Pipe systems are everywhere in engineering, from ship and offshore piping to water supply, process plant and building services, and their design depends on predicting pressure loss accurately. This course introduces viscous fluid flow in pipes, focusing on friction losses, local losses, friction-factor selection and the analysis of practical single-pipe and pipe-network systems using standard fluid mechanics methods. It starts from the extended Bernoulli equation and the Reynolds number, derives the Darcy-Weisbach equation from a force balance, and explains what controls the friction factor, from Nikuradse’s experiments to the Moody chart, the Colebrook-White equation and explicit approximations. It then covers minor losses in fittings and transitions, the analysis of single pipelines to find pressure drop, flow rate or diameter, hydraulic and energy grade lines, and the analysis of pipes in series, parallel and branched networks with iterative solution methods.
Course at a glance: Duration 20 hours · Self-paced online · 8 sections, 43 lessons, a 130-page downloadable course book
What you will learn
- Explain how viscosity causes energy loss in pipe flow and relate head loss to the extended Bernoulli equation.
- Classify pipe flow using the Reynolds number and apply laminar-flow friction relationships.
- Apply the Darcy-Weisbach equation to calculate head loss and pressure drop in pipe systems.
- Determine an appropriate friction factor using the Moody chart, empirical equations and roughness data.
- Quantify local losses in fittings and transitions using loss coefficients.
- Solve single-pipeline problems for pressure drop, flow rate, pipe diameter and intermediate pressures.
- Analyse pipes in series, parallel and branched networks using iterative methods.
Inside the course: a high-level summary, section by section.
Real fluid flow
The course starts by moving from ideal to real fluids. The Bernoulli equation describes energy conservation along a streamline for an ideal fluid, but in a real pipe, viscosity converts some mechanical energy into heat. The extended Bernoulli equation adds a head-loss term to account for this, so that pressure head, velocity head and elevation at two points are linked through the losses between them. In a horizontal pipe of constant diameter, the head loss shows up directly as a pressure drop.
The Reynolds number, the ratio of inertial to viscous forces, classifies flow as laminar, transitional or turbulent. Laminar pipe flow has a parabolic velocity profile and an exact solution for pressure drop, the Hagen-Poiseuille relationship. The section closes by introducing the three classic design problem types: finding the pressure drop for a known flow and pipe, finding the flow rate for a known pressure drop, and finding the diameter required to carry a given flow within an allowable loss.
The Darcy-Weisbach equation
A force balance on a pipe element relates wall shear stress to pressure drop, introducing the hydraulic mean depth, the ratio of flow area to wetted perimeter. From this, the general Darcy-Weisbach equation is derived, expressing head loss in terms of a friction factor, pipe length, diameter and velocity head. Friction factor conventions are clarified, since different textbooks define factors that differ by a constant multiple, and the discharge form of the equation expresses losses in terms of flow rate. The physical dependencies of loss show how strongly head loss depends on diameter, which has major implications for design. Comparing the Darcy-Weisbach equation with the laminar solution gives an exact laminar friction factor that depends only on the Reynolds number.
Friction factor selection
For turbulent flow, the friction factor depends on both Reynolds number and the relative roughness of the pipe wall. Nikuradse’s experiments with sand-roughened pipes revealed the different regimes, from smooth-pipe behaviour to fully rough flow, where the friction factor no longer depends on Reynolds number. The Moody chart presents these relationships for commercial pipes, and the course explains how to read it correctly. The Colebrook-White equation is the standard implicit formula behind the chart, and explicit approximations allow direct calculation without iteration. Typical roughness values for materials such as drawn tubing, commercial steel, cast iron and concrete are reviewed, with a reminder that ageing and fouling increase roughness in service.
Local losses
Major losses arise from friction along pipe lengths, while minor or local losses arise at fittings, valves, bends, entrances, exits and changes of section. These are expressed in loss-coefficient form as a multiple of the velocity head. The sudden enlargement loss can be derived from momentum and energy principles, while the sudden contraction loss is linked to the formation of a vena contracta. Boundary-layer separation explains the physical origin of these losses, and typical fitting coefficients are presented for design use. In short, complex systems, minor losses can exceed friction losses.
Single-pipeline analysis
The energy equation for pipelines brings friction and local losses together with pumps, turbines and elevation changes. The course shows how to calculate pressure drop and head loss, how to find the flow rate when the friction factor depends on the unknown velocity, and how to find the pipe diameter needed for a given flow, both of which require iteration. Intermediate pressure points can be checked to avoid low pressures that could cause cavitation or air release. Hydraulic and total head lines provide a visual tool for understanding how energy changes along a pipeline, and a worked pipeline method summarises a reliable step-by-step approach.
Pipe networks
Pipes in series carry the same flow, with total head loss equal to the sum of individual losses. Pipes in parallel share the same head loss, with the flow dividing between branches according to their resistance. Branched networks connecting several reservoirs or demand points require simultaneous solution of continuity and energy equations. Iterative solution methods, such as successive approximation and the Hardy Cross approach, are introduced, and a network analysis workflow sets out how to organise calculations for larger systems.
Why this matters in practice
Undersized pipes waste pumping energy and may fail to deliver required flow; oversized pipes waste capital and space. Accurate pressure-loss calculations underpin the selection of pumps, the sizing of piping for ships, offshore platforms, process plant and utilities, and the diagnosis of performance problems in existing systems. Even when software is used, engineers need to understand the underlying methods to set up models correctly, choose sensible roughness and loss data and check that results are plausible. This course provides that foundation in a compact, practical form.
Key takeaways
You leave able to apply the extended Bernoulli and Darcy-Weisbach equations, choose friction factors from the Moody chart or Colebrook-White equation, quantify local losses, solve the three classic pipeline design problems and analyse series, parallel and branched networks.
How you study
The course is delivered fully online and is self-paced, so you can fit roughly 20 hours of study around professional commitments. Lessons combine clear explanation with examples, diagrams and short interactive checks, and the main sections end with graded quizzes (6 in total) so you can confirm you can apply each method before moving on. A 130-page course book can be downloaded and printed for offline reading and later reference.
Course contents
- Real Fluid Flow: Viscosity and Shear Stress; Extended Bernoulli Equation; Reynolds Number and Regimes; Laminar Pipe Flow; Design Problem Types
- Darcy-Weisbach Losses: Force Balance in a Pipe; General Darcy-Weisbach Derivation; Friction Factor Conventions; Discharge Form of Darcy-Weisbach; Physical Dependencies of Loss; Laminar Friction Factor
- Friction Factor Selection: What Controls Friction Factor; Nikuradse’s Findings; Reading the Moody Chart; Colebrook-White Equation; Explicit Approximations; Typical Roughness Values
- Local Losses: Major and Minor Losses; Loss-Coefficient Form; Sudden Enlargement Loss; Sudden Contraction Loss; Boundary-Layer Separation; Typical Fitting Coefficients
- Single-Pipeline Analysis: Energy Equation for Pipelines; Pressure Drop and Head Loss; Finding Flow Rate; Finding Pipe Diameter; Intermediate Pressure Points; Hydraulic and Total Head Lines; Worked Pipeline Method
- Pipe Networks: Pipes in Series; Pipes in Parallel; Branched Pipe Networks; Network Analysis Workflow
- Summary: Key Takeaways
Who this course is for
This course suits engineering graduates and practising mechanical, marine, offshore, civil, chemical and building services engineers who design or troubleshoot piping systems, as well as students revising fluid mechanics. Basic knowledge of fluid properties and the Bernoulli equation is helpful.
Frequently asked questions
How long does Fluid Mechanics: Pipe Flow & Pressure Loss take?
The course is designed for about 20 hours of study. It is self-paced and fully online, so you can spread it over a few weeks or complete it more quickly.
What is covered?
The course is organised into 8 sections with 43 lessons, moving from foundations to applied methods, as summarised above.
Is there material to keep after the course?
Yes. A downloadable 130-page course book accompanies the lessons for offline reading and later reference.
How is progress checked?
Each main section closes with a graded quiz (6 in total). The quizzes test understanding of the concepts and methods explained in the lessons rather than memorisation, and you can review the relevant lessons before attempting them.
Can I record this study for my own professional development?
Yes. The course notebook includes a self-assessment of the course objectives before and after study, a reflection page and a learning log, which you can use to keep your own record of professional development.
Duration: 20 hours
Related courses: B08 – Design of Auxiliary Systems; H02 – Energy Policy and Economics; C06 – FEM Masterclass for Ship Structures; B13 – Marine Engineering — Propulsion, Auxiliary Systems & Control Engineering
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