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Fundamental of Fluid Mechanics (Lecture 3)

Dr.Eng Denny Widhiyanuriyawan, ST, MT

Department of Mechanical Engineering,Brawijaya University

Malang, Indonesia

Email: denny_w@ub.ac.id

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Chapter 3

Fluid Statics

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Main Topics

The Basic Equations of Fluid StaticsPressure Variation in a Static FluidHydrostatic Force on Submerged SurfacesBuoyancy

Forces : Body Force

Surface Force

Body Forces : - Gravity force

- Electromagnetic Force

- Corriolis Force

- Centrifugal Force

Surface Forces : - Pressure Force

- Viscous Force (ShearForce)

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The Basic Equationsof Fluid Statics

Body Force (gravitasi force yg sering digunakan dalam MF)

Jika elemen fluida dalam bentuk kubus maka dV=dx.dy.dz

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The Basic Equationsof Fluid Statics

Surface Force

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The Basic Equationsof Fluid Statics

Surface Force

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The Basic Equationsof Fluid Statics

Surface Force

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The Basic Equationsof Fluid Statics

Total Force

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Newton’s Second Law

dadmadF

Fluida static a = 0

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The Basic Equationsof Fluid Statics

Newton’s Second Law

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The Basic Equationsof Fluid Statics

0

x

p

0xg

0

y

p

0yg

gz

p

ggz

Depan belakang

kanan kiri Atas bawah

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The Basic Equationsof Fluid Statics

Pascal’s Law

s

y

sins

x

cos

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The Basic Equationsof Fluid Statics

zypApF xxx ABFE ..

zxpApF yyy CDEF ..

zspApF sss ABCD ..

Surface Force Body Force

- mg = - Vg = - (dxdydz/2) g

syx ppp Pascal’s Law

Buktikan

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The Basic Equationsof Fluid Statics

Vertically

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The Basic Equationsof Fluid Statics

Horizontally

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The Basic Equationsof Fluid Statics

Generally

Cari Kesetimb

angan gaya2nya

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The Basic Equationsof Fluid Statics

Pressure-Height Relation

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Pressure Variation in aStatic Fluid

Incompressible Fluid: Manometers

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Pressure Variation in aStatic Fluid

Compressible Fluid: Ideal Gas

Need additional information, e.g., T(z) for atmosphere

Hydrostatic Condition: U.S. Standard AtmosphereIdealized Representation of the Mid-Latitude Atmosphere

Linear Variation, T = Ta - z

Isothermal, T = To

Standard Atmosphere is used in the design of aircraft, missiles and

spacecraft.

Stratosphere:

Troposphere:

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Pressure Variation in aStatic Fluid

In the sea level surface p0, 0 and z0 = 0. • po = 101,303 Pa (14.696 lb/in2) = lapse rate (koefisien muai untuk

udara) = 0,00650 K/m. For U.S Standard AtmosphereTo = 15oC = 288.15 K (59oF or

518.67oR)

Troposphere

Rg

o T

zpp

01

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Pressure Variation in aStatic Fluid

Stratosphere

Temperature constant

T=Tc=216,7 K=319,1 oR

Zc=11 km (36000ft)

Pc=22600 Pa (3,28 lb/in2)

c

c

RTzzg

cepp

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Pressure Variation in aStatic Fluid

Ionosphere

DISCONTINUM FLUID

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Hydrostatic Force on Submerged Surfaces

Plane Submerged Surface

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Hydrostatic Force on Submerged Surfaces

Plane Submerged Surface

We can find FR, and y´ and x´,by integrating, or …

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Hydrostatic Force on Submerged Surfaces

Plane Submerged Surface• Algebraic Equations – Total Pressure Force

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Hydrostatic Force on Submerged Surfaces

Plane Submerged Surface• Algebraic Equations – Net Pressure Force

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Hydrostatic Force on Submerged Surfaces

Curved Submerged Surface

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Hydrostatic Force on Submerged Surfaces

Curved Submerged Surface• Horizontal Force = Equivalent Vertical Plane Force• Vertical Force = Weight of Fluid Directly Above

(+ Free Surface Pressure Force)

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Buoyancy

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Buoyancy

For example, for a hot air balloon (Example Problem 3.8):

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Examples 3.2

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Examples 3.2

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Examples 3.2

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Examples 3.2

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Examples 3.2

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Examples 3.8

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Examples 3.8

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Examples 3.8

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Examples 3.8

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Examples 3.8

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Examples 3.9

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Examples 3.9

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Examples 3.9

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Examples 3.9

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Examples 3.36

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Examples 3.36

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Examples 3.36

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Examples 3.36

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Examples 3.36

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Practice -q3.77 (optional)

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Project (3) – q 3.60