FORCES 6. Pressure in fluids and hydraulic systems
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Suitable for GCSE/IGCSE Physics/Science courses or their equivalent
This page will answer help you answer questions like e.g.
What is a fluid? What is the formula for pressure?
What causes pressure in liquids?
How do you calculate pressure in a liquid?
How do hydraulic systems work?
What do we use hydraulic systems for?
Particle theory, Fluids and Pressure
Gases and liquids are fluids because the particles are free to move around.
In fluids the inter-particle attractive forces are sufficiently weak to prevent a solid forming, allowing free random movement of the molecules of a liquid or gas.
Because of the weaker inter-particle force, the particles of gas will spread out to fill any space available.
The particles in a liquid are held much closer together because of greater inter-particle forces giving liquids a much greater density than gases.
Liquids have a uniform density (same throughout its bulk) which only increases very slightly under extremely high pressures because there is so little free space.
However, there is considerable space between gaseous particles and its is relatively easy to compress the particles closer together e.g a bicycle pump filled with air or water. The air is easily compressed and the water isn't. The water can ruin the pump but you can't compress the water in it. High pressure water pistols rely on compressed air NOT compressed water.
In moving around the particles of a fluid collide with each other and with any surface they are in contact with.
Although the mass of an individual particle is minute and each collision involves the transfer of an equally minute amount of kinetic energy, collectively the trillions of collisions cause a pressure to be exerted in both gases and liquids.
The maximum pressure exerted in a fluid is considered to be due to the collective force of the particle collisions acting at right angles (normal, 90o, perpendicular) to the surface on which the collisions take place i.e. any surface in contact with the fluid.
Pressure is defined as force per unit area and is calculated from the simple formula
Liquid fluids have a much greater density than gaseous fluids, so for similar depths (or heights) of gas and liquid, liquids will create a much greater pressure because of the greater weight (due to gravity) of substance acting on the same surface area.
Q1.1 If a weight of 200 N acts on a surface of 5 m2, calculate the pressure created.
Q1.2 What force must be applied to a surface area of 0.0025 m2, to create a pressure of 200,000 Pa?
Q1.3 In a hydraulic lift system, what must the surface area of a piston be if a pressure of 300 kPa is used to give a desired upward force of 2000 N?
Pressure in a liquid - density and depth factors
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 and almost no change with increased pressure (hear you can consider liquids to be incompressible).
The density in a fluid varies 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.
You can calculate the pressure 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
Example calculations (the gravitational field effect is taken as 9.8 kg/N in these questions).
Q2.1 Calculate the pressure created by a 30 m depth of water given the density of water is 1000 kg/m3 and gravity 9.8 N/kg.
Q2.2 The density of sea water is ~1025 kg/m3, the maximum depth of the Atlantic ocean is ~8500 m (8.5 km).
Q2.3 At what depth in water is the increased pressure five times greater than atmospheric pressure (101 kPa)?
Q2.4 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
Hydraulic systems - mechanical devices for the transmission of forces in liquids
Hydraulics is how we can use fluids (e.g. air or oil) to transfer force to achieve some useful work e.g. operating machinery like car jacks, car brakes or JCB digging machines.
As we have said above, pressure in fluids is caused by particle collisions with themselves and the surface of a container.
These collisions cause a net force at right angles to all surfaces the fluid is in contact with. Hence the equation
However, there is an important new idea to understand the applications of hydraulics.
The pressure in a fluid is transmitted equally in all directions.
AND, for the purposes of calculations, you consider the force involved to act at right-angles to the surface.
Since liquids are incompressible, if a force is applied to any point in an enclosed fluid system the net force is transmitted to any other point in the fluid (gas or liquid). This is the basis of all hydraulic systems.
The principles and calculations involving hydraulic systems.
The diagram above illustrates the idea of using a hydraulic system to apply a small force to produce a large force - an example of a force multiplier system to effect a mechanical advantage (remember moments and lever systems!)
The formula for pressure is P = F/A (already dealt with in detail on this page).
Therefore: P1 = F1input/A1 and output P2 = F2output/A2
BUT, P1 = P2 because the pressure at any given moment in time is the same throughout the hydraulic system.
Therefore: F1/A1 = F2/A2, rearranging gives the output force F2 = F1 x A2/A1
So the ratio of the two piston areas (A2/A1) gives you the force multiplying effect.
Note: In hydraulic systems, piston 1 is in the master cylinder and piston 2 is in a slave cylinder (can be several of them).
Q3.1 In a simple hydraulic system piston 1 has a cross-section area of 0.000050 m2, and piston 2 has a cross-section area of 0.00025.
Q3.2 A medium sized car typically weighs 1000 kg. (gravity force 9.8 N/kg)
Some applications of hydraulic systems
Hydraulic jack system.
Four hydraulic piston and cylinder systems are used to jack up the red van. The fluid can be oil or compressed air.
The Land Rover (left) and the red van (right) both have hydraulic brake systems.
Key for the 5 photographic diagrams: S = suspension spring; H = the pipe conveying the hydraulic brake fluid force.
D = the brake drum and disc on which the brake pads in casing P are forced into contact with the smooth disc by the hydraulic transmitted force when you press the brake pedal.
A conveys speed of rotation information for the correct functioning of the advanced ABS braking system.
How does the brake system of a motor vehicle work?
When you press on the brake pedal of motor vehicle, the force is transmitted through the brake fluid liquid by a pipe system (in modern cars it is aided by an electric pump system). The braking mechanism involves several pistons and cylinders, known as the master cylinder (activated by the pedal) and slave cylinders on the brake drums (4 of the latter in the case of 4 wheeled vehicles). The transmitted force pushes the brake pads onto the brake disc on the brake drum and the resulting friction reduces the speed of the vehicle. When you take you foot off the brake pedal, the force is no longer transmitted and springs move the brake pads away from the brake discs to avoid unnecessary friction.
'Hydraulic' photographs by courtesy of Mark Raw of M T R Autotech Ltd garage, Castleton, North Yorkshire, England
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