College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
The change in pressure (ΔP) is directly proportional to the density of the fluid (ρ), the acceleration due to gravity (g), and the height of the fluid column (h). This relationship is known as the hydrostatic pressure equation and is a fundamental concept in the study of fluid mechanics.
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The change in pressure (ΔP) is directly proportional to the density of the fluid (ρ), the acceleration due to gravity (g), and the height of the fluid column (h).
The hydrostatic pressure equation is used to calculate the pressure at a given depth in a fluid, which is important in the design of hydraulic systems and the analysis of buoyancy.
Manometers are commonly used to measure the pressure of fluids by measuring the height of a column of fluid in a U-shaped tube.
The buoyant force exerted on an object immersed in a fluid is equal to the weight of the fluid displaced by the object, which can be calculated using the hydrostatic pressure equation.
The hydrostatic pressure equation is a fundamental concept in the study of fluid mechanics and is used to analyze a wide range of phenomena, including the behavior of liquids and gases in various applications.
Review Questions
Explain how the hydrostatic pressure equation (ΔP = ρgh) is used to calculate the pressure at a given depth in a fluid.
The hydrostatic pressure equation, ΔP = ρgh, states that the change in pressure (ΔP) is directly proportional to the density of the fluid (ρ), the acceleration due to gravity (g), and the height of the fluid column (h). This equation can be used to calculate the pressure at a given depth in a fluid by substituting the known values for the fluid's density and the depth of the fluid column. For example, if you know the density of water (1000 kg/m³) and the depth of a pool (2 meters), you can use the equation to calculate the pressure at the bottom of the pool: ΔP = (1000 kg/m³) × (9.8 m/s²) × (2 m) = 19,600 Pa or approximately 2 meters of water column.
Describe how the hydrostatic pressure equation is used to analyze the buoyant force exerted on an object immersed in a fluid.
The hydrostatic pressure equation, ΔP = ρgh, is fundamental to understanding the concept of buoyancy. The buoyant force exerted on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. This weight can be calculated using the hydrostatic pressure equation, where ΔP represents the change in pressure between the top and bottom of the object, ρ is the density of the fluid, and h is the height of the fluid column displaced by the object. By applying the hydrostatic pressure equation to the volume of fluid displaced, you can determine the buoyant force acting on the object, which is an important consideration in the design of ships, submarines, and other floating structures.
Analyze how the hydrostatic pressure equation can be used to explain the operation of a manometer, a device used to measure fluid pressure.
The hydrostatic pressure equation, ΔP = ρgh, is the underlying principle behind the operation of a manometer, a device used to measure the pressure of a fluid. A manometer typically consists of a U-shaped tube filled with a fluid, such as water or mercury. When the fluid in the manometer is subjected to a pressure difference, the fluid level in the two sides of the tube will differ. By measuring the height difference (h) between the two fluid levels, and knowing the density of the fluid (ρ), the pressure difference (ΔP) can be calculated using the hydrostatic pressure equation. This allows the manometer to provide a direct measurement of the pressure in the fluid system being studied. The simplicity and accuracy of this approach make manometers a widely used tool in the field of fluid mechanics and related applications.