fc-civ hidrcana: channel hydraulics flow mechanics...
Post on 17-May-2018
234 Views
Preview:
TRANSCRIPT
Eusebio Ingol Blanco, Ph.D.
Civil Engineering Program, San Ignacio de Loyola University
FC-CIV HIDRCANA: Channel Hydraulics Flow Mechanics Review
Pressure
Objective
• Determine the variation of pressure in a
fluid at rest.
• Compute pressure using manometers
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
Pressure
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
• Pressure is defined as a normal force exerted by a
fluid per unit area.
1Pa = 1 N/m2
1kgf/cm2 = 14.223 psi
Pressure
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
Pgage = Pabs - Patm
Pvac = Patm - Pabs
Absolute pressure: The actual pressure at a given position. It is measured
relative to absolute vacuum (i.e., absolute zero pressure).
Gage pressure: The difference between the absolute pressure and the local
atmospheric pressure. Most pressure-measuring devices are calibrated to
read zero in the atmosphere, and so they indicate gage pressure.
Vacuum pressures: Pressures below atmospheric pressure.
Pressure at a Point
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
• Pressure is the compressive force per unit area but it is not a vector.
Pressure at any point in a fluid is the same in all directions.
Forces acting on a wedge-shaped fluid element
in equilibrium.
PPPP
zgPP
PP
yxandzybyDividing
lzlx
zyxgmgW
zyxgylPxyPmaF
ylPzyPmaF
zz
xx
321
32
31
32
31
02
1
0
sincos
2/
02
1cos:0
0sin:0
The last term of the last equation drops out as ∆z →0 and the
wedge becomes infinitesimal
Pressure Variation with Depth
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
• In static fluid, pressure varies only with elevation in the
fluid.
zzgPPP
yxbyDividing
zzz
zyxgmgW
zyxgyxPyxPmaF zz
12
12
21 0:0
Free-body diagram of a rectangular
fluid element in equilibrium.
z2
z1
gdz
dP
2
1
12 gdzPPP
If density changes significantly with elevation, dividing previous
equation by ∆z, and taking the limit as ∆z→0. This yields:
When the variation of density with elevation is known
Pressure Variation with Depth
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
zPzgPP aboveabovebolow
ghPorghPP gageatm
The pressure of a fluid at rest increases with
depth (as a result of added weight). Pressure in a liquid at rest increases linearly
with distance from the free surface.
The vertical distance is sometimes used
as a measure of pressure, and it called
the Pressure head
Pressure Variation with Depth
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
• If is a constant dz
dp
zp
zzpp
dzdpz
z
p
p
)( 1212
2
1
2
1
head) ic(piezometrconstant zp
h
z = 0
1
2
z = z1, p = p1
z = z2, p = p2
zp
22
11 z
pz
p
Elevation head
Pressure head
Piezometric head
http://www.ce.utexas.edu/prof/mckinney/ce319f/ce319f.html
Pressure Head
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
z = 0
1
2
1z
1p /2p
2z
constant zp
Open Tank
http://www.ce.utexas.edu/prof/mckinney/ce319f/ce319f.html
Pressure Head
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
z = 0
3
1z
1p
2z
constant zp
3z
2p
3p
2
1
Pressurized Tank
http://www.ce.utexas.edu/prof/mckinney/ce319f/ce319f.html
Under Hydrostatic Conditions
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
The pressure is the same at all points on a horizontal plane in a
given fluid regardless of geometry, provided that the points are
interconnected by the same fluid.
Pressure using manometers
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
The manometer is commonly
used to measure small and
moderate pressure differences.
ghPP
PP
atm
2
21
The pressure anywhere in the tank and
at position 1 has the same value due to
the gravitational effects are negligible.
Why P1 =P2?
Example 3-5
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
A manometer is used to measure the pressure of a gas in a tank. The fluid
has SG = 0.85, and the manometer column height is 55 cm. Local
atmospheric pressure is 96 kPa. Find the absolute pressure within the tank.
Solution
Assumption:
The density of the gas in the tank is much lower
than the density of the manometer fluid
Properties:
SG = 0.85, ρwater = 1000 kg/m3
Analysis:
ρ = SG (ρHO2 ) = (0.85)(1000kg/m3)= 850 kg/m3
P = Patm + ρgh
kPa
mN
kPa
smkg
NmsmmkgkPa
ghPP atm
6.100
/1000
1
/.1
1)55.0)(/81.9)(/850(96
22
3
Pressure using manometers
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
For immiscible fluids:
1. Pressure change across a fluid column of height h is ΔP = ρgh
2. Pressure increases downward in a given fluid and decrease upward
3. Two points at the same elevation in a continues fluid at rest are at the same pressure
Example 3-6
Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.
Solution
Assumption: The air pressure in the tank is uniform
Properties: The densities water, oil, and mercury are given
Analysis: Starting with the pressure at point 1 at the air-
water interface.
P1 + ρwater g h1 + ρoil g h2 - ρmercury g h3 = P2 = Patm
P1 = Patm - ρwater g h1 - ρoil g h2 + ρmercury g h3
P1 = 129.65 kPa
1N = kg.m/s2, 1kPa = 1000 N/m2
top related