9.13
Presión de fluido sobre una placa plana de ancho variable
Cuando una placa plana está sumergida en un fluido, el fluido ejerce presión sobre la placa. Esta presión puede dar lugar a diferentes fenómenos, incl…
Cuando una placa plana de ancho variable se sumerge en un fluido, el fluido ejerce presión sobre la placa.
La distribución de la presión en la placa se puede calcular determinando la fuerza que actúa sobre una tira de área diferencial de la placa.
La magnitud de la fuerza es igual al producto de la presión y el área diferencial, donde la presión es proporcional a la profundidad de la tira en el fluido.
Sustituyendo la presión en la ecuación de fuerza e integrándola se obtiene la fuerza resultante.
Expresando la integral del área en términos de la profundidad del centroide de la placa, se obtiene la fuerza resultante como el producto del área de la placa y la presión en su centroide. Esto es equivalente al volumen bajo la distribución de presión.
La línea de acción de la fuerza resultante pasa a través del centroide de este volumen e intersecta la placa en el centro de presión.
En tales casos, el centroide de la placa no siempre coincide con el centro de presión de la placa.
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Q1: How is the resultant force calculated on a submerged flat plate with variable width?
The resultant force is calculated by integrating the force acting on each differential area strip across the entire plate. Since pressure increases with depth, the resultant force equals the plate's total area multiplied by the pressure at its centroid depth. This resultant is equivalent to the volume under the pressure distribution curve.
Q2: Why do the centroid of a plate and its center of pressure differ?
The centroid represents the geometric center of the plate, while the center of pressure is where the resultant force actually acts. For plates with variable width, pressure distribution is non-uniform, causing the line of action of the resultant force to pass through the centroid of the pressure volume rather than the plate's geometric centroid.
Q3: What role does the pressure distribution volume play in determining hydrostatic force?
The pressure distribution volume represents the three-dimensional shape formed by pressure values across the plate's surface. The resultant hydrostatic force equals this volume's magnitude, and its line of action passes through the centroid of this volume, intersecting the plate at the center of pressure.
Q4: How does depth affect the pressure force on a submerged plate?
Pressure increases linearly with depth in a fluid. For a differential area strip at depth, the force magnitude equals pressure times the strip's area. Since deeper portions experience greater pressure, they contribute more to the total resultant force, which is why the resultant force location depends on the pressure distribution pattern.
Q5: What is the relationship between plate area and resultant force magnitude?
The resultant force magnitude equals the plate's total area multiplied by the pressure at the plate's centroid depth. This relationship simplifies calculations by converting the complex pressure distribution into a single equivalent force, making it easier to analyze the overall hydrostatic effect on the plate.
Q6: How does variable plate width affect pressure distribution analysis?
Variable width changes how pressure distributes across the plate surface. The integration process accounts for changing widths at each depth, requiring careful calculation of differential area elements. The resulting pressure distribution volume has an irregular shape, making the center of pressure location distinct from the geometric centroid.
Q7: How does fluid pressure over flat plate of constant width compare to variable width plates?
With constant width, pressure distribution forms a uniform rectangular volume, simplifying calculations and aligning the center of pressure more predictably. Variable width plates create irregular pressure volumes where the center of pressure deviates significantly from the geometric centroid, requiring more detailed integration analysis.