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Fluid Mechanics: Mahalingam3 Lecture #7 - continued Read section 2.5, MYO, 3rd edition on absolute/gage pressure/textbook convention, concept of pressure head on page 46 Manometry - Demo Assumptions: Static fluid, gravity is the only body force, z axis vertical h1h1 h2h2 A B Read and 2.7, MYO, 3rd edition for other pressure measuring devices
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Fluid Mechanics: Mahalingam 1
Lecture #7
• Recap lecture #6- Developed equation to describe pressure in the atmosphere
• Focus of today’s lecture- Verify problem solution you were expected to compete from last lecture- Examine hydrostatic forces on planar submerged surfaces with the goal of finding magnitude and line of action of net hydrostatic force
gdzdp
z
yx
Rg
TzTpp
a
aa
- Applied hydrostatics principles to problems
Problem Set # 2, due on Friday, September 10th: 2.10, 2.20, 2.24, 2.28, 2.36
Fluid Mechanics: Mahalingam 2
Lecture #7 - continued
(1)-known AA PP (2)-)( 12 wAD llPP
(3)- AE PP )4( EF PP
(5)-2lSGPP wFG (6)-1lPP wGB
=> )7(12 llSGPP wwAB )8( RPP wAC
To Express Pc in terms of mm’s of Hg)9(Hg) of smm'(
Hg
wAC
RPP
• Substitute numerical values
kPa 1.1031000/)]2)(9800()3)(8.0)(9800[(60 BP
)9(mm 6.22910)9800)(6.13(
)]3)(9800()1000)(60[(Hg) of smm'( 3
CP
D
E F
GB
AC•
l1
l2
l3
Water
Fluid Mechanics: Mahalingam 3
Lecture #7 - continued
• Read section 2.5, MYO, 3rd edition on absolute/gage pressure/textbook convention, concept of pressure head on page 46
• Manometry - Demo
1 2
Assumptions: Static fluid, gravity is the only body force, z axis vertical dzdp /
h1
h2A
B
)1(11 hPP AB
)2(22Atm hPPB
1122gage
1122Atm
]or
)3( Thus,
hhP
hhPP
A
A
• Read 2.6.3 and 2.7, MYO, 3rd edition for other pressure measuring devices
Fluid Mechanics: Mahalingam 4
Lecture #7 - continued
• Hydrostatic forces on submerged surfaces
- Begin by considering forces on planar surfaces- Basic ideas are the same when considering curved surfaces
• Planar surface analysis
Goal
• To find magnitude of force on a planar surface submerged in a fluid• To find location of net force or Center of Pressure
Fluid Mechanics: Mahalingam 5
y
z
h dyy
dF
dApdF dAh
Lecture #7 - continued
dAydAhFA A
)sin(
)1(sin AdAy
)2(Define AydAyA
c
Here yc is the y-coordinate of centroid of area
sinThus cAyF
yc
hc
)3( Ahc A
R dFyyF AdAy2sin
A
Rc dAyyyA 2sinsin
)4(
2
c
AR yA
dAyy
yR
F
x
y
x
dA
Fluid Mechanics: Mahalingam 6
Lecture #7 - continued
• Introduce Module 2 briefly (Surface tension module) at the end of lecture
• At the beginning of lecture, point to website for course
http://stripe.colorado.edu/~mcen3021
