Introduction
Physics
Grade 10 TAC
May 11-15,2020
Pressure
Objective: 1. calculate the pressure acting on a surface
2. describe how pressure increases with the depth in a fluid.
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 combined effects of these particle collisions produces a net resultant force at right angles to the surface of contact.
e.g. the pressure of gases in a container or the atmospheric air pressure around you.
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
pressure = force ÷ area, P = F / A, F = P x A, A = F / P
P, pascals (Pa); F, force in newtons (N); A, area on which force acts in square metres (m2)
A force of 1 N acting on 1 m2 creates a pressure of 1 Pa
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.
The greater the density of a material, the greater the number of collisions can take place, creating a greater pressure.
This concept is most applicable to gases, which are so easily compressed under pressure, so considerably increasing their density.
Also, the greater the column of fluid e.g. water, the greater the pressure created - the greater weight acting on a given area.
Task
Process
Example of pressure (P = F/A) calculations
Q1.1 If a weight of 200 N acts on a surface of 5 m2, calculate the pressure created.
pressure = force ÷ area, P = F / A = 200 / 5 = 40 Pa
Q1.2 What force must be applied to a surface area of 0.0025 m2, to create a pressure of 200,000 Pa?
P = F / A, rearranging gives: F = P x A = 200000 x 0.0025 = 500 N
Q1.3 In a hydraulic lift system, what must the surface area of a piston be in cm2 if a pressure of 300 kPa is used to give a desired upward force of 2000 N?
P = F / A, rearranging gives: A = F / P = 2000 / 300000 = 0.00667 m2
What is the piston surface area in cm2?
1 m2 = 100 cm x 100 cm = 10000 cm2, so the area of the piston = 10000 x 0.00667 = 66.7 cm2
pressure in a liquid = depth of liquid x density of liquid x gravitational field strength
P = hρg
P, pascals (Pa); h = depth in metres (m); ρ = density (kg/m3), 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 / m2 = m x kg/m3 x 9.8 N/kg
unit analysis: on the right the kg cancel out, m/m3 = 1/m2, you are left with N/m2 !!
Example calculations involving liquid pressure (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.
P = hρg
P = 30 x 1000 x 9.8 = 294 000 Pa (2.94 x 105 Pa, 294 kPa)
Note: Atmospheric pressure is about 101 kPa, so a diver at these depths will experience a much greater pressure than on the surface. Increase in pressure causes more gases to dissolve in the blood stream. This can have serious consequences if time isn't allowed for the body pressure to adjust to the new external pressure. The bends, also known as decompression sickness disease, occurs in divers when dissolved gases (mainly nitrogen) come out of solution in bubbles and can affect any body area including joints, lung, heart, skin and brain. The effects can be fatal.
Q2.2 The density of sea water is ~1025 kg/m3, the maximum depth of the Atlantic ocean is ~8500 m (8.5 km).
(a) Calculate the water pressure at this depth.
P = hρg
P = 8500 x 1025 x 9.8 = 85 400 000 Pa (to 3 sf, 85.4 MPa, 85400 kPa, 8.54 x 107 Pa, 8.54 x 104 kPa)
(b) By what factor is the pressure greater at these depths compared to the ocean surface?
Atmospheric pressure is ~101 kPa
Pressure at bottom of ocean ÷ pressure at surface = 85400 ÷ 101 = 846 (3 sf).
Note: This extraordinary increase in pressure mean to explore this 'alien' world you need a very strong submersible craft. However, evolution has allowed all sorts of creatures to live down at these depths, all fully pressure adjusted over time! If you (theoretically) brought any such creatures rapidly to the surface and exposed them to normal pressure, it would kill them!
Q2.3 At what depth in water is the increased pressure five times greater than atmospheric pressure (101 kPa)?
5 x 101 = 505 kPa, 505000 Pa, density of water 1000 kg/m3
P = hρg, rearranging gives h = P/ρg = 505000/(1000 x 9.8) = 51.5 m
Note: The pressure increase in water increases by about the value of atmospheric pressure for every 10 m.
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
Calculate density of the solvent.
P = hρg, rearranging gives ρ = P/hg = 306000/(12.5 x 9.8) = 2498 kg/m3
Evaluation
1. a) Explain what is meant by the term ‘pressure’. [2]
b) State the SI unit of pressure. [1]
c) State TWO instruments used to measure pressure. [2]
d) A cyclist and his bicycle have a combined mass of 55 kg. The total area of the tyres in contact with the road is
2.2 x 10-3 m2. Calculate the pressure exerted on the ground. [5]
[gravitational field strength, g = 10 Nkg-1]
2. A scuba diver is at a depth of 45 m below the surface of the sea. The density of seawater throughout the water
column above the scuba diver-is 1150 kgm-3. [atmospheric pressure = 100 kPa]
Calculate:
a) the pressure acting on the scuba diver due to the seawater only. [3]
b) the total pressure acting on the scuba diver. [2]