Q35: The viscosity and unit weight of the percolating fluid are reduced to 65% and 95% respectively due to rise in temperature. If other things remain constant the coefficient of permeability will be:
📝 Detailed Explanation
This question applies the Kozeny-Carman relationship (k ∝ γw/μ, see Q11, Q28) numerically, computing the percentage change in permeability resulting from a given temperature-driven change in the pore fluid’s viscosity and unit weight.
Given: viscosity reduced to 65% of its original value (μ₂ = 0.65μ₁); unit weight reduced to 95% of its original value (γw2 = 0.95γw1).
Step 1 — Ratio of new to old permeability: since k ∝ γw/μ, k₂/k₁ = (γw2/γw1) × (μ1/μ2) = 0.95/0.65 = 19/13
Step 2 — Percentage change: (k₂ − k₁)/k₁ = 19/13 − 1 = 6/13
Percentage change = (6/13) × 100 ≈ 46.15%, an INCREASE
✅ Why “increased by 46%” Is Correct
Combining both the viscosity reduction (which increases k, since k ∝ 1/μ) and the unit weight reduction (which decreases k, since k ∝ γw) into a single ratio gives k2/k1 = 19/13 ≈ 1.4615 — a net 46.15% INCREASE in permeability, since the viscosity effect (which increases k) outweighs the unit weight effect (which decreases k).
🔑 Key Point
Even though BOTH given percentages (65% viscosity, 95% unit weight) look like decreases, the NET effect on permeability is still an increase — because permeability increases as viscosity decreases (μ in the denominator), and this effect outweighs the (smaller) decrease from reduced unit weight.
💡 Key Concepts for Students
- This is the direct numeric application of the qualitative relationship confirmed in Q11 and Q28: k ∝ γw/μ, with viscosity’s effect in the denominator and unit weight’s effect in the numerator.
- Rising temperature is the most common real-world cause of exactly this combination (lower viscosity, slightly lower unit weight) — warmer water flows more easily, which is why permeability tests are often standardized to a reference temperature (commonly 27°C) for comparability.
- Working with the ratio k2/k1 directly (rather than trying to track absolute values) is the cleanest way to solve this type of “percentage change” permeability problem.
- See the Going Deeper section for why temperature specifically affects both viscosity and unit weight, and why standard permeability reporting corrects for this.
📚 Going Deeper: Temperature Correction in Permeability Testing
Since permeability depends on the pore fluid’s viscosity and unit weight (Kozeny-Carman, see Q11), and both of these properties change with temperature, a permeability value measured at one temperature isn’t directly comparable to one measured at another temperature unless a correction is applied.
As temperature rises, water’s viscosity drops fairly significantly (water at 30°C is noticeably less viscous than at 10°C), while its unit weight drops only slightly. Since permeability is inversely proportional to viscosity, this net effect is that measured permeability INCREASES with temperature, even though the soil’s own structural properties (particle size, void ratio) haven’t changed at all — exactly the effect calculated numerically in this question.
To make permeability values comparable across different testing conditions, laboratory results are conventionally corrected to a standard reference temperature (commonly 27°C in Indian practice) using exactly this k ∝ γw/μ relationship — dividing out the actual test temperature’s fluid properties and substituting the reference temperature’s properties instead. This is why permeability reports often specify “K at 27°C” rather than just a bare K value.