Which of the following equation means 'the free surface of water is parallel to the bed of the channel'? (where \(\frac{d \theta}{d x} =\) variation of the water depth along the bottom of the channel)

Question

Question

Download Solution PDF

Which of the following equation means 'the free surface of water is parallel to the bed of the channel'? (where \(\frac{d \theta}{d x} =\) variation of the water depth along the bottom of the channel)

This question was previously asked in

HPCL Engineer Civil 23 Dec 2023 Official Paper

Download PDF Attempt Online

View all HPCL Engineer Papers >

\( \frac{d h}{d x}=\text { negative } \)
\( \frac{d h}{d x}=\text { positive } \)
\( \frac{d h}{d x}=\infty \)
\( \frac{d h}{d x}=0 \)

Answer 1

Parallel Free Surface:

When we say that the free surface of water is parallel to the bed of the channel, we mean that the water surface is not inclined relative to the bed. This occurs when the water depth remains constant along the length of the channel. Mathematically, this condition is represented as:

\({dh \over{dx} } = 0\)

When, \({dh \over{dx} } = 0\), it means that the derivative of the water depth with respect to the horizontal distance is zero. This implies that there is no change in water depth h as you move along the channel (i.e., the water surface is flat and parallel to the channel bed).

Understanding the Other Options

1. \({dh \over{dx} } = positive\) This indicates that the water depth \( h \) decreases as you move downstream along the channel. This would imply a declining water surface, not parallel to the bed.

2. \({dh \over{dx} } = negative\) This indicates that the water depth \( h \) increases as you move downstream along the channel. This would imply a rising water surface, not parallel to the bed.

3.\({dh \over{dx} } = infinity\): This is a theoretical and practically unrealistic scenario indicating a vertical water surface. In reality, this doesn't occur in normal channel flow

Download Solution PDF

Question

Which of the following equation means 'the free surface of water is parallel to the bed of the channel'? (where \(\frac{d \theta}{d x} =\) variation of the water depth along the bottom of the channel)

Answer (Detailed Solution Below)

Detailed Solution

More Open Channel Flow Questions

More Fluid Mechanics Questions