Question

In a sand stowing arrangement, the slurry has a sand concentration of 35% by volume. The specific gravity of sand grain is 2.6. The concentration of sand by weight, in percent, in the slurry is \(\underline{\hspace{1cm}}\). (round off to one decimal place)

Hint:

To find the concentration by weight, use the specific gravity of sand and convert the mass from volume.

Answer 1

Correct Answer: 57

Let the volume of slurry be 1 cubic meter. Then:
Volume of sand = 35% of 1 m\(^3\) = 0.35 m\(^3\)
Volume of water = 65% of 1 m\(^3\) = 0.65 m\(^3\)
The mass of sand is:
\[ \text{Mass of sand} = \text{Volume of sand} \times \text{Specific gravity of sand} \times \text{Density of water} \] \[ \text{Mass of sand} = 0.35 \times 2.6 \times 1000 = 910 \, \text{kg} \] The mass of water is:
\[ \text{Mass of water} = 0.65 \times 1000 = 650 \, \text{kg} \] Total mass of the slurry = \( 910 + 650 = 1560 \, \text{kg} \) Now, the weight concentration of sand is:
\[ \text{Weight percentage of sand} = \frac{910}{1560} \times 100 = 58.33% \] Thus, the concentration of sand by weight in the slurry is \( \boxed{58.3%} \).