CE2703 Course Notes 04-3
(b) Force on a Curved Surface
The way to study the forces associated with submerged curved surfaces is to resolve the
net force into a horizontal and a vertical component.
[case i] fluid above the curved surface
A
Free Body
A
A
FV
CE2703 Course Notes 08-2
Critical Reynolds numbers = dividing points between the three types of flow
for normal cases of flow in straight pipes of uniform diameter and usual roughness,
the critical values may be taken as:
laminar < (Re = 2000) < transitio
CE2703 Course Notes 09-2
LAMINAR example
An oil (SG = 0.85, = 1.8 x 10-5 m2 s-1) in a refinery flows through a 10-cm-diameter
pipe at 0.5 Ls-1. Is the flow laminar or turbulent? Find the head loss per metre of pipe
length.
TURBULENT example1
The head loss
CE2703 Course Notes 04-4
resultant:
Compute the resultant force
FR =
FH2 + FV2
Compute the angle of inclination of FR relative to the horizontal:
F
= tan 1 V
FH
Show the resultant force, and the component forces on a diagram, and where
they act.
[cas
CE2703 Course Notes 06-5
Venturi meter
The Venturi meter is a device for measuring discharge in a pipe. It consists of a rapidly converging
section that increases the velocity of flow (and hence reduces the pressure). It then returns to
the original dimen
CE2703 Course Notes 02-6
Surface of Equal Pressure
the hydrostatic pressure in a body of water varies with the vertical distance measured
from the free surface of the water body. In general, all points on a horizontal surface in
the water have the same pr
CE2703 Course Notes 05-3
VISCOSITY (Mott Chapter 2)
absolute or dynamic viscosity: resistance to shear determined by its cohesion and its
rate of transfer of molecular momentum
kinematic viscosity: ratio of dynamic viscosity to density
REAL FLUID
IDEAL FL
CE2703 Course Notes 04-1
Section 4: Forces due to Static Fluids (Mays2005, Chapter 3)
Forces due to Static Gases:
The distribution of pressure within a gas is approximately uniform, so we can assume that
the force from a gas present under pressure is acti
CE2703 Course Notes 07-1
Section 7: Energy (Mott Chapter 7)
FULL ENERGY EQUATION:
p1
V12
p2
V22
+ z1 +
h p / t = + z2 +
+ hL
g
2g
g
2g
LOSSES
Example:
If the difference in elevation between points A and B is 10 m and the pressures at A and B
are 160 and
CE2703 Course Notes 10-1
Section 10 Minor Losses
Energy losses are proportional to the velocity head of the fluid as it flows through the
system. Values for energy losses are usually given in terms of a resistance coefficient, k:
"V 2 %
hL = k $ '
# 2g &
CE2703 Course Notes 04-1
Section 4: Buoyancy and Stability (Mott Chapter 5)
Buoyancy: A body in a fluid, whether floating or submerged, is buoyed up by a force equal to
the weight of the fluid displaced.
(a) SUBMERGED BODY
B
A
H
W
C
D
K
FB
Buoyancy
The bu
CE2703 Course Notes 02-2
BUT! in the z-direction,
Fz = pB dx dy pD dx dy - dW = 0
Fz = p dx dy (p +
p
dz ) dx dy - g dx dy dz = 0
z
p =
z
so
p
p
Because
= 0 and
= 0 there is no variation of pressure with horizontal distance.
y
x
pressure is constant in a
CE2703 Course Notes 06-1
Energy Considerations in STEADY Flow (Mott Chapters 6,7)
KINETIC ENERGY
a body of mass m when moving at a velocity V possesses a kinetic energy,
KE = 1 mV2
2
1
1
mV 2
(V )V 2
KE
V2
= 2
=
= 2
weight
gV
gV
2g
(note units of length)
CE2703 Course Notes 04-2
(b) FLOATING BODY
H
A
W
B
K
FB
Buoyancy
FB = weight of Volume AKB = Volume displaced
Example 1:
A 0.3-m-long, 7.5-cm-diameter wood cylinder is placed in a body of water. If the wood has a
SG = 0.5, how much of the cylinder is unde