---
title: "Settling velocity of discrete particle 0.17 mm at 21°C"
subject: "Water Supply Engineering"
chapter: 6
key: "semester_5/water_supply_engineering:sed-c70o"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/sed-c70o
site: BCT Engineering
---

# Settling velocity of discrete particle 0.17 mm at 21°C

Water Supply Engineering · Chapter 6: Water Treatment

- Asked in: 2070 Chaitra (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-c70o
- 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 0.17 mm; specific gravity 2.65 in water. The temperature of fluid is 21°C.

## Short answer

Stokes' law yields 2.66 cm/s, Re=4.62, requiring transition-zone correction. Iterative solution gives a settling velocity of approximately 2.06 cm/s (20.6 mm/s).

## 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
$d=0.17$ mm $=0.017$ cm, $S_s=2.65$, $\nu=0.00978$ cm²/s (at 21 °C, about 0.978 centistokes), $g=981$ cm/s².

#### Step 1: Stokes' law (trial)
$$
v_s=\frac{g(S_s-1)d^2}{18\nu}=\frac{981\times1.65\times0.017^2}{18\times0.00978}=2.657\ \text{cm/s}
$$
$$
Re=\frac{v_s d}{\nu}=\frac{2.657\times0.017}{0.00978}=4.62
$$
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 | 2.657 | 4.62 | 6.932 | 2.301 |
| 2 | 2.301 | 4.00 | 7.842 | 2.163 |
| 3 | 2.163 | 3.76 | 8.270 | 2.106 |
| 4 | 2.106 | 3.66 | 8.463 | 2.082 |
| 5 | 2.082 | 3.62 | 8.548 | 2.072 |
| 6 | 2.072 | 3.60 | 8.585 | 2.067 |

The values converge to $v_s=2.06$ cm/s, $Re=3.6$, $C_d=8.61$.

**Answer: settling velocity $v_s\approx2.06$ cm/s ($20.6$ mm/s), with $Re=3.6$.** (Stokes' law would overestimate it as 2.66 cm/s.)

## Check yourself

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

1. What is d = 0.17 mm in cm and nu at 21 C?
   A. 0.017 cm and 0.00978 cm2/s
   B. 0.17 cm and 0.00978 cm2/s
   C. 0.0017 cm and 0.978 cm2/s
   D. 0.017 cm and 0.0978 cm2/s
   Answer: A. 0.17 mm = 0.017 cm and 0.978 centistokes = 0.00978 cm2/s. (Key point: Unit conversion)

2. The Stokes trial gives vs = 2.657 cm/s and Re = 4.62. What follows?
   A. Re > 1, so use the transition zone formula
   B. Stokes is valid
   C. Particle is in turbulent zone
   D. Answer is 2.657 cm/s
   Answer: A. Stokes' law is valid only for Re < 1. (Key point: Stokes check)

3. What is the final settling velocity?
   A. About 2.06 cm/s
   B. About 2.66 cm/s
   C. About 0.206 cm/s
   D. About 4.6 cm/s
   Answer: A. The trial and error converges to 2.06 cm/s with Re = 3.6 and Cd = 8.61. (Key point: Final result)

## Close variants set in other exams

- [Settling velocity of discrete particle 0.14 mm at 25°C](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ased-j66) — Water Supply Engineering, chapter 6, asked 2×

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