Mass$-$Volume Calculation Assignment

$/10$

Complete the following questions on engineering grid paper.

Draw the block diagram for each question; label the quantities.

Show $6$ significant digits in your calculations. Minimum decimals required:

$\backslash$table$[[,$Mass,Volume,Densities$*,$w and S$,$e and n$],[$Units$,$kg$,$g$,m^3,c{m}^3,k\frac{g}{m^3},\%,$Unitless$],[$Required decimals,$2,3,5,3,2,1,3]]$

$*$Retain $2$ decimals when using densities in calculations: report final value to nearest whole $k\frac{g}{m^3}$

An undisturbed cylindrical soil specimen was obtained from a Shelby tube for the purpose of compressive strength testing. The prepared specimen had a diameter of $7\mathrm{.}21$ cm and a height of $15\mathrm{.}52$ cm $.$ The mass of the specimen was measured as $1157\mathrm{.}40$ g $.$ The relative density of the soil is $2\mathrm{.}75.$ After strength testing, the sample was oven dried; the moisture content was determined to be $31\mathrm{.}8\%.$

Use the given information to calculate the following quantities:

a$.$ Bulk $($wet$)$ density

b$.$ Dry density

c$.$ Void ratio

d$.$ Porosity

e$.$ Degree of saturation

$(5)$

$2.$ The results of an in$-$situ density test on a soil sample indicated a bulk $($wet$)$ density of $1910k\frac{g}{m^3}.$ The relative density of the soil is $2\mathrm{.}72.$

a$.$ A small representative sample of the soil was used for a moisture content test. Use the test results in the table to calculate the moisture content of the soil.

$\backslash$table$[[$Wet mass plus tare,$881\mathrm{.}63,$g$],[$Dry mass plus tare,$771\mathrm{.}38,$g$],[$Mass of tare,$165\mathrm{.}60,$g$]]$

Note: The masses given in this section are used to calculate the moisture content only; they cannot be used on the block diagram $($they do not represent the total sample, and the matching volume is unknown$).$

Using the given information and the calculated moisture content, calculate the following quantities:

b$.$ Dry density

c$.$ Void ratio

d$.$ Porosity

e$.$ Degree of saturation

$(5)$

Mass$-$Volume Calculation Assignment