater management and flood control
Irrigation and agricultural water delivery
Building HVAC and plumbing systems

Turbine Applications in Civil Engineering

Hydroelectric power generation at dams
Small-scale hydro projects in water distribution systems (energy recovery)
Pumped storage facilities
Industrial process water energy recovery

Conclusion:

Understanding how pumps and turbines interact with the Bernoulli Energy Equation is essential for civil engineers working with fluid systems. Pumps add energy (represented by +H_A), turbines extract energy (represented by -H_E), and real machines always operate with less than 100% efficiency.

The distinction between energy and power, combined with proper application of the modified Bernoulli equation, allows engineers to properly size equipment, predict system performance, and design efficient hydraulic infrastructure.

Remember that in real-world applications, you must always account for friction losses, minor losses at fittings, and equipment efficiencies to produce accurate and reliable designs. The theoretical equations provide the foundation, but engineering judgment and experience turn theory into successful infrastructure.

📍This post is part of FLUID MECHANICS COMPLETE Lessons. Also, if you want to avail the complete Cheat Sheet just click the “shop now” below.

Fluid Mechanics and Hydraulics Cheat Sheet

Master the fundamentals of fluid mechanics with this complete Fluid Mechanics Cheat Sheet designed for civil engineering students and exam reviewers. This digital guide summarizes the most important formulas, concepts, and equations. Not only it is aesthetic but also categorized by topics.

$5.00

Shop now

CH 8: BERNOULLI’S EQUATION

CH 10: LAMINAR VS TURBULENT