Level tube design – reason bubble size stays constant in a constant-level tube In a constant level tube, the bubble length remains essentially constant during small tilts because the upper wall of the tube is made with which characteristic?

Introduction / Context:
Bubble tubes in spirit levels are precision glass vials whose internal curvature governs sensitivity and bubble behavior. Two general designs exist: sensitive level tubes and constant-level tubes. The latter are shaped so that the bubble length stays nearly unchanged during small angular changes, simplifying reading and keeping the bubble steady within the graduation marks. This question examines the geometric reason behind that behavior.

Given Data / Assumptions:

• We consider a constant-level tube (not a highly sensitive, strongly curved vial).
• Bubble size stability is desired across typical operating tilts.
• Internal surface curvature can be varied across the upper wall.

Concept / Approach:

Bubble length depends on the internal curvature of the vial and the volume of the gas pocket. By giving the upper wall a relatively large radius of curvature (i.e., making it very slightly curved), the cross-sectional profile changes very gently with position. Small tilts displace the bubble without appreciable change in its volume distribution along the tube, so its apparent length remains practically constant within the graduations. A smaller radius (tighter curvature) or a strongly convex profile would change the cross-sectional area more rapidly, causing bubble length variation.

Step-by-Step Solution:

Verification / Alternative check:

Instrument design texts describe constant-level tubes as having long radii to moderate sensitivity and stabilize bubble size, in contrast to sensitive vials where short radii increase sensitivity but change bubble length noticeably.

Why Other Options Are Wrong:

Smaller radius: increases curvature and sensitivity, altering bubble length more with tilt.

Flat or convex downwards: do not achieve the desired constancy and would impair predictable graduations.

Common Pitfalls:

Confusing sensitivity with constant-length behavior; assuming all spirit levels use the same vial geometry.

Final Answer:

Of relatively larger radius