Question

Using current meter for measuring flow velocity in a stream having depth of \(1 \, \text{m}\), the observation readings should be taken at:
• at \(0\) depth of flow
• at \(0\) and \(0.2\) depth of flow
• at \(0.2\) and \(0.6\) depth of flow
• at \(0.2\) and \(0.8\) depth of flow

• A. at \(0\) depth of flow
• B. at \(0\) and \(0.2\) depth of flow
• C. at \(0.2\) and \(0.6\) depth of flow
• D. at \(0.2\) and \(0.8\) depth of flow

Hint:

Important current meter observation methods:
• One-point method: \[ \text{Velocity measured at }0.6d \]
• Two-point method: \[ \text{Velocity measured at }0.2d \text{ and }0.8d \] Memory Trick: \[ \boxed{\text{“2 and 8 give average velocity estimate”}} \]

Answer 1

The Correct Option is D

Concept: A current meter is an instrument used in hydrology and open channel hydraulics for measuring the velocity of flowing water in rivers, canals, and streams. The velocity of flow in a stream is not uniform throughout the depth because of:
• Friction at the channel bed
• Resistance near boundaries
• Turbulence effects
• Variation in shear stress Generally:
• Velocity is minimum near the bed due to friction.
• Velocity gradually increases upward.
• Maximum velocity usually occurs slightly below the water surface. Since velocity varies with depth, observations are taken at specified depths so that the average velocity over the vertical section can be estimated accurately. The most commonly used methods are:
• One-point method
• Two-point method For accurate measurements, especially in streams of moderate depth, the two-point method is preferred.

Step 1: Understanding the two-point method. In the two-point method, velocity observations are taken at: \[ 0.2d \quad \text{and} \quad 0.8d \] where:
• \(d\) = total depth of flow The average velocity is then determined as: \[ V = \frac{V_{0.2d}+V_{0.8d}}{2} \] This method gives a very reliable estimate of mean velocity in open channel flow.

Step 2: Applying the concept to the given problem. The depth of stream is: \[ d = 1 \, \text{m} \] Therefore, observations should be taken at: \[ 0.2d = 0.2 \times 1 = 0.2 \, \text{m} \] and \[ 0.8d = 0.8 \times 1 = 0.8 \, \text{m} \] Hence readings should be taken at: \[ 0.2 \, \text{m and } 0.8 \, \text{m depth} \]

Step 3: Analyzing all options carefully. Option (A): At \(0\) depth of flow This means measurement at the water surface only. Velocity at surface does not represent average stream velocity accurately. Hence: \[ \boxed{\text{Option (A) is incorrect}} \] Option (B): At \(0\) and \(0.2\) depth of flow These observation points are not standard for current meter average velocity estimation. Hence: \[ \boxed{\text{Option (B) is incorrect}} \] Option (C): At \(0.2\) and \(0.6\) depth of flow Although \(0.6d\) is used in the one-point method, this pair is not the standard two-point method. Hence: \[ \boxed{\text{Option (C) is incorrect}} \] Option (D): At \(0.2\) and \(0.8\) depth of flow This exactly corresponds to the standard two-point current meter method. Hence: \[ \boxed{\text{Option (D) is correct}} \] Final Conclusion: For stream velocity measurement using a current meter, the standard two-point observation depths are: \[ 0.2d \quad \text{and} \quad 0.8d \] Therefore, for a stream depth of \(1\,\text{m}\), observations should be taken at: \[ \boxed{0.2\,\text{m and }0.8\,\text{m}} \] Hence, the correct answer is: \[ \boxed{(D)\ \text{at }0.2\text{ and }0.8\text{ depth of flow}} \]