14.3 Measuring and Using Pressure

The pressure in a fluid is measured with a pressure gauge. The fluid pushes against some sort of spring, and the spring’s displacement is registered by a pointer on a dial.

Many pressure gauges, such as tire gauges and the gauges on air tanks, measure not the actual or absolute pressure $p$ but what is called gauge pressure. The gauge pressure, denoted g is the pressure in excess of 1 atm. That is,

p_{g} = p - 1 atm

(14.6)

You must add $1 atm = 101.3 kPa$ to the reading of a pressure gauge to find the absolute pressure $p$ that you need for doing most science or engineering calculations: $p = p_{g} + 1 atm$ .

A photograph of a tire pressure gauge. — A tire-pressure gauge reads the gauge pressure $p_{g}$ , not the absolute pressure p.

EXAMPLE 14.5 An underwater pressure gauge

An underwater pressure gauge reads 60 kPa. What is its depth?

MODEL The gauge reads gauge pressure, not absolute pressure.

SOLVE The hydrostatic pressure at depth d, with $p_{0} = 1 atm,$ is $p = 1 atm + ρ g d$ . Thus the gauge pressure is

p_{g} = p - 1 atm = (1 atm + ρ g d) - 1 atm = ρ g d

The term $ρ g d$ is the pressure in excess of atmospheric pressure and thus is the gauge pressure. Solving for d, we find

d = \frac{60, 000 Pa}{(1000 {kg/m}^{3}) (9.80 {m/s}^{2})} = 6.1 m