Hydrometry – Cup/propeller current meter calibration and use Given two calibration points (50 s counts): 12 rev → 0.25 m/s and 30 rev → 0.46 m/s. What velocity will 50 revolutions in 1 minute indicate?

Introduction / Context:
Current meters are calibrated by relating flow velocity v to rotation rate N (revolutions per second). A linear relation v = a + b * N is commonly used over practical ranges. With two calibration points, we can determine a and b and then compute velocity for any observed count rate.

Given Data / Assumptions:

• Calibration point 1: 12 revolutions in 50 s → N1 = 12/50 rps, v1 = 0.25 m/s.
• Calibration point 2: 30 revolutions in 50 s → N2 = 30/50 rps, v2 = 0.46 m/s.
• Observation: 50 revolutions in 60 s → N = 50/60 rps.
• Assume linear v–N relation: v = a + b * N within this range.

Concept / Approach:

Use the two given calibration pairs to solve for a and b. Then substitute the measured N to get the indicated velocity. This is the standard field practice for converting meter counts to flow velocity in open-channel gauging.

Step-by-Step Solution:

Verification / Alternative check:

Check reasonableness: 0.60 m/s lies above 0.46 m/s, consistent with the higher rotation rate (50 in 60 s is faster than 30 in 50 s). Linear interpolation/extrapolation is mild and within calibration range.

Why Other Options Are Wrong:

0.42 and 0.50 are too low for the higher rotation rate; 0.73 is too high relative to the linear calibration.

Common Pitfalls:

Using revolutions per minute directly without converting to rps in the calibrated formula, or mixing up the 50 s calibration period with the 60 s observation period.

Final Answer:

0.60