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Zorluk: ZorInferences from the Text

In his first-century treatise De Aquis Urbis Romae, Sextus Julius Frontinus, appointed water commissioner (curator aquarum) of Rome in 97 CE, cataloged the municipal aqueducts and highlighted a persistent administrative crisis: the volume of water recorded at public distribution reservoirs (castella) was significantly less than the intake volume calculated at the upland source springs. Frontinus attributed this discrepancy entirely to illicit siphoning by landowners tapping conduits along their routes and to corrupt water-men (aquarii) installing distribution pipes (calices) with interior diameters exceeding their official stamps. However, modern hydraulic analyses indicate that Frontinus calculated volumetric flow solely by summing pipe cross-sectional areas—measured in standardized quinariae—without accounting for flow velocity or hydraulic gradient. Because water entered conduits from steep upland springs at high velocities, a given cross-sectional area at the intake admitted far more water per second than an identical cross-sectional area could discharge through the low-velocity, horizontal pipes at urban distribution points. As a result, comparing cross-sectional areas across different gradients inevitably yielded an apparent mathematical deficit in water volume.

Based on the passage, which of the following is most strongly supported concerning Frontinus's administrative audits?

  1. A
    They successfully eliminated illicit siphoning by establishing standardized stamped measurements for all urban delivery pipes.
  2. B
    They overestimated the actual volume of water entering the system at the upland springs because the steep gradient impeded steady conduit inflow.
  3. They would have signaled an apparent shortfall in delivered water even within an aqueduct system completely free of illegal diversion or pipe tampering.Cevap
  4. D
    They prompted Roman authorities to replace lead distribution pipes with masonry channels to equalize water pressure across municipal districts.
  5. E
    They systematically underestimated the extent of corruption among water-men by assuming that water velocity remained constant throughout the aqueduct network.

Cevap

Frontinus's administrative audits would have signaled an apparent shortfall in delivered water even within an aqueduct system completely free of illegal diversion or pipe tampering.
The passage states that water at steep upland intakes moved at high velocity, admitting far more water per second per unit of cross-sectional area than the lower-velocity urban distribution pipes could discharge. Because Frontinus evaluated total volume strictly by cross-sectional area rather than volumetric flow rate (Q=A⋅vQ = A \cdot v), comparing these areas inherently generated an apparent arithmetic deficit. Consequently, even in a hypothetical scenario where no water was siphoned and no pipes were illicitly enlarged, his calculation method would still mathematically indicate an unaccounted-for shortfall.

Adım Adım Çözüm

1
Identify the foundational premise of Frontinus's auditing methodology as described in the text.
Frontinus measured water volume strictly by cross-sectional pipe area (quinariae) without factoring in flow velocity or hydraulic gradient.
Establishing the specific measurement flaw is critical to evaluating the logical downstream effects of his calculations.
2
Synthesize the physical conditions at the intake springs versus the urban discharge points.
Intake water moved at high velocity due to steep gradients, whereas urban distribution water moved at lower velocities through horizontal pipes.
This physical disparity explains why equal cross-sectional areas transported unequal volumes of water per second.
3
Deduce the mathematical consequence of comparing cross-sectional capacities across these differing velocity zones.
Even if 100% of the water reached the destination with zero theft, the urban pipes would require a larger cross-sectional area to discharge the intake volume at lower speed; thus, a direct comparison of cross-sectional areas produced an inherent arithmetic deficit.
This directly entails that an apparent deficit would appear regardless of whether any actual illicit diversion occurred.

Anahtar Kavram

Drawing a necessary logical inference by synthesizing two related textual premises regarding hydraulic physics and administrative measurement methodology.
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Inferences from the Text

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