What is the height of a water barometer at atmospheric pressure?

Verified step by step guidance

1. Understand the principle: A water barometer works based on the principle of hydrostatic equilibrium, where the weight of the water column balances the atmospheric pressure. The equation governing this is: $P=\rho gh$, where $P$ is the atmospheric pressure, $\rho$ is the density of water, $g$ is the acceleration due to gravity, and $h$ is the height of the water column.
2. Identify the known values: Atmospheric pressure at sea level is approximately $1.013\times 10^5$ Pascals, the density of water is approximately $1000$ kg/m³, and the acceleration due to gravity is $9.8$ m/s².
3. Rearrange the hydrostatic equilibrium equation to solve for height: $h=\frac{P}{÷}$. This isolates the height of the water column.
4. Substitute the known values into the equation: Replace $P$ with $1.013\times 10^5$ Pa, $\rho$ with $1000$ kg/m³, and $g$ with $9.8$ m/s².
5. Perform the division to calculate the height: The result will give the height of the water column in meters, which represents the height of the water barometer at atmospheric pressure.

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of air above a given point, typically measured in pascals (Pa) or millimeters of mercury (mmHg). At sea level, standard atmospheric pressure is approximately 101.3 kPa or 760 mmHg. This pressure is crucial for understanding how fluids behave in various contexts, including barometers.

Barometer

A barometer is an instrument used to measure atmospheric pressure. The most common type, the mercury barometer, consists of a glass tube filled with mercury, inverted in a dish of mercury. The height of the mercury column in the tube indicates the atmospheric pressure, with higher columns corresponding to higher pressure.

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium due to the force of gravity. In the context of a barometer, this principle explains how the height of the liquid column (like mercury or water) is determined by the balance between atmospheric pressure and the weight of the liquid. The height of the liquid column is directly proportional to the atmospheric pressure acting on it.