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1.4 PRESSURE. 1.4.1 Pressure in a fluid 1.4.2 The effect of gravity on pressure 1.4.3 The effect of gas temperature on pressure 1.4.4 Propagation of waves 1.4.5 Attenuation of waves. Pressure = Force / Area. Force F 1 Area A 1. Force F 2 Area A 2. F 2 = F 1  A 2 /A 1. Piston.

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1 4 pressure
1.4 PRESSURE
  • 1.4.1 Pressure in a fluid
  • 1.4.2 The effect of gravity on pressure
  • 1.4.3 The effect of gas temperature on pressure
  • 1.4.4 Propagation of waves
  • 1.4.5 Attenuation of waves
pressure force area
Pressure = Force / Area

Force F1 Area A1

Force F2 Area A2

F2 = F1 A2/A1

pressure intensifier

Piston

Cylinder

Low

Pressure P1

Area A1

Pressure Intensifier

High Pressure P2, AreaA2

Seal (O Ring)

The pressure is increased by a factor A1/A2

where A2 and A1 are the areas of each

end of the piston.

Force = P1A1 = P2A2

therefore P2 = A1

P1 A2

1 4 pressure1
1.4 PRESSURE
  • 1.4.1 Pressure in a fluid
  • 1.4.2 The effect of gravity on pressure
  • 1.4.3 The effect of gas temperature on pressure
  • 1.4.4 Propagation of waves
  • 1.4.5 Attenuation of waves
pressure and depth
Pressure and depth

The pressure at a depth h metres below an open surface of a liquid is given by:

where  is the density (1000 kg/m3 for water) and g is 9.81 m/s2.

units of pressure
Units of Pressure

0.99 Atmospheres

= 1 Bar

= 100 kPa (kilo Pascal)

= 0.1 N/mm2

= 10 m water head

mercury barometer
Mercury Barometer

Sealed End

Vacuum

Pressure in mm of mercury

Approx 1 m.

Would be 10 m for water

Mercury

Open End

1 4 pressure2
1.4 PRESSURE
  • 1.4.1 Pressure in a fluid
  • 1.4.2 The effect of gravity on pressure
  • 1.4.3 The effect of gas temperature on pressure
  • 1.4.4 Propagation of waves
  • 1.4.5 Attenuation of waves
ideal gas equation
Ideal Gas Equation

There is an approximate equation which may be used to calculate the change in pressure in a gas when it is heated. The "ideal gas equation" is:

where:

P1, V1, and T1 are the pressure, volume and temperature before the change and P2 etc. are the values for after the change. Note that T must be in Kelvin, not centigrade.

1 4 pressure3
1.4 PRESSURE
  • 1.4.1 Pressure in a fluid
  • 1.4.2 The effect of gravity on pressure
  • 1.4.3 The effect of gas temperature on pressure
  • 1.4.4 Propagation of waves
  • 1.4.5 Attenuation of waves
schematic diagram of movement of an element of a solid

L2

Weight

Bar.

L1

Schematic diagram of movement of an element of a solid

The force on the weight will cause it to accelerate: F=ma

where:

F is the force = stress  area

m is the mass = Al1

and a is the acceleration

Thus: F = EyA/l2

The solution to this "simple harmonic motion"

progress of a wave on a solid
Progress of a wave on a solid

Movement of a wave. Pressures at time T and T+T. The velocity of the wave is the frequency  the wavelength

Displacement y

Position x

definitions for waves
Definitions for waves
  • Frequency in the number of complete cycles per second
  • Wavelength is the distance from a point on a wave to the identical point on the next wave
  • Velocity = frequency  wavelength
pressure waves in a solid
Pressure waves in a solid
  • E = Young's modulus
  • v = pulse velocity
  • d = density
  •  = Poisson's ratio
elastic deformation of fluid
Elastic deformation of fluid

We define the bulk modulus B as follows:

1 4 pressure4
1.4 PRESSURE
  • 1.4.1 Pressure in a fluid
  • 1.4.2 The effect of gravity on pressure
  • 1.4.3 The effect of gas temperature on pressure
  • 1.4.4 Propagation of waves
  • 1.4.5 Attenuation of waves