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.

Answered: Image /qna-images/answer/09b3682b-21da-4dc2-b9a3-9e316449bdd4.jpg

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

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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