A 2.0 m wide rectangular channel was carrying a flow with a velocity of 2.0 m/s. Due to sudden operation of a downstream gate, a positive surge of velocity 4.5 m/s and travelling upstream was generated. If the depth of flow after the passage of the surge is 3.6 m, calculate the velocity of flow after the passage of the surge. What was the discharge before the passage of the surge?
A 2.0 m wide rectangular channel was carrying a flow with a velocity of 2.0 m/s. Due to sudden operation of a downstream gate, a positive surge of velocity 4.5 m/s and travelling upstream was generated. If the depth of flow after the passage of the surge is 3.6 m, calculate the velocity of flow after the passage of the surge. What was the discharge before the passage of the surge?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Flow Dynamics in Rectangular Channels
Consider a 2.0-meter wide rectangular channel that was carrying a flow with a velocity of 2.0 m/s. Due to the sudden operation of a downstream gate, a positive surge with a velocity of 4.5 m/s traveling upstream was created. If the depth of flow after the passage of the surge is 3.6 meters, the following calculations can be made:
#### 1. Velocity of Flow after the Passage of the Surge:
To determine the new velocity of flow after the surge passes, we use the principle of conservation of mass (continuity equation):
\[ Q = A \times V \]
Where:
- \( Q \) is the discharge (flow rate).
- \( A \) is the cross-sectional area of the flow (\( width \times depth \)).
- \( V \) is the velocity of flow.
Before the surge:
\[ A_1 = b \times h_1 \]
\[ V_1 = \text{initial velocity} = 2.0 \, \text{m/s} \]
After the surge:
\[ A_2 = b \times h_2 \]
\[ V_2 = \text{new velocity (after surge)} \]
Given data:
- Width of the channel, \( b \) = 2.0 meters.
- Initial velocity, \( V_1 \) = 2.0 m/s.
- Depth after surge, \( h_2 \) = 3.6 meters.
#### 2. Discharge before the Passage of the Surge:
The cross-sectional area before the surge can be calculated as:
\[ A_1 = b \times h_1 \]
However, note that the initial depth \( h_1 \) before the surge is not given directly. Let's denote \( Q_1 \) as the discharge before the surge, given by:
\[ Q_1 = A_1 \times V_1 \]
Since \( h_1 \) is missing, we will assume the initial discharge needs to be provided or inferred from alternative methods.
### Calculation Process:
1. **Calculate the discharge before the surge:**
\[ Q_1 = b \times h_1 \times V_1 \]
2. **Determine the new velocity after the surge:**
\[ Q_2 = Q_1 \]
\[ A_2 = b \times h_2 \]
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Transcribed Image Text:### Flow Dynamics in Rectangular Channels
Consider a 2.0-meter wide rectangular channel that was carrying a flow with a velocity of 2.0 m/s. Due to the sudden operation of a downstream gate, a positive surge with a velocity of 4.5 m/s traveling upstream was created. If the depth of flow after the passage of the surge is 3.6 meters, the following calculations can be made:
#### 1. Velocity of Flow after the Passage of the Surge:
To determine the new velocity of flow after the surge passes, we use the principle of conservation of mass (continuity equation):
\[ Q = A \times V \]
Where:
- \( Q \) is the discharge (flow rate).
- \( A \) is the cross-sectional area of the flow (\( width \times depth \)).
- \( V \) is the velocity of flow.
Before the surge:
\[ A_1 = b \times h_1 \]
\[ V_1 = \text{initial velocity} = 2.0 \, \text{m/s} \]
After the surge:
\[ A_2 = b \times h_2 \]
\[ V_2 = \text{new velocity (after surge)} \]
Given data:
- Width of the channel, \( b \) = 2.0 meters.
- Initial velocity, \( V_1 \) = 2.0 m/s.
- Depth after surge, \( h_2 \) = 3.6 meters.
#### 2. Discharge before the Passage of the Surge:
The cross-sectional area before the surge can be calculated as:
\[ A_1 = b \times h_1 \]
However, note that the initial depth \( h_1 \) before the surge is not given directly. Let's denote \( Q_1 \) as the discharge before the surge, given by:
\[ Q_1 = A_1 \times V_1 \]
Since \( h_1 \) is missing, we will assume the initial discharge needs to be provided or inferred from alternative methods.
### Calculation Process:
1. **Calculate the discharge before the surge:**
\[ Q_1 = b \times h_1 \times V_1 \]
2. **Determine the new velocity after the surge:**
\[ Q_2 = Q_1 \]
\[ A_2 = b \times h_2 \]
\[
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