If P, Y and Z are weights of cement, fine aggregates and coarse aggregates respectively and W/C is the water cement ratio, the minimum quantity of water to be added to first batch is obtained by the equation: (A) 0.1P + 0.3Y + 0.1Z = W/C × P (B) 0.3P + 0.1Y + 0.01Z = W/C × P (C) 0.4P + 0.2Y + 0.01Z = W/C × P (D) 0.5P + 0.3Y + 0.01Z = W/C × P
Correct Answer: B. Only B
📚 Detailed Explanation: Minimum Water Formula for First Batch
Why B (0.3P + 0.1Y + 0.01Z = W/C × P) is correct: When concrete is first batched, the dry aggregates and cement will absorb some of the mixing water before the mix reaches its target water-cement ratio. The formula accounts for this absorption:
• 0.3P: Cement absorbs about 30% of its weight in water during initial hydration contact.
• 0.1Y: Fine aggregates (sand) absorb about 10% of their weight in water (surface moisture factor).
• 0.01Z: Coarse aggregates absorb about 1% of their weight in water (lower absorption due to lower surface area ratio).
The sum of all absorbed water equals the total water needed = (W/C) × P (water-cement ratio multiplied by the cement weight).
• 0.3P: Cement absorbs about 30% of its weight in water during initial hydration contact.
• 0.1Y: Fine aggregates (sand) absorb about 10% of their weight in water (surface moisture factor).
• 0.01Z: Coarse aggregates absorb about 1% of their weight in water (lower absorption due to lower surface area ratio).
The sum of all absorbed water equals the total water needed = (W/C) × P (water-cement ratio multiplied by the cement weight).
Formula Breakdown
| Term | Meaning | Coefficient |
|---|---|---|
| 0.3P | Water absorbed by cement (P kg) | 0.3 (30%) |
| 0.1Y | Water absorbed by fine aggregate (Y kg) | 0.1 (10%) |
| 0.01Z | Water absorbed by coarse aggregate (Z kg) | 0.01 (1%) |
| W/C × P | Required water = water-cement ratio × cement weight | — |
- Correct formula: 0.3P + 0.1Y + 0.01Z = (W/C) × P
- Used to compute additional water needed in the first batch when dry aggregates are used.
- Subsequent batches use the standard w/c ratio directly since aggregates are pre-wetted.