# Unit Weight

## Unit Weights and Densities of Soil

**Symbols and Notations**

γ, γ_{m} = Unit weight, bulk unit weight, moist unit weight

γ_{d} = Dry unit weight

γ_{sat} = Saturated unit weight

γ_{b}, γ' = Buoyant unit weight or effective unit weight

γ_{s} = Unit weight of solids

γ_{w} = Unit weight of water (equal to 9810 N/m^{3})

W = Total weight of soil

W_{s} = Weight of solid particles

W_{w} = Weight of water

V = Volume of soil

V_{s} = Volume of solid particles

V_{v} = Volume of voids

V_{w} = Volume of water

S = Degree of saturation

w = Water content or moisture content

G = Specific gravity of solid particles

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## Physical Properties of Soil

**Phase Diagram of Soil**

Soil is composed of solids, liquids, and gases. Liquids and gases are mostly water and air, respectively. These two (water and air) are called voids which occupy between soil particles. The figure shown below is an idealized soil drawn into phases of solids, water, and air.

**Weight-Volume Relationship from the Phase Diagram of Soil**

total volume = volume of soilds + volume of voids

$V = V_s + V_v$

volume of voids = volume of water + volume of air

$V_v = V_w + V_a$

total weight = weight of solids + weight of water

$W = W_s + W_w$

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## Problem 01 - Buoyancy

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## 014 Review Problem - Weight of concrete surge chamber when full of water

**Problem 14**

A concrete surge chamber with circular cross section and vertical inner walls has an inside diameter of 100 ft. The outer walls taper uniformly. The outer walls taper uniformly ¼ in. to 1 ft. of rise, and at the base the thickness is 5 ft. The height of the surge chamber is 150 ft. above the pressure tunnel, and the material used in its construction weighs 150 lb. per cu. ft. Find the total weight of the chamber when full of water.

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## 005 Review Problem - Weight of gravity dam

**Problem 5**

If the gravity whose cross section is shown in the figure weighs 150 lb. per cu. ft., find the total weight of a section of a dam 50 ft. long.

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## Properties of common materials

Material | Unit weight (kN/m ^{3}) |
Density (kg/m ^{3}) |
Specific Gravity |

Aluminum | 26.095 | 2660 | 2.66 |

Brass | 81.423 | 8300 | 8.3 |

Brick | 19.62 | 2000 | 2.0 |

Cast iron | 70.632 | 7200 | 7.2 |

Concrete | 23.544 | 2400 | 2.4 |

Copper | 87.407 | 8910 | 8.91 |

Earth (dry) | 12.557 | 1280 | 1.28 |

Earth (wet) | 17.266 | 1760 | 1.76 |

Glass | 25.408 | 2590 | 2.59 |

Ice | 8.829 | 900 | 0.9 |

Lead | 111.540 | 11,370 | 11.37 |

Mercury | 133.416 | 13,600 | 13.6 |

Oil | 8.829 | 900 | 0.9 |

Water (fresh) | 9.81 | 1000 | 1.0 |

Water (sea) | 10.104 | 1030 | 1.03 |

Wood (hard) | 7.848 | 800 | 0.8 |

Wood (soft) | 4.709 | 480 | 0.48 |

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## 010 Volume of snow blocks in an igloo

**Example 010**

An igloo or Eskimo hut is built in the form of a hemispherical shell with an inside diameter of 12 ft. If the igloo is constructed of snow block having a uniform thickness of 2 ft and weighing 40 lb/ft^{3}, find the weight of the igloo, neglecting the entrance. Also, if fresh air contains 0.04% carbon dioxide, find the amount of this gas in the igloo when freshly ventilated.

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## 005 Weight of ivory billiard balls

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## 003 Weight of an iron shell

**Example 003**

An iron ball 10 cm in diameter weighs 4 kg. Find the weight of an iron shell 5 cm thick whose external diameter is 50 cm.

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