Momentum theory

Ministry of Higher Education & Scientific Research
Foundation of Technical Education
Technical College of Basrah
CH6: Momentum Theory
Training Package
in
Fluid Mechanics
Modular unit 6
Momentum Theory
By
Risala A. Mohammed
M.Sc. Civil Engineering
Asst. Lect.
Environmental & Pollution Engineering Department
2011

1- Over view
1-1 Target population
For the students of second class in
Environmental engineering Department in
Technical College

1-2 Rationale
The study of momentum equation is
important in the calculation of the force that applied
on the pipe wall, this equation has widely use in fire
fighting system, steam boilers , nozzles and pipe
bends.

1-3 Central Idea
The main goal of this chapter is to know the
momentum theory and its application.

1-4 Instructions
1- Study over view thoroughly
2- Identify the goal of this modular unit
3- Do the Pretest and if you :-
*Get 9 or more you do not need to proceed
*Get less than 9 you have to study this modular
4- After studying the text of this modular unit , do the post test
and if you :-
*Get 9 or more , so go on studying modular unit seven
*Get less than 9 , go back and study the modular unit six

1-5 Performance Objectives
At the end of this modular unit the student will be able to :-
1. Explain the conservation of mass principle
2. Drive the linear momentum equation.
3. Calculate the force applied on pipe bends, reducers and
moving vanes due to the change of momentum of flow
per unit time in that direction( impulse).

2- Pre test
Q1)) ( 5 mark)
Referring to Fig. 23-9, a 2-in-diameter stream of water strikes a 4-ft-square door which is at
an angle of 30° with the stream's direction, The velocity of the water in the stream is 60.0 ft/s
and the jet strikes the door at its center of gravity. Neglecting friction, what normal force
applied at the edge of the door will maintain equilibrium?
Q2) ( 5 mark)
A jet of water with an area of 4 in2 and a velocity. of 175 fps strikes a single vane which
reverses it through 1000 without friction loss. Find the force exerted if the vane moves (8) in
the same direction as the jet with a velocity of 65 fps; (b) in a direction opposite to that of the
jet with a velocity of ,65 fps,
Not
Check your answers in key answer page

Conservation of Mass
 The conservation of mass relation for a closed system undergoing a
change is expressed as msys = constant or dmsys/dt= 0, which is a
statement of the obvious that the mass of the system remains constant
during a process.
 For a control volume (CV) or open system, mass balance is expressed
in the rate form as
 where min and mout are the total rates of mass flow into and out of the
control volume, respectively, and dmCV/dt is the rate of change of mass
within the control volume boundaries.
 In fluid mechanics, the conservation of mass relation written for a
differential control volume is usually called the continuity equation.

-
Conservation of Mass Principle
The conservation of mass principle for a control volume can be expressed as: The
net mass transfer to or from a control volume during a time interval t is equal to
the net change (increase or decrease) in the total mass within the control volume
during t. That is,
where ∆mCV= mfinal – minitial is the change in the mass of the control volume during the
process. It can also be expressed in rate form as

-
Impulse- momentum equation
Newton Second law:
the acceleration of a body is proportional to the net force acting on it and is inversely
proportional to its mass.
The impulse-momentum equation is one of the basic tools (other being continuity and
Bernoulli', equations) for the solution of flow problems. Its application leads to the solution of
problems in fluid mechanics which cannot be solved by energy principles alone. Sometimes it
is used in conjunction with the energy equation to obtain complete solution of engineering
problems.
The momentum equation is based on the law of conservation of momentum or momentum
principle which state as follows:
“the net force acting on amass of fluid is equal to change in momentum of flow per
unit time in that direction”

-
Applications of impulse-momentum equation
The impulse-momentum equation is used in the following types of problems:
1.To determine the resultant force acting on the boundary of flow passage by
a stream of fluid as the stream changes its direction, magnitude or both.
Problems of this type are:
(i) Pipe bends, (ii) Reducers (iii) Moving vanes, (iv) Jet propulsion. etc.
2.To determine the characteristic of flow when there is an abrupt change of
flow section.
Problems of this type are:
i) Sudden enlargement ii) Hydraulic jump in channel

-
Steady flow momentum equation
The entire flow space may be considered to be made up of innumerable stream tubes. Let us
consider one such stream tube lying in the X- Y plane and having steady flow of fluid. Flow can be
assumed to the uniform and normal to the inlet and outlet areas.
Let, V1,P1 = Average velocity and density (of fluid mass) respectively at the entrance
And
V2,P2=Average velocity and density respectively at the exit.
Further let the mass of fluid in the region 1 234
shifts to new position r 2' 3' 4' due to the effect
of external forces on the stream after a short
interval. Due to gradual increase in the flow area
in the direction of flow, velocity of fluid mass
and hence the: momentum is gradually reduced.
Since the area. I' 2' 3 4 is common to both the
regions 1 2 3 4 and I' 2' 3' 4' therefore, it will not
experience any change in momentum. Obviously,
then the changes in momentum of the fluid
masses in the sections 1 2 2' l' and 43 3' 4' will
have to be considered

-
Steady flow momentum equation

Example(1)

Example(2)

Example(3)

Example( 4)

Example (5)

Example(5)

Example(6)

Post test
Q1)) ( 5 mark)
A Fig. shown a curved pipe section of length 40 ft that is attached to the straight pipe section as
shown. Determine the resultant force on the curved pipe, and find the horizontal component of the
jet reaction. All significant data are given in the figure. Assume an ideal liquid with g = 551b/ft3.
Q2)) ( 5 mark)
In a 45° bend a rectangular air duct of I m2 cross-sectional area is gradually reduced to 0.5 m2
area. Find the magnitude and direction of force required to hold the duct in position if the
velocity of low at 1 m2 section is 10 ms, and pressure is 30kNlm2.Take the specific of air as 0.0116
kNlm3

Key answer
Pre test
))
1
Q
))
2
Q

Key answer
Post test
))
1
Q

Key answer

Key answer
Q2

Post test

References
CH1: Fluid Properties
1. Evett, J., B. and Liu, C. 1989 “2500 solved problems in fluid mechanics and
hydraulics” Library of Congress Cataloging- in-Publication Data, (Schaum's
solved problems series) ISBN 0-07-019783-0
2. Rajput, R.,K. 2000 “ A Text Book of Fluid Mechanics and Hydraulic
Machines”. S.Chand & Company LTD.
3. White, F., M. 2000 “ Fluid Mechanics”. McGraw-Hill Series in Mechanical
Engineering.
4. Wily, S., 1983 “ Fluid Mechanics”. McGraw-Hill Series in Mechanical
Engineering.

Momentum theory

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Momentum theory

Similar to Momentum theory (20)

More from Dr.Risalah A. Mohammed

More from Dr.Risalah A. Mohammed (9)

Recently uploaded

Recently uploaded (20)

Momentum theory