A long glass tube, sealed at one end, has an inner diameter of 10.0 mm. The tube is filled with

step 1 For this question, you're asked to determine the height of a water column at a pressure of 755 m

A long glass tube, sealed at one end, has an inner diameter...

A long glass tube, sealed at one end, has an inner diameter of 10.0 $\mathrm{mm}$. The tube is filled with water and inverted into a pail of water. If the atmospheric pressure is $755 \mathrm{mmHg}$, how high (in $\mathrm{mmH}_{2} \mathrm{O}$ ) is the column of water in the tube $\left(d\right.$ of $\mathrm{Hg}=13.5 \mathrm{~g} / \mathrm{mL} ; d$ of $\left.\mathrm{H}_{2} \mathrm{O}=1.00 \mathrm{~g} / \mathrm{mL}\right) ?$

Key Concepts

Atmospheric Pressure

Atmospheric pressure is the force per unit area exerted by the weight of the atmosphere on a surface. It plays a fundamental role in fluid mechanics by providing the external pressure that supports columns of fluids and influences phenomena such as fluid flow, boiling points, and the behavior of sealed containers when inverted or exposed to vacuum conditions.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the gravitational force acting on it. This principle, encapsulated in the equation P = ?gh, where ? is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column, is essential for calculating the weight of a fluid column and determining how high a column can be supported by a given pressure difference.

Conversion of Pressure Units

Conversion of pressure units is critical when working with different fluids that have various densities or when comparing measurements made in different unit systems. For instance, converting the pressure from one unit, such as mmHg, to another, such as mmH?O, requires understanding the relative densities of the fluids involved and ensuring consistency in evaluating forces and heights in fluids.

Pressure Equilibrium in Sealed Inverted Tubes

In a sealed inverted tube filled with fluid, pressure equilibrium is achieved when the external atmospheric pressure balances the weight of the fluid column. This equilibrium provides the basis for using hydrostatic pressure relations to calculate the maximum height the fluid column can reach in the tube, and is fundamental to the operation of devices like barometers and certain types of fluid manometers.

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