Mud 70% sand and 30% water Sand density = 165 lbm/ft3 (2.65 g/cm3) Water density 62.3 lbm/ft3 (1g/cm3)
Mud density = ???
Mud density M/V = (sand Mass+ water Mass)/(sand volume + water volume)
Volume mass/density
Mud density (sand mass+ water mass)/ [(sand mass/sand density)+ (water mass/water density)]
Mud density 110.4 lbm/ft3 1769 kg/m3
The Correct Answer and Explanation is :
Let’s calculate the correct density of the mud mixture using the given data.
Given:
- Sand proportion: 70% by mass
- Water proportion: 30% by mass
- Sand density: 165 lbm/ft³ (2.65 g/cm³)
- Water density: 62.3 lbm/ft³ (1 g/cm³)
Step 1: Define the Mass Proportions
Let’s assume a total mud mass of 100 lbm for simplicity:
- Sand mass = 70 lbm
- Water mass = 30 lbm
Step 2: Compute the Volume of Sand and Water
Using the formula:
[
V = \frac{M}{\text{Density}}
]
- Volume of sand = ( \frac{70}{165} ) = 0.4242 ft³
- Volume of water = ( \frac{30}{62.3} ) = 0.4815 ft³
Step 3: Compute the Mud Density
[
\text{Mud Density} = \frac{\text{Total Mass}}{\text{Total Volume}}
]
[
\text{Mud Density} = \frac{70 + 30}{0.4242 + 0.4815}
]
[
\text{Mud Density} = \frac{100}{0.9057} = 110.4 \text{ lbm/ft³}
]
Conversion to kg/m³:
[
110.4 \times 16.0185 = 1769 \text{ kg/m³}
]
Explanation:
Mud density depends on the combined mass and volume of sand and water. Since sand is denser than water, it occupies less volume per unit mass. By using the correct proportion of sand and water masses and their respective densities, we determine the total volume and, subsequently, the density of the mud mixture.
The calculated density of 110.4 lbm/ft³ (1769 kg/m³) aligns with expectations, considering the higher density of sand. The density of the mud is between sand and water densities but closer to sand’s due to its higher mass proportion.
Now, I will generate an image representing the density composition of mud visually.
Here is the scientific illustration showing the composition of mud with 70% sand and 30% water. It visually represents the density distribution with labeled layers and annotations for clarity. Let me know if you need any modifications or further explanations!