Transport Phenomena – 1 CHEN 10031

1st Year Chem Eng & Pet Eng

Renold Building C16

Dr Hosam Aleem

Week 3 – 13/10/2014

Today

• Pressure

• Hydrostatic Pressure

• Pressure Measurement

Pressure

• Pressure is Force per unit Area

P = F/A

• Units of pressure

Units of force/ Units of area

N/m2 (or N.m-2) Pascal, Pa

Many other units are still common in industry, e.g. psi, bar, mm Hg, etc.

Atmospheric Pressure

• Atmospheric Pressure

1 atm = 101.325 kPa

14.7 psi

1.01325 bar

760 mm Hg (Torr) The unit Torr is named after an Italian physicist called

E. Torricelli (No, not a type of Pasta!)

• Pressure measuring devices normally measure the difference between the pressure to be measured and atmospheric pressure.

Pressure Scale

Absolute Pressure = Gauge Pressure + Atmospheric Pressure

P abs = P gauge + P atm

Pressure Scale

Absolute Pressure = Gauge Pressure + Atmospheric Pressure

P abs = P gauge + P atm

Atmospheric pressure

Absolute vacuum

Below atmospheric

pressure – vacuum or

suction

Above atmospheric

pressure

Atmospheric pressure = 1 atm = 101325 Pa

= 760 mm Hg ≈ 1 bar ≈ 15 psi (all absolute)

= 0 pressure (in any units) gauge

2 atm = 202650 Pa

= 1520 mm Hg ≈ 2 bar ≈ 30 psi (all absolute)

= 1 atm = 101325 Pa

= 760 mm Hg ≈ 1 bar ≈ 15 psi (all gauge)

Absolute vacuum

= 0 pressure (in any units) absolute

= –1 atm = –101325 Pa

= –760 mm Hg ≈ –1 bar ≈ –15 psi (all gauge)

Today

• Pressure

• Hydrostatic Pressure

• Pressure Measurement

Fluid Mechanics – The big picture

Fluid Mechanics

Fluid Statics

Hydrostatics Aerostatics

Fluid Dynamics

Hydrodynamics Aerodynamics

Hydrostatics

Is the study of (incompressible) fluids at rest.

More formally:

Is the study of fluid problems in which there is no relative motion between fluid elements.

Thus no shear stress

Variation of Pressure with position in a Fluid at rest • Consider a fluid element in the form of a cube of

dimensions xyz inside the fluid.

• The fluid is at rest, no motion All forces acting on the fluid element must be in

equilibrium, for all directions. • Remember that force is related to pressure by P = F/A

x

y

z

x

y

z

Horizontal direction

Forces in the x-direction Fx = Px . yz

Fx+x = Px +x . yz

At Equilibrium

Fx = Fx+x

Px . yz = Px +x . yz

Px = Px +x

but Px +x = Px + Px

Thus Px = 0

no change in pressure in the horizontal direction Same argument applies to y direction

x

y

z

x

y

z

Fx Fx+x

Px Px+x

Vertical direction

Forces in the z-direction

Fz = Pz xy

Fz+z = Pz +z xy

Fg = m g

= ρ (xyz) g

At Equilibrium

Fz+z + Fg = Fz

Pz +z xy + ρ (xyz) g = Pz xy

x

y

z

x

y

z

Fz+z

Fz

Pz+z

Pz

Fg

Fz+z + Fg = Fz

Pz +z xy + ρ (xyz) g = Pz xy

Pz +z xy - Pz xy = - ρ (xyz) g

Dividing by the volume

Taking the limit as z 0

P – P0 = - ρgz

Pressure Profile

P – P0 = - ρgz

Can also be expressed as

P = ρgh

where h is the depth,

the opposite of z the elevation

In general, the difference in pressure between any two points with h difference in depth is

P = ρgh

Another view

P – P0 = ρgh

P = P0 + ρgh

If P0 is atmospheric pressure

Pgauge = ρgh

For gases Pressure is the same in all directions

Hydrostatic Pressure in a Tank

P = ρgh

Pressure Profile NB: a number to remember, every 10 m of water is

approximately 1 atm (Prove)

Tank with Two Liquids

P = ρagha+ ρbghb

X

Tank with Two Liquids and a Gas

P = Pg + ρagha+ ρbghb

Today

• Pressure

• Hydrostatic Pressure

• Pressure Measurement

Pressure Measurements

Mercury Barometer At the surface of the mercury

we have

Pressure due to mercury column

= Atmospheric Pressure

P0 = ρgh

For Mercury we have

ρ = 13560 kg/m3

h = 760 mm = 0.760 m

U-Tube Manometer

(not Manometer)

Points A and A’ are at the

same horizontal level

So must have same pressure

PA = PA’

P1 = P2 + ρgh

To increase the range we can increase either h or ρ or both

U-Tube Manometer in Pilot Plant - JCB

Bourdon Gauge

• Very common in industry because it is reliable, easy to use, does not need a source of power, etc. • Curved metal tube with elliptic cross section • Hence pressure generates a force that causes the tube to expand outward • Returns back to shape when pressure is removed or reduced, due to the elasticity of the metal.

Only one Pressure Gauge was harmed in the making of this slide!

Today

• Pressure

• Hydrostatic Pressure

• Pressure Measurement