Manometer capillarity avoidance – minimum tube diameter To minimize meniscus curvature and avoid significant capillary correction in pressure measurement, the manometer tube should have at least what internal diameter?

Introduction / Context:
Capillary rise or depression in narrow tubes distorts liquid column readings in manometers, especially with water and clean glass. Selecting a sufficiently large internal diameter helps keep errors negligible without complex meniscus corrections.

Given Data / Assumptions:

• Clean glass tube and water (or similar wetting fluid).
• Room temperature conditions where surface tension is typical.
• Objective: keep capillary rise/depression small relative to resolution.

Concept / Approach:

Capillary height is inversely proportional to tube radius: h_c ≈ 2 σ cos θ / (ρ g r). Increasing diameter (2r) reduces h_c rapidly. Practical laboratory and field practice often adopts ≥ 6 mm I.D. to make capillary corrections negligible for routine measurements.

Step-by-Step Solution:

Verification / Alternative check:

Using typical values (σ ≈ 0.072 N/m, θ ≈ 0°, ρ ≈ 1000 kg/m^3) gives small h_c when r ≥ 3 mm. Many textbooks recommend 6–10 mm I.D.; 6 mm is the common minimum.

Why Other Options Are Wrong:

(a) and (b) are too small; capillarity is significant. (d) and (e) are acceptable but unnecessarily large relative to the “minimum” asked; the conventional cut-off is about 6 mm.

Common Pitfalls:

Ignoring contact-angle effects with dirty or coated tubes; forgetting that mercury behaves oppositely (depression instead of rise). Always read at consistent meniscus position if correction is unavoidable.

Final Answer:

6 mm