Plumbing Connection Autumn 2016

4 2

PLUMBING CONNECTION

AUTUMN 2016

Let’s get back to pressure…

If you place an empty coffee cup on the table, there is a

certain Pressure created between the bottom of the cup and

the table (Fig. 1). The magnitude of the Pressure depends on

the Weight of the cup and on the Area of the cup’s base. The

unit of Pressure is the Pascal (Pa). This is defined and the

number of Newton’s (Weight force) divided by the number

of square metres (Area). If you filled the coffee cup up with

coffee, the cup’s Weight (N) would increase, which means

the Pressure (Pa) between the cup’s base and the table

would also increase. Pressure is also measured in multiples

of Pascals like kilopascals (kPa) and Megapascals (MPa). For

fluid systems we usually measure Pressure in kPa, while for

construction materials (concrete and steel) we generally

measure pressure in MPa. Great, so what’s a coffee cup got

to do with fluid or pipe pressures? Let’s have a look…

Now that we have filled the cup with coffee, there are

also (static) Pressure forces acting inside the cup on the

walls and the base due to the Weight of the coffee (Fig. 1).

This Pressure increases as the depth increases due to the

Weight of the fluid (coffee) above. This is a fundamental

concept of Fluid Mechanics (for liquids): “The pressure at a

particular point below the surface is directly proportional to

the height of the liquid above the point.” This means that the

static Pressure in a liquid is caused by the Weight of the fluid

atoms (or molecules) above it.

Different fluids contain different molecules so they can

have different Weights and densities. Density is defined as

the weight of a fluid per unit volume. The unit of Density is

kilograms per cubic meter (kg/m3). The symbol for Density

is the Greek symbol,

, (pronounced rho). Fresh water has

a density of approximately 1000kg/m3. Oil generally has a

density of around 900kg/m3 which is why oil floats on water.

Concrete has a density of around 2400kg/m3 which is why

it sinks in water. Salt water is slightly more dense than fresh

water at around

= 1030kg/m3. This is why it is a bit easier

for us to swim in salt water than fresh water. You may have

seen photos of people floating around on the Dead Sea.

This is because it has a very high salt concentration with a

density of 1240kg/m3. Humans have an average density of

around 985kg/m3, so we can easily float on the Dead Sea.

HYDRAULIC CLASSROOM

DR TERRY LUCKE

The formula for the pressure at a particular point in a

liquid is shown in Equation 1:

P =

gH …Eqn. 1

Where:

P = Pressure (Pa),

= density (kg/m3),

g = acceleration due to gravity (9.8m/s2), and

H = height of fluid above point (m).

When dealing with fluids, we normally like the answer to

Eqn. 1 to be expressed in kPa. To do this, we simply divide

the answer by 1000. Here is an example to illustrate:

Example 1: What is the water pressure (kPa) acting on the

internal base of the tank shown in Figure 2?

Solution using Eqn 1:

P =

gH = 1,000kg/m3 x 9.8m/s2 x 3.5m = 34,300Pa

However, the question asks for the Pressure in kPa, so we

simply divide this answer by 1000, i.e. 34,300/1000 = 34.3.

So the pressure acting on the base of the tank is 34.3kPa

(answer).

This process is always the same regardless of the liquid

being used. The main thing to remember is to make sure you

are using the correct Density for the liquid in question. For

example, if the fluid in example one was Oil (

= 900kg/m3),

the base pressure would be approximately 30.9kPa (check

this for yourself!).

One of the most important concepts to understand

regarding static liquid pressures is that the pressure at a

certain point below the surface is only influenced by the

height (H) of the liquid above it. It makes absolutely no

difference what shape the fluid above or beside the point

is. For example, the water pressure acting on the inside

wall of a massive dam 50m below the surface is exactly

the same as the water pressure acting on the walls of a

Ø5mm diameter vertical tube, 50m below the water surface.

However, in this case the pressure would probably be too

great for the tube which may cause it to explode.

Many pipes are pressure rated to indicate the strength

of the pipe walls. A common classification system is the PN

(Nominal Pressure) rating system. It is pretty simple really;

a pipe with a PN4 classification can safely withstand an

internal fluid pressure of 400kPa. A PN6 pipe can withstand

600kPa and a PN12 pipe can withstand 1200kPa, etc…

FIGURE 1 – COFFEE CUP PRESSURE

Total Weight (N)

Pressure on Walls

and Base (Pa)

Contact Area of

Base (m

)

Pressure between

Cup and Table (Pa)

Pressure

Increase