measuring pressure sph4c. static pressure head for any point in a static fluid, the height of the...

Measuring PressureMeasuring PressureSPH4C

Static Pressure HeadStatic Pressure HeadFor any point in a static fluid, the

height of the column above that point is called the static pressure head.

A dam must be thicker or stronger at greater depths to withstand the increased pressure.

Static Pressure HeadStatic Pressure HeadThe formula for the pressure

exerted is:

Where D is the density of the fluid,h is the height, and g = 9.8 m/s2.

DhgA

ghADAgVD

Amg

AFp

BarometersBarometersIn mercury barometers, it is the

static pressure head that indicates the external air pressure.

The higher the atmospheric pressure, the higher the static pressure head.

BarometersBarometersIn mercury barometers, it is the

static pressure head that indicates the external air pressure.

The higher the atmospheric pressure, the higher the static pressure head.

Question: Why do we use mercury in barometers instead of water?

Water LevelWater LevelLiquid in connected containers

exposed to the same air pressure will be at the same height.

The shape and orientation of the containers makes no difference to the height.

SiphonsSiphonsThis is often phrased as “water

seeks its own level,” and is why water will even flow uphill in a siphon if it can reach a lower point at the end of the siphon.

Note that the siphon needs to be full of liquid to connect the two containers.

ManometersManometersManometers can be used to

measure variations in pressure.

When more pressure is applied to the left side of the tube, there will be a difference in the heights of the liquid.

Gauge pressureGauge pressureThis variation in pressure from

atmospheric pressure is called the gauge pressure:

atmabsg ppppressurecatmospheripressureabsolutepressuregauge

Tire pressure gauges measure gauge pressure: the pressure over and above atmospheric pressure.

Gauge pressure exampleGauge pressure examplePressure is applied to one end of a

water manometer so that the difference between the two heights is 10 cm.

(a) What is the gauge pressure applied?

(b) What is the absolute pressure applied?

Gauge pressure exampleGauge pressure example(a) What is the gauge pressure

applied?

2

3

8.910.0

1000

sm

mkg

gmh

D

Gauge pressure exampleGauge pressure example(a) What is the gauge pressure

applied?

2

3

8.910.0

1000

sm

mkg

gmh

D

Gauge pressure exampleGauge pressure example(a) What is the gauge pressure

applied?

2

3

8.910.0

1000

sm

mkg

gmh

D

kPaor

PamDhgpsm

mkg

980.0

980)8.9)(10.0)(1000( 23

Gauge pressure exampleGauge pressure example(b) What is the absolute pressure

applied?

kPakPakPa

ppp atmgabs

28.1023.101980.0