---
title: "Settling velocity of discrete particle 0.14 mm at 25°C"
subject: "Water Supply Engineering"
chapter: 6
key: "semester_5/water_supply_engineering:sed-j66"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/sed-j66
site: BCT Engineering
---

# Settling velocity of discrete particle 0.14 mm at 25°C

Water Supply Engineering · Chapter 6: Water Treatment

- Asked in: 2066 Jestha (old course)
- Video: [Problem on Settling velocity](https://www.youtube.com/watch?v=eCBOdujRNLY) — CV221 Water Supply Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/water_supply_engineering/sed-j66
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-6

## Question

Determine the settling velocity of a discrete particle having the diameter 0.14 mm; specific gravity 2.61 in water. The temperature of fluid is 25°C.

## Short answer

Stokes' law gives 1.93 cm/s but Re=3.02, so transition formula is applied. After trial and error, settling velocity converges to 1.57 cm/s (15.7 mm/s) with Re=2.5.

## Answer

Settling velocity of a discrete spherical particle is first tried with Stokes' law, and the Reynolds number is checked. If $Re>1$ the transition formula must be used.

#### Data
$d=0.14$ mm $=0.014$ cm, $S_s=2.61$, $\nu=0.00893$ cm²/s (at 25 °C, about 0.893 centistokes), $g=981$ cm/s².

#### Step 1: Stokes' law (trial)
$$
v_s=\frac{g(S_s-1)d^2}{18\nu}=\frac{981\times1.61\times0.014^2}{18\times0.00893}=1.926\ \text{cm/s}
$$
$$
Re=\frac{v_s d}{\nu}=\frac{1.926\times0.014}{0.00893}=3.02
$$
Since $Re>1$, Stokes' law is not valid and the flow is in the transition zone ($1<Re<1000$).

#### Step 2: Transition zone (Fair and Geyer)
$$
C_d=\frac{24}{Re}+\frac{3}{\sqrt{Re}}+0.34,\qquad v_s=\sqrt{\frac{4g(S_s-1)d}{3C_d}}
$$
Trial and error:

| Trial | $v$ assumed (cm/s) | $Re=vd/\nu$ | $C_d$ | new $v$ (cm/s) |
|---|---|---|---|---|
| 1 | 1.926 | 3.02 | 10.015 | 1.716 |
| 2 | 1.716 | 2.69 | 11.092 | 1.630 |
| 3 | 1.630 | 2.56 | 11.606 | 1.594 |
| 4 | 1.594 | 2.50 | 11.843 | 1.578 |
| 5 | 1.578 | 2.47 | 11.950 | 1.571 |
| 6 | 1.571 | 2.46 | 11.998 | 1.568 |

The values converge to $v_s=1.57$ cm/s, $Re=2.5$, $C_d=12.04$.

**Answer: settling velocity $v_s\approx1.57$ cm/s ($15.7$ mm/s), with $Re=2.5$.** (Stokes' law would overestimate it as 1.93 cm/s.)

## Check yourself

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

1. Why was Stokes' law rejected for the 0.14 mm particle?
   A. The trial Reynolds number was 3.02, which is more than 1
   B. The particle is larger than 1 mm
   C. The water temperature is above 40 °C
   D. The specific gravity is less than 1
   Answer: A. Stokes' law is valid only for Re < 1. The trial gave Re = 3.02, so the transition zone applies. (Key point: Check Stokes first)

2. Which drag coefficient expression is used in the transition zone?
   A. Cd = 24/Re
   B. Cd = 0.4
   C. Cd = 24/Re + 3/sqrt(Re) + 0.34
   D. Cd = 18/Re + 0.34
   Answer: C. Fair and Geyer's expression adds the 3/sqrt(Re) and 0.34 terms to the Stokes term 24/Re. (Key point: Transition drag coefficient)

3. Why must the transition-zone velocity be found by trial and error?
   A. The viscosity is unknown
   B. Cd depends on Re, and Re depends on the unknown settling velocity
   C. Gravity changes with each trial
   D. The particle diameter changes while settling
   Answer: B. vs needs Cd, Cd needs Re = vs d/ν, and Re needs vs, so the value is iterated until it converges. (Key point: Why trial and error)

4. What does the iteration converge to, and how does it compare with Stokes' law?
   A. About 1.57 cm/s, and Stokes' law underestimates it
   B. About 1.93 cm/s, and Stokes' law is exact
   C. About 3.02 cm/s, with Re = 1.57
   D. About 1.57 cm/s, and Stokes' law (1.93 cm/s) overestimates it
   Answer: D. The converged vs is 1.57 cm/s with Re about 2.5. Ignoring the extra drag in the transition zone makes Stokes' law give too high a velocity. (Key point: Final result)

## Close variants set in other exams

- [Settling velocity of discrete particle 0.17 mm at 21°C](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ased-c70o) — Water Supply Engineering, chapter 6, asked 2×

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- [Settling velocity of silica particle 0.02 cm at 20°C](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ased-c69) — Water Supply Engineering, chapter 6
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- [Settling tank 30 m x 3 m, 0.03 mm at 25°C; 0.025 mm at 20°C](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ased-k72) — Water Supply Engineering, chapter 6, asked 3×
- [Settling tank 30 m x 3 m; velocity for 0.02 mm](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ased-bk68) — Water Supply Engineering, chapter 6, asked 2×

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