**6.3 ****
Pressure in a liquid - density and depth factors - calculations**

Density is a measure of how close the
particles are together.

The more compact they are, the greater the density.

As already mentioned, in liquids the density
is uniform throughout and because there is so little space between the particles
the density only slightly decreases with increase in temperature with the
increased kinetic energy of the particles.

However, the volume shows almost no
change with increased pressure (so here you can consider
liquids to be virtually incompressible).

All liquids expand on heating - observe a
mercury or alcohol thermometer.

**
The
pressure in a fluid varies AND increases with depth** - it
doesn't matter whether you are dealing with gases like the
atmosphere or liquids
like the water of a lake or ocean.

The greater the height/depth of fluid, the greater the weight
of particles that gravity is pulling down, hence the increase in force per unit
area at a particular level, hence the increase in pressure.

**
The pressure in a fluid acts in all
directions (← → ↑ ↓) because the particles are moving and colliding
with each other, and the sides of the container, at random in all directions.**

**
Liquid pressure significantly increases with depth as
the weight of the column of liquid increases.**

A simple experiment can demonstrate this
rule using a tall container with holes in the side. When you fill it with
water, the water gushes out of the holes, but the lower the hole, the
greater the water pressure, the faster the water comes out and travels a
greater distance.

**A note on dam construction** (e.g. reservoir for
water supply or hydroelectric power plant)

Since water pressure increases with depth, to resist
this increase in pressure, the width of a dam must also be increased
to combat the increased force on the dam wall.

The width of the dam is much greater at its base
compared the top of the dam wall.

**The pressure also increases with
increase in density of the fluid** - so air and water differ significantly
for a pressure created at a specific depth of fluid (densities: air density
1.2 kg/m^{3} and water 1000 kg/m^{3} at room temperature).

**From your own experience you may
have observed:**

Sometimes in a car descending or
ascending a few hundred metres on a road can make your ears 'pop'
and hurt slightly because of the change in pressure with height.

BUT, you only have to dive into a
few metres of water to experience the same effect on your ears. As
you suddenly into the water, the pressure is suddenly increased on
your ear drums - the pain comes from the greater external water
pressure than the internal body pressure on the other side of your
ear drum. However, for most people, when under the water at shallow
depths, the pressures become equal quite quickly

You can calculate the pressure at a given
depth created by the
weight of liquid
in the earth's gravitation field using the following formula:

**pressure in a liquid = depth of liquid x
density of liquid x gravitational field strength**

**
P = hρg**

**P**, pressure
in pascals (**Pa**);
**h** = depth in metres (**m**); **ρ** = density (**kg/m**^{3}),

and the
gravitational field strength =
**g** = **9.8 N/kg** (on the Earth's surface)

**Unit connections**

Taking the formula P = h
x ρ x g 'apart' in terms of units.

pressure = force per
unit area = height of column of material x density of material x
gravitational constant

**N / m**^{2}
= m x kg/m^{3} x 9.8 N/kg

unit analysis: on
the right the kg cancel out, m/m^{3} = 1/m^{2}, you are
left with **N/m**^{2} !!

**
Note: Upthrust force in fluids and flotation etc. are covered
in **

FORCES 7. Pressure & upthrust in liquids, why do
objects float or sink in a fluid?, variation of atmospheric pressure with
height

**
Example calculations involving liquid
pressure**

(the gravitational field effect is taken as 9.8 kg/N in these questions).

**
Q1** Divers have to be
careful when working at depth in water and need to carefully control the
dissolving of gases in their blood stream.

(a) Calculate the
pressure created by a 30 m depth of water given the density of water is 1000
kg/m^{3}

(b) Comment on the
dangers when diving at great depths and how to avoid dangerous problems.

Worked out
ANSWERS to the pressure in liquid questions

**
Q2** The density of sea water
is ~1025 kg/m^{3}, the maximum depth of the Atlantic ocean is ~8500 m
(8.5 km).

(a) Calculate the water
pressure at this depth.

(b) By what factor is
the pressure greater at these depths compared to the ocean surface?

Worked out
ANSWERS to the pressure in liquid questions

**
Q3** At what depth in water
is the increased pressure five times greater than atmospheric pressure (101
kPa)?

Worked out
ANSWERS to the pressure in liquid questions

**
Q4** At a depth of 12.5 m of
a chemical solvent the pressure at the bottom of the storage tank due to the
solvent was 306 kPa

Calculate density of the
solvent.

Index physics Forces notes 6. Forces & pressure in
fluids, calculations

**
Keywords, phrases and learning objectives for forces involving **
**pressure situations**

Be able to solve problems and answer calculation
questions on the forces and creating pressure in liquids - be able
to do calculations using the formulae **P = F/A** and **P = hρg**
with the appropriate units.

Know how, and explain why, pressure in a liquid
increases with increase in density or increase in depth.

Be able to describe a simple experiment that shows
variation in liquid pressure with depth.

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Index physics Forces notes 6. Forces & pressure in fluids, calculations