---
title: "Laminar/turbulent flow and friction factor"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:laminar-turbulent-friction-factor"
source: https://www.bctengineer.com/q/semester_6/hydro_power/laminar-turbulent-friction-factor
site: BCT Engineering
---

# Laminar/turbulent flow and friction factor

Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics

- Asked in: 2079 Chaitra, 2+4 marks
- Video: [Solved Example of Turbulent flow | Friction Factor | Maximum velocity | Shear Stress| Turbulent Flow](https://www.youtube.com/watch?v=22IMwpVnYuI) — Professor Nidhi Trivedi
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/laminar-turbulent-friction-factor
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Define laminar and turbulent flows. Water flows through a 700 mm diameter pipe with flow rate 1200 lps. Calculate the value of friction factor if the head loss in 50 m of pipe length is 0.6 m.

## Short answer

Laminar flow: smooth parallel layers, Re<2000. Turbulent flow: random eddies, Re>4000. For D=0.7m, Q=1.2m³/s, L=50m, hf=0.6m: V=3.118m/s, V²/2g=0.4956m. Darcy-Weisbach gives f = hf D / (L V²/2g) = 0.017. Re≈2.2×10⁶, turbulent.

## Answer

#### Laminar and turbulent flow
- **Laminar flow:** fluid particles move in smooth, parallel layers without mixing; viscous forces dominate; $Re < 2000$ in pipes. Example: thick oil in a thin tube.
- **Turbulent flow:** particles move randomly with eddies and mixing; inertia forces dominate; $Re > 4000$ in pipes. Example: water in a penstock.

#### Numerical
**Given:** $D = 0.7$ m, $Q = 1200$ L/s $= 1.2$ m³/s, $L = 50$ m, $h_f = 0.6$ m.

Velocity:
$$
\begin{aligned}
A &= \frac{\pi}{4}(0.7)^2 = 0.3848\ \text{m}^2 \\
V &= \frac{Q}{A} = \frac{1.2}{0.3848} = 3.118\ \text{m/s} \\
\frac{V^2}{2g} &= \frac{3.118^2}{2 \times 9.81} = 0.4956\ \text{m}
\end{aligned}
$$

Darcy–Weisbach equation:
$$
h_f = f\frac{L}{D}\frac{V^2}{2g}
$$
$$
\begin{aligned}
f &= \frac{h_f\, D}{L}\cdot\frac{2g}{V^2} \\
&= \frac{0.6 \times 0.7}{50 \times 0.4956} = 0.01695
\end{aligned}
$$

**Answer:** Darcy friction factor $f \approx 0.017$. (If the form $h_f = \frac{4fLV^2}{2gD}$ is used, the coefficient of friction is $f/4 \approx 0.0042$.) At $V = 3.12$ m/s in a 0.7 m pipe, $Re \approx 2.2\times10^6$, so the flow is turbulent.

## Check yourself

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

1. Which describes laminar flow?
   A. Random, inertia dominant
   B. Eddies and mixing, Re > 4000
   C. Re between 2000 and 4000 only
   D. Smooth parallel layers, viscous forces dominate, Re < 2000
   Answer: D. Laminar flow has layered motion with viscous forces dominant; turbulent flow has eddies. (Key point: Laminar vs turbulent)

2. Which equation gives f from head loss?
   A. h_f = V^2/2g
   B. h_f = f (L/D)(V^2/2g)
   C. h_f = f D/L
   D. h_f = f L V
   Answer: B. Darcy-Weisbach: f = h_f D 2g / (L V^2). (Key point: Formula used)

3. What is the velocity for Q = 1.2 m^3/s in a 0.7 m pipe?
   A. 1.714 m/s
   B. 3.118 m/s
   C. 0.5 m/s
   D. 6.24 m/s
   Answer: B. V = Q/A = 1.2/0.3848 = 3.118 m/s. (Key point: Velocity)

4. What is the Darcy friction factor?
   A. 0.017
   B. 0.0042
   C. 0.068
   D. 0.17
   Answer: A. f = 0.6 x 0.7 / (50 x 0.4956) = 0.01695; 0.0042 would be the f/4 form. (Key point: Friction factor)

## Related in Hydro Power

- [Discharge and head loss in horizontal pipe](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Apipe-discharge-head-loss) — Hydro Power, chapter 1
- [Head loss with enlarged central pipe length](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Apipe-replaced-central-length) — Hydro Power, chapter 1
- [Head loss and flow direction in tapering oil pipe](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atapering-pipe-oil-flow) — Hydro Power, chapter 1
- [Water hammer in 200 mm pipe](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Awater-hammer-200mm-pipe) — Hydro Power, chapter 1
- [Head loss at sudden enlargement](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Asudden-enlargement-loss) — Hydro Power, chapter 1
- [Flow between reservoirs (15 cm and 25 cm pipe)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Areservoirs-pipeline-15-25cm) — Hydro Power, chapter 1

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