---
title: "Moody's chart basis and uses"
subject: "Hydraulics"
chapter: 1
key: "semester_4/hydraulics:moody-chart-describe"
source: https://www.bctengineer.com/q/semester_4/hydraulics/moody-chart-describe
site: BCT Engineering
---

# Moody's chart basis and uses

Hydraulics · Chapter 1: Pipe flow

- Asked in: 2077 Chaitra, 2+4+2 marks
- Video: [Moody chart and how to use it? (with Animation Fluid Mechanics)](https://www.youtube.com/watch?v=1gt8PzM-Sfo) — NiLTime
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/moody-chart-describe
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-1

## Question

Describe Moody's Chart. What are the basis to draw such a diagram? State its uses.

## Short answer

Moody’s chart plots Darcy–Weisbach friction factor f versus Reynolds number Re for circular pipes, with curves for relative roughness k/D. It is based on laminar, smooth, and rough pipe equations. It is used to determine f, head loss, flow regime, and for pipe design problems.

## Answer

#### Description
Moody's chart is a graph of the Darcy-Weisbach friction factor $f$ against the Reynolds number $Re$ for flow in circular pipes, with a family of curves for different **relative roughness** $k/D$ (equivalent sand roughness / diameter). Both axes are logarithmic: $Re$ (from about $10^3$ to $10^8$) on the horizontal axis, $f$ (about 0.008 to 0.1) on the vertical axis, and the relative roughness is marked on the right-hand scale.

```text
 f
 0.1 |\ laminar     critical     k/D curves
     | \  f=64/Re   zone    _________ 0.05
 0.05|  \          |      __/   ______ 0.01
     |   \_        |  ___/ ___/ ______ 0.001
 0.02|     \______ |_/ ___/   _______  0.0001
     |  smooth pipe curve ___/  (rough: flat lines)
 0.01|                   transition|  fully rough
     +--------------------------------- Re (log)
     10^3   10^4    10^5   10^6    10^7
```

Regions of the chart:

| Region | Re | f depends on |
|---|---|---|
| Laminar | < 2000 | $Re$ only, $f = 64/Re$ (straight line) |
| Critical zone | 2000 to 4000 | Unstable, not reliable |
| Smooth turbulent | > 4000 | $Re$ only (lowest curve) |
| Transition (partly rough) | middle | both $Re$ and $k/D$ (Colebrook-White) |
| Fully rough | right of dashed line | $k/D$ only (horizontal lines) |

#### Basis of the chart
1. **Laminar flow:** Hagen-Poiseuille law gives $f = 64/Re$.
2. **Smooth pipes:** Blasius ($f = 0.316/Re^{0.25}$, $Re < 10^5$) and Prandtl's universal law $\dfrac{1}{\sqrt f} = 2\log_{10}(Re\sqrt f) - 0.8$.
3. **Rough pipes:** von Karman-Prandtl law from Nikuradse's sand-roughened pipe experiments, $\dfrac{1}{\sqrt f} = 2\log_{10}\dfrac{D}{k} + 1.14$.
4. **Transition region:** the Colebrook-White equation, which joins the smooth and rough laws:
$$
\frac{1}{\sqrt f} = -2\log_{10}\left(\frac{k/D}{3.7} + \frac{2.51}{Re\sqrt f}\right)
$$
Moody plotted this equation using the *equivalent* roughness of commercial pipes (Nikuradse's artificial roughness corrected to commercial pipe behaviour).

#### Uses
- To find $f$ for a given $Re$ and $k/D$, then the head loss $h_f = \dfrac{fLV^2}{2gD}$.
- To identify the flow regime (laminar, smooth, transition, rough) of a pipe.
- To solve the three types of pipe problems (find $h_f$, find $Q$, find $D$), by iteration.
- To get the equivalent roughness $k$ of an old or commercial pipe from test data.
- To compare materials and judge how much capacity is lost as a pipe ages and becomes rough.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does the Moody chart plot?
   A. Head loss against discharge
   B. Friction factor f against Re for different relative roughness k/D
   C. Velocity against diameter
   D. Shear stress against viscosity
   Answer: B. It plots f versus Re on log scales with curves for k/D. (Key point: Chart axes)

2. In the fully rough zone, on what does f depend?
   A. Re only
   B. Both Re and k/D
   C. k/D only
   D. Neither
   Answer: C. The curves become horizontal, so f depends only on relative roughness. (Key point: Fully rough region)

3. Which equation underlies the transition region of the chart?
   A. Blasius equation
   B. Hagen-Poiseuille equation
   C. von Karman-Prandtl rough law only
   D. Colebrook-White equation
   Answer: D. Colebrook-White joins the smooth and rough laws. (Key point: Transition basis)

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