---
title: "Kerosene flow: smooth, rough or transition"
subject: "Hydraulics"
chapter: 1
key: "semester_4/hydraulics:kerosene-pipe-rough-or-smooth"
source: https://www.bctengineer.com/q/semester_4/hydraulics/kerosene-pipe-rough-or-smooth
site: BCT Engineering
---

# Kerosene flow: smooth, rough or transition

Hydraulics · Chapter 1: Pipe flow

- Asked in: 2078 Chaitra, 4 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/kerosene-pipe-rough-or-smooth
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-1

## Question

Kerosene (density = 800 kg/m³) flows in a 20 cm diameter pipe with a mean velocity of 5 m/s. The pipe has an equivalent sandgrain roughness of 0.5 mm. If the friction factor f = 0.02. Is the pipe behaving as rough, smooth or in transition?

## Short answer

With V=5 m/s, f=0.02, D=0.2 m, ν≈2.38×10⁻⁶ m²/s, shear velocity u₊ = V√(f/8)=0.25 m/s. Roughness Reynolds number Re₊ = u₊k/ν ≈ 52.6, which lies in the transition regime (4–100), so the pipe behaves in transition.

## Answer

The type of boundary is decided by the roughness Reynolds number $Re_* = \dfrac{u_* k}{\nu}$ (Nikuradse): smooth $Re_* < 4$, transition $4 \le Re_* \le 100$, rough $Re_* > 100$.

**Data.** $D = 0.2$ m, $V = 5$ m/s, $k = 0.5$ mm, $f = 0.02$, $\rho = 800$ kg/m³. The viscosity is not given, so it is assumed that for kerosene at about 20 °C, $\mu \approx 1.9\times10^{-3}$ Pa s, giving $\nu = \mu/\rho = 2.375\times10^{-6}$ m²/s.

**Shear velocity**
$$
u_* = V\sqrt{\frac{f}{8}} = 5\sqrt{\frac{0.02}{8}} = 0.250\ \text{m/s}
$$

**Roughness Reynolds number**
$$
Re_* = \frac{u_*k}{\nu} = \frac{(0.250)(0.0005)}{2.375\times10^{-6}} = 52.6
$$
Check: laminar sub-layer thickness $\delta' = \dfrac{11.6\nu}{u_*} = 0.110$ mm, which is smaller than $k = 0.5$ mm, but $k/\delta' \approx 4.5$ lies in the transition range (0.25 to 6).

Since $4 < Re_* < 100$ (about 53), the pipe is neither smooth nor fully rough.

**Answer:** The pipe behaves in the **transition** regime ($Re = 421053$, $k/D = 0.0025$, $Re_* \approx 53$). The conclusion is the same for any realistic kerosene viscosity ($\nu$ between 1.9 and 2.8 $\times10^{-6}$ m²/s).

## Check yourself

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

1. Which ranges of roughness Reynolds number classify pipe behaviour?
   A. Smooth < 4, transition 4 to 100, rough > 100
   B. Smooth < 100, transition 100 to 1000, rough > 1000
   C. Smooth < 2000, rough > 4000
   D. Smooth < 1, rough > 10
   Answer: A. Nikuradse limits are 4 and 100 for u*k/nu. (Key point: Classification)

2. What is u* for V = 5 m/s and f = 0.02?
   A. 0.5 m/s
   B. 0.125 m/s
   C. 0.250 m/s
   D. 1.0 m/s
   Answer: C. u* = V sqrt(f/8) = 5 x 0.05 = 0.25 m/s. (Key point: Shear velocity)

3. With Re* of about 53, how does the pipe behave?
   A. Hydrodynamically smooth
   B. Fully rough
   C. Laminar
   D. In transition
   Answer: D. 4 < 53 < 100, so the pipe is in the transition regime. (Key point: Conclusion)

## Related in Hydraulics

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