# Pressure

### Is pressure a scalar or a vector?

At KS3 and GCSE pressure is learnt as a force acting on a solid surface.

This type of pressure is a vector (as it matters which way you push!).

BUT at A level you do not study that type of pressure - the type you study is pressure in fluids (link at the bottom of the page) - in fluids pressure acts equally in ALL directions - therefore it is a scalar quantity... if they ask you whether pressure is a scalar or a vector - answer scalar - because they are not thinking of the pushing on an area of a solid!

### Presure exerted on solids

When a force acts on a solid object it can make it accelerate if it can make it change its state of motion.

However, sometimes a force acts on a solid object and that object cannot respond by moving, instead the force creates pressure on that object. This can result in the object being deformed in some way (having an indent appear on its surface or being 'squashed'). Sometimes this is permanent, sometimes when the pressure is removed the object returns to its original shape. For an object that is able to recover its original shape, elastic
potential energy
stored in the object when work is done on the object to change its shape.It is then released when the object regains its shape.

So, we can think of pressure as being the result of a force acting on an object.

You cannot tell the pressure effect that a force will have simply by its size. The contact area (only the area in contact! ... not the total surface area!) between the force and the object is also important).

### THE GENERAL EQUATION

This can be written as:

 A toddler cannot hit very hard.... but give that toddler a geological hammer (very unwise and dangerous!!!) and a blow from a toddler could kill you! The force would be small but the contact area would be tiny (the point of the geological hammer) Similarly, you wouldn't want to take a blow from a karate expert..... but if that blow was delivered to a large block of wood on your stomach the pressure would be small because the contact area would be great. The block could be broken in two but the blow would not hurt you at all.

### UNITS

Pressure is usually expressed in how much force (in newtons) is applied to one metre squared:

This unit can be expressed as a single word - the pascal (note the capital 'P' and small case 'a').

In exams and tests you will sometimes find it expressed in how much force (in newtons) is applied to one square centimetre:

Work in whatever units you are given.... don't change from one to another unless you are told to. However there is a relationship between the two units.

A square metre is ten thousand square centimetres, therefore the pressure in pascal is always ten thousand times bigger than the pressure expressed in N/cm2

### PERFORMING CALCULATIONS

Always lay your calculations out carefully.

• Extract information from the question and list it on the right hand side of the page
• Ensure that you write in the units for the values too!
• Write out the basic equation
• If necessary work out values required from the information given
• Substitute the numbers into the equation
• Put in the correct unit