9.13
可变宽度平板上的流体压力
当平板浸入到流体中时，流体对平板将会施加压力。这种压力可以导致出现许多不同的现象，其中包括阻力和浮力。为了能够了解流体在不同宽度平板上的行为，则有必要对其中所施加的压力分布来进行分析。
可以通过确定作用在板上微分面积条中的力来计算板上的压力分布。因此，力的大小等于压力和微分面积的乘积。压力也可以用流…
当一块宽度变化的平板浸没在流体中时，流体会对平板施加压力。
通过确定作用在平板微分面积条带上的力，可以计算出平板上的压力分布。
力的大小等于压力与微元面积的乘积，其中压力与流体中条带的深度成正比。
将压力代入力的方程并进行积分，可得到合力。
将面积积分用平板形心的深度表示时，可得合力等于平板面积与其形心处压强的乘积。这等同于压强分布曲面下的体积。
合力的作用线通过该体积的形心，并在压强中心处与平板相交。
在这种情况下，平板的形心并不总是与平板的压力中心重合。
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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.