Pressure and its Measurement

Under Pressure?

What the curriculum thinks you need to know:

PC_BK_22 Pressure: absolute and relative pressure; gauge pressure
PC_BK_64 Pressure transducers
PC_BK_24 Cylinders and pipelines, Bourdon gauge

What you need to know (The theory):

Pressure

Pressure is the amount of force applied to an object per unit surface area.

So if we think of a syringe, we apply a force to the plunger and that force is then ‘shared’ over the area of the end of the plunger. The area of the plunger is much larger on a 20ml than on a 2ml syringe. The force applied to the plunger on the 20ml syringe is shared over a larger surface area, so a smaller pressure is produced than the 2ml where it is shared over a small area. This explains why its easier to inject with a 2ml syringe than a 20ml (or even worse, a 50ml syringe!).

pressure_1

Relative pressures produced by same forces on different size syringes.

People get confused about pressure units. Keep it simple. Use the definition above. Its a unit of force per unit of area.

The SI unit for pressure is the Pascal.

One Pascal is defined as one newton acting on one metre square (N/M2)

Remember one newton is the force required to make one kilogram accelerate by one metre per second per second.

The Pascal is then this unit of force, distributed over a certain area.

Now, the Pascal is a very small unit. It is equivalent to about 100g acting over 1m2 (remember on earth, 1kg has a downward force of about 9.8N due to gravity, hence one newton is approx 100g). This is why you usually see the kilopascal unit (1kPa = 1000Pa).

The atmosphere pushes down on everything on the earths surface due to gravity. The force created here is 101.325kPa. Although the actual value changes slightly due to weather conditions and similar, this value is known as standard atmospheric pressure. Hence one atmosphere (1atm) equals 101.325kPa.

This brings us onto the idea of absolute vs relative pressure. Things in the earths atmosphere will always be under pressure of some sort so there is (almost) never zero pressure present. The only place there is zero pressure is in a true vacuum, which is almost impossible to actually make!

The Problem with this is that we like the idea of zero pressure, so when WE are not exerting any force, then that is zero. It just makes sense to our brains!

Relative pressure is a pressure which is measured relative to another pressure. So for instance an oxygen cylinder which is ’empty’ doesn’t have zero pressure in it. When exhausted the internal pressure will equal the external (atmospheric) pressure. Hence, we want that pressure to read as zero as no gas will flow out of the cylinder as the internal and external pressures are equal.

Gauge (or relative) pressure is defined as the absolute pressure minus the reference pressure (usually, but not always atmospheric pressure).

Measuring pressure

In its simplest form, pressure is measured using either a barometer or a manometer.

pressure_2

Barometer vs Manometer

These are simply ‘U’ shaped tubes with some kind of fluid in them. One end of the tube is open to the pressure which is being measured. The other is open to a reference pressure. The only difference between a manometer and a barometer is what the reference pressure is.

In a Barometer, the reference is a vacuum. This is because we use a barometer to measure atmospheric pressure which is an absolute pressure value. The slight caveat here is that it actually isn’t a vacuum as the fluid in the barometer (mercury etc) produces a vapour pressure so there is a small pressure present (the SVP of mercury at 20oC is 2.3kPa, so very small). Exam alert! The college love asking what this ‘vacuum’ is called. Its called a Torricellian Vacuum, after Evangelista Torricelli who first described its presence.

Meanwhile a Manometer measures a pressure relative to atmospheric pressure, so the other end of the tube is open to the atmosphere.

The fluid within the ‘U’ shaped tube is pushed from the vacuum/atmospheric end and from the ‘measured pressure’ end. The relative pressures at both these ends push the fluid around the tube and the relative height of each end of the fluid is indicative of the pressure difference between both ends.

pressure_3

Relative height of column needed with different fluids.

This is where the idea of odd pressure units come from. Think of cmH2O and mmHg, how is that a force/area thing?!

Simply, these are the pressure differences needed to move a column of fluid in a barometer/manometer.

1mmHg is the pressure needed to move a column of mercury up one millimetre.

1cmH2O is the pressure needed to move a column of water up one centimetre.

These are really complicated aren’t they! Now the college likes the conversion factors needed to move between these units. Look at the bottom of the page to see the table. You just have to learn this I’m afraid!

Looking at these it becomes obvious why certain liquids are used for certain applications. One atmosphere produces movement of 760mm with mercury, whilst the same pressure moves water 1033cm!! So water is totally unsuitable for higher pressure applications. This is why mmHg is used for blood pressure measurement traditionally as a water sphygonomanometer would be… Huge.

We hardly ever use traditional manometers in clinical practice. The only one we do use is the traditional sphygmomanometer. Most pressure measurement devices are the ones seen below….

What you need to know (How it works in practice):

Bourdon Gauge

The Bourdon gauge is a simple device which measures pressure. It consists of a pointer attached to one end of a small caliber tube. This tube is coiled around and is closed at the pointer end, with the other end being attached to the source of the pressure that needs to be measured.

As the pressure applied to the end of the tube increases, the tube tries to straighten out. This then twists the pointer which will indicate a different pressure on the gauge.

pressure_4.jpg

The Bourdon Gauge

Pressure transducer (including differential pressure transducers)

So in this post we said in the post on electrical components that a transducer is a device which changes one type of energy into another (usually electrical). Now pressure transducers normally change pressure into an electrical signal. This is useful as it gives us a signal which a computer can understand and display to us in a numerical or graphical format.

pressure_5

Example of a strain gauge

We’ve already said in previous posts that as a strip of metal is stretched it gets both longer and thinner. This means that the resistance of the wire will increase two ways. Now if we make a wire in the shape above and stretch it, the resistance increases more than a single length of wire.

The wire is placed within a diaphragm that comes into contact with the fluid you’re trying to measure the pressure of (think an arterial line set). Any increase in pressure stretches this diaphragm and hence the wires and increases the resistance.

If we then put this as a part in a wheatstone bridge, then as the diaphragm is stretched, then a voltage is produced. This can then be calibrated against the pressure change and displayed on a computer monitor.

Random Exam factoids (i.e. the things the college like asking):

  1. Torricellian vacuum – This is the bit above a column of mercury in a barometer. It simply contains the vapour of mercury, so isn’t really a true vacuum.
  2. Conversion of pressure units – The college LOVE this. Just learn the below table:
KiloPascal (kPa) mmHg cmH2O Bar
1 Atmosphere (atm) 101.32 760 1033 1.01

© Sam Beckett and Physics4FRCA, 2018. Unauthorized use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited.

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