Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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**Problem 9-128** **Objective:** Determine the magnitude of the resultant force acting on the gate ABC due to hydrostatic pressure. The gate has a width of 1.5 m, and the density of water (\(\rho_w\)) is 1.0 Mg/m³. **Diagram Description:** The diagram presents a cross-sectional view of a gate submerged in water, hinged at point A and supported by a block at point B. The geometry is triangular with the following details: - The gate is inclined at an angle of \(60^\circ\) to the horizontal. - The height from the water surface to point B is marked as 1.5 m. - The segment BC is vertical with a length of 2 m. - The part from the block at B to C is horizontal and measures 1.25 m. - The width of the gate is given as 1.5 m. **Technical Explanation:** To determine the resultant force on the gate due to the hydrostatic pressure, consider the following steps: 1. **Calculate the Hydrostatic Force:** The pressure exerted by the fluid at any depth is given by \( P = \rho \cdot g \cdot h \), where: - \(\rho\) is the fluid density, - \(g\) is the acceleration due to gravity, - \(h\) is the depth below the fluid surface. 2. **Determine the Position of the Center of Pressure:** The center of pressure is the centroid for hydrostatic loading, factoring in both depth and gate geometry. 3. **Compute the Moments:** Using moment calculations, find the tendency of this force to cause rotation about the hinge point A. For educational purposes, these calculations demonstrate how principles of fluid statics and engineering mechanics are applied to real-world scenarios involving submerged gates and fluid forces.
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Transcribed Image Text:**Problem 9-128** **Objective:** Determine the magnitude of the resultant force acting on the gate ABC due to hydrostatic pressure. The gate has a width of 1.5 m, and the density of water (\(\rho_w\)) is 1.0 Mg/m³. **Diagram Description:** The diagram presents a cross-sectional view of a gate submerged in water, hinged at point A and supported by a block at point B. The geometry is triangular with the following details: - The gate is inclined at an angle of \(60^\circ\) to the horizontal. - The height from the water surface to point B is marked as 1.5 m. - The segment BC is vertical with a length of 2 m. - The part from the block at B to C is horizontal and measures 1.25 m. - The width of the gate is given as 1.5 m. **Technical Explanation:** To determine the resultant force on the gate due to the hydrostatic pressure, consider the following steps: 1. **Calculate the Hydrostatic Force:** The pressure exerted by the fluid at any depth is given by \( P = \rho \cdot g \cdot h \), where: - \(\rho\) is the fluid density, - \(g\) is the acceleration due to gravity, - \(h\) is the depth below the fluid surface. 2. **Determine the Position of the Center of Pressure:** The center of pressure is the centroid for hydrostatic loading, factoring in both depth and gate geometry. 3. **Compute the Moments:** Using moment calculations, find the tendency of this force to cause rotation about the hinge point A. For educational purposes, these calculations demonstrate how principles of fluid statics and engineering mechanics are applied to real-world scenarios involving submerged gates and fluid forces.
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