---
title: "Settling tank 30 m x 3 m, 0.02 mm, SG 2.50"
subject: "Water Supply Engineering"
chapter: 6
key: "semester_5/water_supply_engineering:sed-bk80"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/sed-bk80
site: BCT Engineering
---

# Settling tank 30 m x 3 m, 0.02 mm, SG 2.50

Water Supply Engineering · Chapter 6: Water Treatment

- Asked in: 2080 Baisakh, 6+2 marks
- 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-bk80
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-6

## Question

In continuous flow settling tank 30 m long and 3.0 meter deep, what detention time would you recommend for effective removal of 0.02 mm particles at 20°C? Assume specific gravity of particles = 2.50. Also, describe how temperature affects the removal efficiency of a sedimentation tank.

## Short answer

Stokes' settling velocity vs = 0.0325 cm/s for 0.02 mm particles at 20°C. Detention time = H/vs = 300/0.0325 = 2.57 h. Temperature effect: lower temperature increases viscosity, reducing vs and removal efficiency; design should be based on lowest water temperature.

## Answer

For 100 % removal in an ideal continuous-flow tank, a particle must settle the full depth during the detention time: $t = H/v_s$.

#### Detention time
Data: $d = 0.02$ mm $=0.002$ cm, $S_s = 2.50$, $T = 20$ °C, $\nu = 0.01007$ cm²/s, $H = 3.0$ m $= 300$ cm, $L = 30$ m.

$$
v_s=\frac{981\times(2.50-1)\times0.002^2}{18\times0.01007}=0.0325\ \text{cm/s}
$$
$Re=0.006<1$, so Stokes' law is valid.

$$
t=\frac{300}{0.0325}=9239\ \text{s}=2.57\ \text{h}
$$
Horizontal velocity $=L/t=3000/9239=0.325$ cm/s ($=0.19$ m/min, below 0.3 m/min).

**Answer: recommended detention time = 2.57 h (about 154 min).**

#### Effect of temperature on removal
Settling velocity is inversely proportional to the kinematic viscosity: $v_s \propto 1/\nu$. As the temperature of water falls, the viscosity rises (it is 0.01306 cm²/s at 10 °C and 0.00893 cm²/s at 25 °C), so settling is slower and fewer particles are removed in a given tank. In cold weather the detention time must be longer (or the surface area larger) for the same efficiency. Hence a tank is designed for the lowest water temperature.

## Check yourself

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

1. What detention time is needed for 100% removal in the continuous-flow tank?
   A. t = H/vs
   B. t = L/vs
   C. t = vs/H
   D. t = H x vs
   Answer: A. A particle must settle the full depth in time t, so t = H/vs = 300/0.0325 = 2.57 h. (Key point: Detention time formula)

2. Why is Stokes' law accepted here?
   A. Re = 0.006, which is less than 1
   B. Particles are spherical
   C. Temperature is 20 C
   D. Specific gravity is 2.5
   Answer: A. Stokes' law is valid when the particle Reynolds number is below 1. (Key point: Stokes' law check)

3. How does a fall in water temperature affect removal in a settling tank?
   A. Viscosity rises, settling slows, removal falls
   B. Viscosity falls, settling speeds up
   C. No effect on settling
   D. Density falls and particles float
   Answer: A. vs is proportional to 1/nu, and viscosity rises as water cools. (Key point: Temperature effect)

4. At which temperature is a tank designed?
   A. Highest water temperature
   B. Average annual temperature
   C. Lowest water temperature
   D. Exactly 20 C
   Answer: C. The coldest water has the highest viscosity and the slowest settling, so the tank is designed for it. (Key point: Design temperature)

## Related in Water Supply Engineering

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## Related in other subjects

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