Q1-6 Locharbriggs sandstone has a sorptivity of $2.60 \mathrm{~mm} / \sqrt{\mathrm{min}}$ and is exposed to driving rain in a building. How far will water penetrate into the stone in 12 hours?
(a) $13.4 \mathrm{~mm}$
(b) $69.8 \mathrm{~mm}$
(c) $91.0 \mathrm{~mm}$
(d) $74.4 \mathrm{~mm}$.
Answer
The sorptivity (S) of a material is a measure of the capacity of the material to absorb water by capillarity. It is used in the calculation of capillary absorption of water into unsaturated porous materials. The distance that water will penetrate into a material due to capillary action can be calculated using the formula: d = S * sqrt(t) where: d is the penetration depth, S is the sorptivity of the material, and t is the time. Given that the sorptivity (S) of the Locharbriggs sandstone is 2.60 mm/sqrt(min) and the time (t) is 12 hours, we first need to convert the time to minutes because the sorptivity is given in mm/sqrt(min). There are 60 minutes in an hour, so 12 hours is 12 * 60 = 720 minutes. Substituting the given values into the formula, we get: d = 2.60 mm/sqrt(min) * sqrt(720 min) Calculating the square root of 720 gives approximately 26.83. Multiplying this by the sorptivity gives: d = 2.60 mm/sqrt(min) * 26.83 = 69.8 mm Therefore, the water will penetrate approximately 69.8 mm into the Locharbriggs sandstone in 12 hours. The correct answer is (b) $69.8 \mathrm{~mm}$.
Step 1 ：The sorptivity (S) of a material is a measure of the capacity of the material to absorb water by capillarity. It is used in the calculation of capillary absorption of water into unsaturated porous materials. The distance that water will penetrate into a material due to capillary action can be calculated using the formula: d = S * sqrt(t) where: d is the penetration depth, S is the sorptivity of the material, and t is the time. Given that the sorptivity (S) of the Locharbriggs sandstone is 2.60 mm/sqrt(min) and the time (t) is 12 hours, we first need to convert the time to minutes because the sorptivity is given in mm/sqrt(min). There are 60 minutes in an hour, so 12 hours is 12 * 60 = 720 minutes. Substituting the given values into the formula, we get: d = 2.60 mm/sqrt(min) * sqrt(720 min) Calculating the square root of 720 gives approximately 26.83. Multiplying this by the sorptivity gives: d = 2.60 mm/sqrt(min) * 26.83 = 69.8 mm Therefore, the water will penetrate approximately 69.8 mm into the Locharbriggs sandstone in 12 hours. The correct answer is (b) $69.8 \mathrm{~mm}$.
