Q3. Find the horizontal thrust of the water on each meter of width of the sluice gate shown in the figure. Given y₁ = 2.2 m, y2 = 0.4 m, and y3 = 0.5 m. Neglect friction. Assume steady flow conditions. Continuty Equation Q=Q₂ A₁V₁ = A ₂ V₂ ((2.2) (1)) (v₁) = ((0.4)(1)(v₂) V₁ = 0.181812 O Water Faris2020 Gate FG/w Y2 F₂ Datumn P₁ = P₂ = 0 = Open atm
Q3. Find the horizontal thrust of the water on each meter of width of the sluice gate shown in the figure. Given y₁ = 2.2 m, y2 = 0.4 m, and y3 = 0.5 m. Neglect friction. Assume steady flow conditions. Continuty Equation Q=Q₂ A₁V₁ = A ₂ V₂ ((2.2) (1)) (v₁) = ((0.4)(1)(v₂) V₁ = 0.181812 O Water Faris2020 Gate FG/w Y2 F₂ Datumn P₁ = P₂ = 0 = Open atm
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Subject is fluid mechanics
![**Topic: Analyzing the Horizontal Thrust of Water on Sluice Gates**
**Question 3:**
Determine the horizontal thrust of water on each meter of width of the sluice gate as depicted in the figure. The given values are \( y_1 = 2.2 \, \text{m} \), \( y_2 = 0.4 \, \text{m} \), and \( y_3 = 0.5 \, \text{m} \). Neglect friction and consider steady flow conditions.
**Solution Approach:**
1. **Continuity Equation:**
- The principle of conservation of mass gives us the Continuity Equation: \( Q_1 = Q_2 \).
- This equation can be expressed as: \( A_1 V_1 = A_2 V_2 \).
- Substituting the given values:
\[
(2.2)(1)(V_1) = (0.4)(1)(V_2)
\]
- Solving the equation, we find:
\[
V_1 = 0.1818 V_2
\]
**Detailed Explanation of Diagram:**
- The diagram illustrates a sluice gate with water at different heights \( y_1 \) and \( y_2 \), with markings for \( F_{\text{flow}} \) indicating the direction of flow and \( F_1 \) representing the horizontal thrust on the gate.
- A channel is shown where water flows over a gate and the labels include heights for different sections:
- \( y_1 = 2.2 \, \text{m} \) – the upstream water depth.
- \( y_2 = 0.4 \, \text{m} \) – the downstream water depth.
- The figure also specifies that \( P_1 = P_2 = 0 \), implying open atmospheric pressure at these points.
- The "Datum" line indicates a reference level for the measurements.
This analysis helps to understand how fluid dynamics concepts like continuity and force balance apply to real-world engineering problems involving sluice gates in channels.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb816de81-d091-4434-aa0d-8a250bb5db6b%2F09b3682b-21da-4dc2-b9a3-9e316449bdd4%2Fp3fqi8a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Analyzing the Horizontal Thrust of Water on Sluice Gates**
**Question 3:**
Determine the horizontal thrust of water on each meter of width of the sluice gate as depicted in the figure. The given values are \( y_1 = 2.2 \, \text{m} \), \( y_2 = 0.4 \, \text{m} \), and \( y_3 = 0.5 \, \text{m} \). Neglect friction and consider steady flow conditions.
**Solution Approach:**
1. **Continuity Equation:**
- The principle of conservation of mass gives us the Continuity Equation: \( Q_1 = Q_2 \).
- This equation can be expressed as: \( A_1 V_1 = A_2 V_2 \).
- Substituting the given values:
\[
(2.2)(1)(V_1) = (0.4)(1)(V_2)
\]
- Solving the equation, we find:
\[
V_1 = 0.1818 V_2
\]
**Detailed Explanation of Diagram:**
- The diagram illustrates a sluice gate with water at different heights \( y_1 \) and \( y_2 \), with markings for \( F_{\text{flow}} \) indicating the direction of flow and \( F_1 \) representing the horizontal thrust on the gate.
- A channel is shown where water flows over a gate and the labels include heights for different sections:
- \( y_1 = 2.2 \, \text{m} \) – the upstream water depth.
- \( y_2 = 0.4 \, \text{m} \) – the downstream water depth.
- The figure also specifies that \( P_1 = P_2 = 0 \), implying open atmospheric pressure at these points.
- The "Datum" line indicates a reference level for the measurements.
This analysis helps to understand how fluid dynamics concepts like continuity and force balance apply to real-world engineering problems involving sluice gates in channels.
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