(Static) Fluid Pressure Transmission

• Liquids are almost incompressible• The molecules that make up a liquid can freely

slip over one another• Therefore any pressure applied to the liquid is

passed on to all parts of the liquid

Applications such as in:

• Biology

And in Physics

• Hydraulic Braking system of a vehicle

An example of the bad

A blow to the eye by a tennis ball can cause more damage than one might expect because of the transmission of the pressure to the back of the eye.

• P1=P2

• Recall Pressure = force/areaP = F

A• It follows then that :F1 = F2

A1 A2

ExampleA = 0.1m2

F= 20NA = 0.2 m2

F=?

Step 1: recall F1 = F2

A1 A2

Step 2: substitute20N = F2

0.1m 0.2mF2 x 0.1= 20 x 0.2Step 2: make unknown the subject of the formula F2 = 20 x 0.2 = 40N 0.1

Your turnA = 0.2m2

F= 60NA = ?F= 25N

Step 1: recall F1 = F2

A1 A2

Step 2: substitute60N = 25N0.2m A2

A2 x 60 = 25 x 0.2Step 2: make unknown the subject of the

formula A2 = 25 x 0.2 = 0.083m2

60

An object within a fluid experiences pressure

• The figure to the right shows a cylinder of liquid of height h and area A.• The weight of the cylinder is its mass m times the acceleration due to

gravity g. This is the force exerted by the cylinder of liquid on whatever is just below it:

• F = m g• The pressure p is this force divided by the area A of the face of the

cylinder.• p = F/A• The mass of the cylinder is the density of the liquid times the volume V.• m = V • The volume is the area A of the face of the cylinder times its height h.• V = A h

• So, the pressure p is:• p = F / A = ρmg / A = ρV g / A = ρAh g / A = ρhg Thus, if , h and g are measured in SI

units, the pressure p will be in pascals. Note that the value is independent of the area of the cylinder.

The three basic states of matter are

• Solids• Liquids and • Gases (for your personal knowledge know there are

also• Bose-Einstein Condensates• Plasmas

The U-Tube

In the figure to the right we show such a U shaped tube filled with a liquid. Note that both ends of the tube are open to the atmosphere. Thus both points A and B are at atmospheric pressure. The two points also have the same vertical height.

Now the top of the tube on the left has been closed. We imagine that there is a sample of gas in the closed end of the tube.The right side of the tube remains open to the atmosphere. The point A, then, is at atmospheric pressure.The point C is at the pressure of the gas in the closed end of the tube.The point B has a pressure greater than atmospheric pressure due to the weight of the column of liquid of height h.The point C is at the same height as B, so it has the same pressure as B. And we have already seen that this is equal to the pressure of the gas in the closed end of the tube.Thus, in this case the pressure of the gas that is trapped in the closed end of the tube is greater than atmospheric pressure by the amount of pressure exerted by the column of liquid of height h.

The point A is at atmospheric pressure.The point C is at whatever pressure the gas in the closed end of the tube has, or if the closed end contains a vacuum the pressure is zero.Since the point B is at the same height as point A, it must be at atmospheric pressure too. But the pressure at B is also the sum of the pressure at C plus the pressure exerted by the weight of the column of liquid of height h in the tube.We conclude that pressure at C, then, is less than atmospheric pressure by the amount of pressure exerted by the column of liquid of height h.If the closed end of the tube contains a vacuum, then the pressure at point C is zero, and atmospheric pressure is equal to the pressure exerted by the weight of the column of liquid of height h. In this case, the manometer can be used as a barometer to measure atmospheric pressure.

• For example, atmospheric pressure varies with the weather and is usually about 100 kilopascals (KPa). Another common unit for measuring atmospheric pressure is mm of mercury, whose value is usually about 760 mm.

• Put another way, if the closed end of the tube in Case 3 above contains a vacuum, the height h is about 760 mm.

• 1atmosphere = 760mmHg = 101.325KPa

In breathing for example

Upon inspiration, the pressure in the alveoli is on the order of 2-3 mmHg below the atmospheric pressure of 760 mmHg. The relaxing of the diagphragm plus the elastic recoil of the alveoli provides a pressure some 3 mmHg above atmospheric pressure to accomplish expiration.

At right is a sketch of a lung model used to demonstrate the nature of the breathing process. A rubber membrane simulates the action of the diaphragm.

There is also pressure in the:• Blood • Middle ear• Eye• Brain• Intestines

For exploration in the ocean (under water)

Significant portion of the Global Biosphere is subjected to high hydrostatic pressure!

Marianas Trench: 38,713 ft (11,800m) deep

16,000 PSI (120MPa)

In Chemistry• Rates of reactions can be increased or decreased by

increasing or decreasing pressure• The atoms or molecules in a gas are very spread out. • For the two chemicals to react, there must be collisions

between their molecules. • By increasing the pressure, you squeeze the molecules

together so you will increase the frequency of collisions between them.

Misconceptions

Force is pressure - In nature, forces exist all around us. - If forces are unbalanced, things move. For example: The Earth pulls on the moon and keeps

it in orbit. The moon pulls back on Earth and creates tides. We don’t think about these gravitational forces

because we do not easily detect the motions they cause.

• In our normal environment, forces are balanced and most things do not move in relation to surrounding objects.

• That’s good because we often lose things even when they are not moving.

• On Earth, all objects that have mass also have weight and this means they put pressure on other objects even where nothing is moving.

• So be careful. Even though something is not moving, there may still be a force that causes pressure.