Therefore:
| 27 | 27 | |||
| N | = | ———————————— | = | —————————— |
| 1.1 n s + (p - 0.9 n s v) | p + n s (1.1 - 0.9 v) |
N being the number of barrels of cement per cu. yd. of mortar.
When the mortar is made so lean that there is not enough cement paste to fill the voids in the sand, the formula becomes:
| 27 | ||
| N | = | ——— |
| 1.1 n s |
A similar line of reasoning will give us a rational formula for determining the quantity of cement in concrete; but there is one point of difference between sand and gravel (or broken stone), namely, that the gravel does not swell materially in volume when mixed with water. However, a certain amount of water is required to wet the surface of the pebbles, and this water reduces the available voids, that is, the voids that can be filled by the mortar. With this in mind, the following deduction is clear, using the nomenclature and symbols above given:
| ng | = | cu. | ft. | of | dry gravel (or stone). |
| ng V | = | " | " | " | voids in dry gravel. |
| 0.9 ng V | = | " | " | " | "available voids" in the wet gravel. |
| p + n s (1.1 - 0.9 v) - 0.9 ng V | = | excess | of | mortar | over the available voids in the wet gravel. |
| ng + p + n s (1.1 - 0.9 v) - 0.9 ng V | = | cu. | ft. | of | concrete from 1 bbl. cement. |
| 27 | |||
| N | = | ——————————————————————— | |
| p + n s (1.1 - 0.9v) + ng (1 - 0.9 V) |
N being the number of barrels of cement required to make 1 cu. yd. of concrete.