In Fig. P2.11, pressure gage A reads 1.5 kPa (gage). The...

In Fig. P2.11, pressure gage $A$ reads 1.5 kPa (gage). The fluids are at $20^{\circ} \mathrm{C}$. Determine the elevations $z,$ in meters, of the liquid levels in the open piezometer tubes $B$ and $C$.

Key Concepts

Fluid Density and Unit Conversion

The density of the fluid, often influenced by temperature, is a critical parameter when converting between pressure and height in a fluid column. In calculations, knowing the fluid density allows for the correct conversion of pressure units, such as kilopascals, into a corresponding elevation head, while the gravitational acceleration provides the necessary link between these quantities.

Piezometer

A piezometer is an instrument typically used to measure the pressure within a fluid by observing the height of the fluid column in an open tube. The difference in elevation between the free surface and the measured point is directly related to the fluid pressure at that point, making piezometers a useful tool for analyzing static pressure in fluids.

Hydrostatic Pressure

This is the pressure exerted by a fluid at equilibrium due to the force of gravity acting on it. The pressure increases with depth according to the relationship P = ?gz, where ? is the fluid density, g is the acceleration due to gravity, and z is the vertical distance below the free surface. This relationship allows one to convert between pressure readings and height differences in a fluid column.

Gauge Pressure

Gauge pressure is the pressure measured relative to the ambient atmospheric pressure rather than the absolute zero pressure of a vacuum. In many applications, including the use of piezometer tubes, gauge pressure readings are used to indicate the pressure difference that is caused solely by the fluid column above the measurement point.

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