---
title: "Volume-moisture relation; specific gravity"
subject: "Sanitary Engineering"
chapter: 8
key: "semester_6/sanitary_engineering:sludge-specific-gravity-95"
source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/sludge-specific-gravity-95
site: BCT Engineering
---

# Volume-moisture relation; specific gravity

Sanitary Engineering · Chapter 8: Sludge Treatment and Disposal

- Asked in: 2073 Magh, 8 marks
- Video: [Specific Gravity and Density of Mixtures - Fluids Physics Problems](https://www.youtube.com/watch?v=ZcJGFZt-NO4) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/sanitary_engineering/sludge-specific-gravity-95
- Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-8

## Question

Discuss about volume moisture content relationship in sludge. Calculate the specific gravity of sludge considering 20% of solid matter in a sludge containing 95% water is composed of fixed mineral solids with specific gravity of 2.65 and 80% is composed of volatile solids with specific gravity 1.0.

## Short answer

Moisture is 95%, solids 5%. Solids specific gravity is 1/(0.2/2.65+0.8/1.0)=1.142. Sludge specific gravity is 1/(0.05/1.142+0.95/1.0)=1.0063.

## Answer

#### Volume-moisture relationship
Sludge consists of water and solids; when the solids are constant, the volume varies inversely with the solids percentage:

$$
\frac{V_1}{V_2}=\frac{100-P_2}{100-P_1}
$$

where $P$ is the moisture content (%). For example, thickening sludge from 98% to 95% moisture reduces the volume to $\dfrac{2}{5}=40\%$ of the original. The relation holds when the sludge specific gravity does not change much, and it explains why a small loss of water greatly reduces volume.

The specific gravity of sludge $S_s$ follows from the masses and specific gravities of its parts:

$$
\frac{W_s}{S_s}=\frac{W_{sol}}{S_{sol}}+\frac{W_w}{S_w}
$$

where $W$ is the weight fraction.

#### Specific gravity of the given sludge

Moisture $=95\%$, so solids $=5\%$ and water $=95\%$ by weight. Of the solids, 20% are fixed ($G=2.65$) and 80% volatile ($G=1.0$).

**Specific gravity of the solids:**

$$
\frac{1}{G_{sol}}=\frac{0.2}{2.65}+\frac{0.8}{1.0}=0.8755\ \Rightarrow\ G_{sol}=1.142
$$

**Specific gravity of the sludge:**

$$
\frac{1}{S_s}=\frac{0.05}{1.142}+\frac{0.95}{1.0}=0.9938\ \Rightarrow\ S_s=1.0063
$$

**Answer: specific gravity of the sludge $\approx 1.0063$ (solids $\approx 1.142$).**

## Check yourself

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

1. How is the specific gravity of a mixture of solids found from weight fractions?
   A. G = sum of (weight fraction x G)
   B. G = the larger of the two values
   C. G = sum of G divided by 2
   D. 1/G = sum of (weight fraction / G of each part)
   Answer: D. Masses add and volumes add, so W/S = sum(W_i/S_i). (Key point: Combining specific gravities)

2. For solids 20% fixed (G=2.65) and 80% volatile (G=1.0), G of the solids is about
   A. 1.142
   B. 1.33
   C. 2.65
   D. 0.875
   Answer: A. 1/G = 0.2/2.65 + 0.8/1.0 = 0.8755, so G = 1.142 (0.875 is 1/G, and 1.33 is the wrong simple average). (Key point: Solids G)

3. With 5% solids (G = 1.142) and 95% water, the sludge specific gravity is about
   A. 1.142
   B. 1.0063
   C. 1.05
   D. 0.9938
   Answer: B. 1/S = 0.05/1.142 + 0.95/1.0 = 0.9938, so S = 1.0063. (Key point: Sludge G)

4. Thickening sludge from 98% to 95% moisture reduces the volume to
   A. 60% of the original
   B. 3% of the original
   C. 40% of the original
   D. Half of the original
   Answer: C. V2/V1 = (100-98)/(100-95) = 2/5 = 40%. (Key point: Moisture drop)

## Related in Sanitary Engineering

- [Digester volume for sludge, moisture 92%](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-digester-volume-92) — Sanitary Engineering, chapter 8, asked 2×
- [Volume-moisture relation; sludge disposal](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Avolume-moisture-sludge-disposal) — Sanitary Engineering, chapter 8
- [Sludge treatment aims; digester volume (94%)](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-aims-digestion-volume-94) — Sanitary Engineering, chapter 8, asked 2×
- [Sludge volume before and after digestion](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-volume-before-after-600kg) — Sanitary Engineering, chapter 8
- [Sludge volume and digester, 4 MLD](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-volume-4mld-digester) — Sanitary Engineering, chapter 8
- [Yearly sludge volume, 6 MLD](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asludge-volume-yearly-6mld) — Sanitary Engineering, chapter 8

## Related in other subjects

- [Quality, moisture content, specific volume of mixture](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aquality-moisture-specific-volume) — Fundamental of Thermodynamics & Heat Transfer, chapter 3
- [Pycnometer data, water content, γsub](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Apycnometer-water-content-submerged) — Soil Mechanics, chapter 2
- [Cylindrical specimen, 95% compaction](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Acylindrical-specimen-relative-compaction) — Soil Mechanics, chapter 5
- [Define moisture content, superheated vapor, etc.](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Amoisture-superheated-definitions) — Fundamental of Thermodynamics & Heat Transfer, chapter 3