NPTEL Course Developer for Fluid Mechanics
Module 04; Lecture 22
Dr. Niranjan Sahoo
IIT-Guwahati
DYMAMICS OF FLUID FLOW
Energy Equation (Conservation of Energy)
In words, the conservation of energy can be stated as,
Time rate of increase in stored energy
1
Ministry of Science and Technology
Department of Technical and Vocational Education
Department of Civil Engineering
CE 2016 Fluid Mechanics
Problems and Solutions
(for Second Semester)
A.G.T.I , Year II
2
1. A venturimeter with a 15cm diameter at inlet
MINISTRY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF TECHNICAL AND VOCATIONAL EDUCATION
GOVERNMNT TECHNOLOGICAL COLLEGF
Second Year A.G.T.I (Mining) Sample Answer
Date: 21-9-06
Final Examination
Time: 8:30 to 11:30
Min-02034 Fluid Mechanics
= =
Q1. A horizont
Fluid Flow
Course No: M06-001
Credit: 6 PDH
Elie Tawil, P.E., LEED AP
Continuing Education and Development, Inc.
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Stony Point, NY 10980
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DOE-HDBK-1012/3-92
JUNE 1992
DOE FUND
Energy Conservation (Bernoullis Equation)
Recall Eulers equation:
dp
+ VdV + gdz = 0
Also recall that viscous forces were neglected, i.e. flow is invisicd
If one integrates Eulers eqn. along a streamline, between two points , &
We get :
2
1
2
dp 2
+ VdV +
Recap: Bernoullis Principle
The sum of pressure plus kinetic energy per unit
volume of a flowing fluid is constant.
P + v2 = constant
pressure
K.E. per unit volume
mass
( = vol )
Result: Relates pressure variations to changes in fluid speed.
Example:
P1
f
Babylon University
College of Engineering
Enviromential Engineering Department
Subject:Water Resourses Engineering
Dr: Naba Shakir Hadi
The Best Hydraulic Section:
It is known that the coneyance of achannel section increase with increase in the
hydraulic
CHAPTER 10. OPEN CHANNEL FLOW
EXAMPLE 1
Example 1. Water flows in a rectangular channel at a depth of 4.0
ft and a flow rate of Q = 200 cfs. Determine the minimum
channel width if the flow is to be subcritical.
V
Q 200 ft 3 / s 50
b width feet and V ft /
Chapter 15
VARIED FLOW IN OPEN
CHANNELS
Fluid Mechanics, Spring Term 2009
Open Channels vs. Closed Conduits
In a closed conduit
there can be a pressure
gradient that drives the
flow.
An open channel has
atmospheric pressure
at the surface.
The HGL is t
VVR 120 Fluid Mechanics
VVR
11. Basic equations VI (4.5-4.6)
Applications momentum equation
Exercises: C54 and C64
VVR 120 Fluid Mechanics
VVR
Example pipe bend. When 300 l/s of water flow through this vertical
300 by 200 mm pipe bend, the pressure at th
VVR 120 Fluid mechanics
VVR
12. Summary 1-11, written test 1
Repetition of hydrostatics and basic equations
Solving typical exam problems (problem 2, 5, 8, and 11
from homepage)
VVR 120 Fluid mechanics
VVR
6. The half sphere container in the figure is fil
VVR 120 Fluid Mechanics
VVR
20. Channel flow II (8.68.9)
Specific energy
Critical depth
Froudes number
Critical section
Exercises: E9, E12, E16, and E21
VVR 120 Fluid Mechanics
VVR
Specific energy, E
Specific energy, E, is important for channel flow.
734
Solutions Manual Fluid Mechanics, Seventh Edition
10.3 Narragansett Bay is approximately 21 (statute) mi long and has an average depth of
42 ft. Tidal charts for the area indicate a time delay of 30 min between high tide at the
mouth of the bay (Newpo
MINISTRY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF TECHNICAL AND VOCATIONAL EDUCATION
GOVERNMNT TECHNOLOGICAL COLLEGF
Second Year A.G.T.I (Mining) Sample Answer
Date: 21-9-06
Final Examination
Time: 8:30 to 11:30
Min-02034 Fluid Mechanics
= =
Q1. A horizont
Chapter 9
Steady Flow in Open channels
Objectives
Be able to define uniform open channel flow
Solve uniform open channel flow using the
Manning Equation
9.1 Uniform Flow in Open Channel
Open-channel flows are
characterized by the presence of
a liquid-gas
CEE 3500 Fall 2005 Final Exam
Name: _ Code: _
_
Enter your answer in this answer sheet by CIRCLING the correct answer. DO NOT FILL the circle.
Turn in the answer sheet only. You can keep the rest of the exam.
_
ANSWER SHEET
_
[1]
(a)
(b)
(c)
(d)
[15]
(a)
2nd Civil Engineering
Hydraulics
2012/2013
AIN SHAMS UNIVERSITY
Faculty of Engineering
Dept. of Irrigation & Hydraulics
ASSIGNMENT NO. 5
Gradually Varied Flow
1)
A rectangular channel 4.0 m wide has a Mannings coefficient of 0. 025. For discharge of 6.0 m
Name_
CEE 332 Hydraulic Engineering: Practice Prelim 2 solution
April 18, 2003 - 2:30-4:30 PM
Closed book, two 8.5 x 11 summary sheets
Note: The last page of this exam is an equation sheet!
Read each problem carefully before beginning to work on the answe
1.060 Engineering Mechanics I I
Spring 2006
Problem Set 8
Due on Monday, May 1st
Important note: Please start a new sheet of paper for each problem in the problem
set. Write the names of the group members who contributed to the solution at the
beginning o
Water Resources Engineering CEE 342
Homework
HW #1 due Jan. 26
2.8.5 The hypothetical velocity distribution in a horizontal, rectangular open channel is V=0.3y (m/s),
where V is the velocity at a distance y (m) from the bottom of the channel. If the verti
Hydraulic Jump
Hydraulic jump can be seen downstream of a spillway during the
release of water in reservoir.
Concrete
bed
Strong velocity
Severe bed erosion
Sand bed
Concrete
bed
Hydraulic
jump
Weak velocity due
to hydraulic jump
Sand bed
1. Measure flow
11. Open Channel Flow Contd
11.5 Hydraulic Jump
A hydraulic jump occurs when water in an open channel is flowing supercritical and is
slowed by a deepening of the channel or obstruction in the channel. The slowing causes the
water to suddenly jump to the
Computation of Uniform Flow
Hydromechanics VVR090
Computation of Uniform Flow
Mannings equation for velocity:
u=
1 2/3
R
S
n
Uniform flow rate:
Q = uA =
1
AR 2 / 3 S
n
Section factor:
AR 2 / 3
Conveyance:
K=
(increases with depth)
1
AR 2 / 3
n
1
Example 5
CHAPTER FIVE
CHAPTER
PRINCIPLES OF OPEN
CHANNEL FLOW
5.1 FUNDAMENTAL
EQUATIONS OF FLOW
EQUATIONS
5.1.1
Continuity Equation
Inflow = Outflow
Area; A1 and A2 and
Velocity; V1 and
V2
Area
x Velocity (A . V) = Discharge, Q
ie. A1 V1 = A2 V2 = Q
5.1.2
5.1.
1
Fundamentals of
open-channel flow
Open channels are natural or manmade conveyance structures that normally
have an open top, and they include rivers, streams and estuaries. An important
characteristic of open-channel flow is that it has a free surface a