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

step 1 All righty, so today we're going to be looking at determining how high this water will be in our

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 $(d \text { of } \mathrm{Hg}=13.5 \mathrm{g} / \mathrm{mL}$ $d$ of $\mathrm{H}_{2} \mathrm{O}=1.00 \mathrm{g} / \mathrm{mL} ) ?$

Key Concepts

Barometric Measurement

This concept involves using a column of fluid, typically mercury in a barometer, to measure atmospheric pressure. In such devices, the height of the fluid column is directly related to the atmospheric pressure. Converting this measurement to a different fluid, like water in this case, requires accounting for the differences in density between the fluids.

Hydrostatic Pressure

This concept refers to the pressure exerted by a fluid at equilibrium due to the force of gravity. In a fluid column, the pressure at any given depth is a result of the weight of the fluid above it, which is calculated as the product of the fluid's density, gravitational acceleration, and the height of the fluid column.

Density and Unit Conversion

Density is the mass per unit volume of a substance and plays a crucial role in relating pressures in different fluids. When comparing columns of different fluids (such as mercury and water), their densities must be accounted for in order to convert the height of a column measured in one fluid to the equivalent height of another, ensuring that the pressures are identical.

Atmospheric Pressure as a Driving Force

Atmospheric pressure is the pressure exerted by the weight of the atmosphere on a surface. In problems involving fluid columns, atmospheric pressure is often the external pressure that pushes the fluid into a tube, and it determines the maximum height to which a fluid can rise when opposing this pressure in a closed or semi-closed system.

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