5.1 Hydrostatics 5.2 Fluid flow 5.3    Pascal Law for pressure 5.4    Archimedean Law 5.5    Continuity equation 5.6    Bernoulli equation. 5.7    Diffusion and endosmosis 5.8    Temperature and

thermal expansion 5.9    Calorimetry and heat transfer

Chapter 5FLUIDS AND THERMAL

Getting point from the Photo ?

Motion of fluids

Part 1

Hydrostatics

• By definition, the fluid is at rest.• Or, no there is no relative motion between

adjacent particles.• No shearing forces is placed on the fluid.• There are only pressure forces and no shear.• Results in relatively “simple” analysis• Note for the pressure variation in the fluid• The force per unit area across any surface is

normal to the surface and is the same for all orientations of the surface.

Fluid StaticsFluid Statics

Learning Check

You are sitting on the area of 1m2, If you change your seat to area of 0,7m2, How does the pressure you make to the seat change ??

Increase 1/0.7=1.42

Part 2

Fluid flow

• What do we mean by “fluids”?

– Fluids are “substances that flow”…. “substances that take the shape of the container”

– Atoms and molecules are free to move .. No long range correlation between positions.

• What parameters do we use to describe fluids?

– Density V

m

LIQUID: incompressible (density almost constant)

GAS: compressible (density depends a lot on pressure)

Part 3

Pascal Law for pressure

Blaise Pascal (1623-1662)

Review Pressure

Pressure

• Pressure is defined as a normal force exerted by a fluid per unit area.

• Units of pressure are N/m2, which is called a pascal (Pa). Pa is too small, in practice, kilopascal (1 kPa = 103 Pa) and megapascal (1 MPa = 106 Pa) are commonly used. Other units include bar, atm, kgf/cm2, mm Hg.

Units

• Standard atmosphere is defined as the pressure produced by a column of mercury 760 mm in height at 0°C

(29.92 in Hg or of water about 10.3 m )

* (rHg = 13,595 kg/m3) under standard gravitational acceleration (g = 9.807 m/s2).

• 1 atm = 760 torr and 1 torr (mmHg) = 133.3 Pa

Pressure Units

• Other units include bar, atm, kgf/cm2, mm Hg.

• 1 bar = 105 Pa

• 1 atm = 101325 Pa = 1.01325 bars

• 1 kgf/cm2 = 9.807 N/cm2 = 9.807 104 N/m2 = 9.807 104 Pa = 0.9807 bar = 0.9679 atm

• 1 atm = 14.696 psi.

• 1 kgf/cm2 = 14.223 psi.

• Mm Hg = 9,8.13,6 =133 Pa

Pressure at a Point:

Pascal’s Law

* Pressure is the normal force per unit normal force per unit areaarea at a given point acting on a given plane within a fluid mass of interest.

Pascal’s Law:Pascal’s Law: the pressure at a point in a fluid at rest, or in motion, is independent of the direction as long as there are no shearing stresses present.

Measurement of Pressure: Barometers

Evangelista Torricelli (1608-1647)

The first mercury barometer was constructed in 1643-1644 by Torricelli. He showed that the height of mercury in a column was 1/14 that of a water barometer, due to the fact that mercury is 14 times more dense that water. He also noticed that level of mercury varied from day to day due to weather changes, and that at the top of the column there is a vacuum.

Animation of Experiment:

Schematic:

Note, often pvapor is very small, 0.0000231 psia at 68° F, and patm is 14.7 psi, thus:

Learning Check Torricelli formula

The Pressure in a homogenous, incompressible fluid at rest depends on the depth of the fluid relative to some reference and is not influenced by the shape of the container.

p = po

p = p1

p = p2

Lines of constant Pressure

For p2 = gh + po

h1

For p1 = gh1 + po

Compute: P1 and P2 ??Give P0=760 mmHg, h1=3cm, h=5cm, =1500kg/m3

Learning Check

211211

22 AFAFPF

A

AF

Compute: F2 = ??Give A1/ A2 =3, F1 =45mmHg

Learning test

W hat happe ns w i t h t w o di f f er ent f l ui ds ?? Consi de r a U t ube cont ai ni ng l i qui ds of densi t y 1 and 2 as show n:Com par e t he de nsi t i es of t he l i qui ds :

A) 1 < 2 B) 1 = 2 C) 1 > 2

If we use the same liquids in a U tube of twice the cross-sectional area as the first, compare the distances between the levels in the two cases (depth of liquid 2 same in both cases).

A) dI < dII B) dI = dII C) dI > dII

I

1

2

dI

II

1

2dII

Hint

C) 1 > 2

• At the depth of the interface, the pressures in each side must be equal.• Since there’s more liquid above this depth on the left side, that liquid must be less dense!

• The pressure depends ONLY on the depth and the density of the fluid.• e.g. consider case I:

B) dI = dII

22 g

pd

1

1 gp

d

1212

11g

pddd

I

1

2

dI

p2d

1d

p

II

1

2 dII

2d1d

Part 4

Archimedean Law

Learning Check

Calculate D =?

If L=10m, H=3m, W=500000 N, g=10 m/s2

water= 1000 kg/m3

H

Learning Check

Example: Submarine Buoyancy and Ballast

• Submarines use both static and dynamic depth control. Static control uses ballast tanks between the pressure hull and the outer hull. Dynamic control uses the bow and stern planes to generate trim forces.

Submarine Buoyancy and Ballast

Normal surface trim SSN 711 nose down after accidentwhich damaged fore ballast tanks

Submarine Buoyancy and Ballast

Damage to SSN 711 (USS San Francisco) after running aground on 8 January 2005.

Submarine Buoyancy and Ballast

Ballast Control Panel: Important station for controlling depth of submarine

Test

• A lead weight is fastened to a large styrofoam block and the combination floats on water with the water level with the top of the styrofoam block as shown.– If you turn the styrofoam+Pb upside down, what happens? styrofoam

Pb

A) It sinks C)B)styrofoam

Pb

styrofoam

Pb

Hint

styrofoam

Pb

C)

styrofoam

Pb

• If the object floats right-side up, then it also must float upside-down.• However, when it is upside-down, the Pb displaces some water.• Therefore the styrofoam must displace less water than it did when it

was right-side up (when the Pb displaced no water).

Part 5

Continuity equation

Learning Check

Write an equation for steady conditions (see ficture below)

???

Part 6Bernoulli equation

Static P Dynamic P Hydrostatic P = const

Static Pressure, Dynamic Pressure and Hydrostatic Pressure have the same unit

Learning Check

Hint:

Use the dynamic pressure

P=F/A=v2/2

Learning Check

Explain this experiment ??