Chapter 2 h Force Vectors
21
2.1 2 1 Scalars & Vectors
Mechanics d l M h i deals with two kinds of quantities: ith t ki d f titi
Scalars  quantities with magnitudes only. eg, mass (kg), length (m), speed (m/s) Vectors  magnitudes, directions and sense
Tutorial 5: Specific Energy (1) Critical Depth & Humps
Q1.
[Q10.29] Water is released from a sluice gate in a rectangular channel 1.5 m
wide such that the flow depth immediately below the sluice is 0.6 m with a
velocity of 4.5 m/s. Find:
(a)
The critical
Tutorial 3 Solution: Uniform Flow & Mannings Formula
Q1: Given Q = 44 m3/s, n = 0.014, A = 0.5(15.1+6.1)3 = 31.8 m2, P = 16.92 m
(a)
Using Manning formula
1
31.8
44
x31.8x
0.014
16.92
2
3
1
So 2
Solving So = 0.0001618 or 162 mm/km
(b)
Q = 22 m3/s, n
Tutorial 4 Velocity Distribution in OC & Most Efficient Cross Section
Q1. Eq. (13):
u V
g yo S o
K
y
1 2.3 log
(13)
yo
2
1
1
3
( 2 ) ( 0.005 ) 2 =6.237 m/s
V=
0.018
Using Mannings Eq for wide ch:
The shear velocity in (13) is u = g y o So = 9.81 x 2 x
Tutorial 4 Velocity Distribution in OC & Most Efficient Cross Section
Q1.
[Q10.4.2] Water flows uniformly in a very wide rectangular channel at a depth y o = 2.0m with bed
slope, So = 0.005 and n = 0.018. Calculate the velocities, u at yvalues of 0.2, 0.
Tutorial 1 Concept of Boundary LayerVelocity Distribution
Q1. [=8.18 in Franzini & Finnemore] Water at 60 o C flows in a 15 mm diameter
copper tube (e = 0.0015 mm) at 0.06 L/s. Find the head loss per 10 m given f =
0.0304. What is the centerline velocity
Tutorial 5: Specific Energy (1) Critical Depth & Humps
Q1. Given b = 1.5 m, y = 0.6 m below sluice opening, and v = 4.5m/s
(a). Supposing the Sp E with y = 0.6m and v = 4.5m/s is the critical E, then
what is the corresponding yc?
i. e . E=Ec =0.6+
2E
4.52
Tutorial 3 Uniform Flow & Mannings Formula
Q1.
[= Q10.5] The crosssection of a portion of the Colorado River Aqueduct is trapezoidal in shape
and is designed to carry a discharge of 44 m 3/s. The base width of the trapezoidal canal is 6.1 m,
the side slo
Tutorial 2 Forces on Immersed Bodies
Q1. A small sphere with diameter of 6 mm is observed to fall through oil of
density 970 kg/m3 and a viscosity of 0.9 kg/ms, at a terminal velocity of 6 cm/s.
Compute the drag coefficient of the sphere in oil. Determine
Tutorial 6: Specific Energy (2) Humps, Depressions & Contractions
Q1.
[Q10.39] A rectangular channel 1.2 m wide carries 1.1 m3/s of water in uniform
flow at a depth of 0.85 m. If a bridge pier 0.3 m wide is placed in the middle of
the channel,
(a) Find th
Tutorial 6: Specific Energy (2) Humps, Depressions & Contractions
Q1.
Channel contraction only
(a) Given
b1 = 1.2 m, Q = 1.1 m3/s, y1 = 0.85 m
At pier location, b2 = b1 0.3 = 0.9 m
rect ch,
V 1=
Q
1.1
=
=1.078 m/ s
A 1 1.2 x 0.85
V 2=
Q
1.1
1.222
=
=
A 2
Fully developed Laminar Flow in Circular Pipes
p
du 2L
rdr
p 2
r C1
u
4 L
(3)
Find C1 using boundary condition, u = 0 (condition of
noslip) at r = D/2, and
pD 2
C1 and D = 2R where R = pipe radius
16L
2
pD
r
1
u r
16L R
2
(3) becomes,

Chapter 3 h Force System Resultants
31
Objectives
To di T discuss the concept of th moment of a f th t f the t f force and d show how to calculate it in two and three dimensions. To determine the moment of a force about an axis. To determine the moment o
Equilibrium of a Rigid Body
Chapter 4
4.1 4 1 Conditions for equilibrium
Recall that R ll th t Any system of external forces acting on a rigid body can be reduced to an equivalent forcecouple system at an arbitrary point O. For equilibrium the net force
Chapter 5 Structural Analysis
Objectives
To h T show how to determine the forces in the members of h t d t i th f i th b f a truss using the method of joints and the method of sections. To analyze the forces acting on the members of frames and machines co
Chapter 6 Geometric Properties and Distributed Loadings
Objectives
To di T discuss the concept of center of gravity and th t f t f it d centroid for a body of arbitrary shape. To show how to locate the centroid for a line an area or line, area, a volume.
Chapter 7 Internal Loadings
Objectives
To show how to use the method of sections for determining the internal loadings in a member To generalize this procedure by formulating equations that can be plotted so that they describe the internal shear and mome
Chapter 8 Stress and Strain
Objective
To introduce the concepts of normal and shear stresses, and to use them in the analysis and design of members subject to axial load and direct shear To define normal and shear strain, and show how they can be determin
Chapter 9 Mechanical Properties of Materials
Objective
To show how stress can be related to strain by using experimental methods to determine stressstrain diagram for a particular material To di T discuss the properties of the stressstrain diagram for
CV1012 Fluid Mechanics
Tutorial 6 Dimension Analysis
1.
The variation p of pressure in static liquids is known to depend on the density , gravity g,
and the elevation difference z. By examining their dimensions, determine the form of the
hydrostatic law o
CV1012 Fluid Mechanics
Tutorial 7 Similitude and model studies
1.
Assume that the flow rate per unit length q along a dam (see figure) depends on the
head H, width b, g, and , develop the general relationship for q in terms of suitable
Pi terms, using b,
CV1012 Fluid Mechanics
Tutorial 9 Pipe Flow (2)
1.
A 0.6 m diameter pipe with roughness = 3 mm carries a flow of 0.4 m 3/s between
two fixed levels. It is to be replaced by a smooth pipe of the same diameter. Estimate
the new flow rate.
Solution :
/D = 0.
CV1012 Fluid Mechanics
Tutorial 8 Pipe Flow (1)
1.
For steady laminar pipe flow:, if the centreline velocity in a 0.1 m diameter tube is 3
m/s, and the fluid has a density of 1260 kg/m 3 and viscosity of 0.9 N.s/m2, calculate
the Reynolds number and the p