![Page 1: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/1.jpg)
Fluid Mechanics-61341
An-Najah National UniversityCollege of Engineering
Chapter [6]
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle Dr. Sameer Shadeed1
Dr. Sameer Shadeed
Chapter [6]
Momentum Principle
![Page 2: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/2.jpg)
Momentum
MomentumMomentum = Mass X Velocity
Momentum Momentum can be linear or angular
Linear:Linear: deals with issues such as collisionsLinear:Linear: deals with issues such as collisions
Angular:Angular: due to rotation of planet
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle2 Dr. Sameer Shadeed
![Page 3: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/3.jpg)
Linear Momentum
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle3 Dr. Sameer Shadeed
![Page 4: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/4.jpg)
Newton’s 2nd Law2nd Law:
Definition of linear momentumlinear momentum:
or
Linear Momentum
Conservation of momentummomentum:
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle4 Dr. Sameer Shadeed
![Page 5: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/5.jpg)
Conservation of Momentum
The conservationconservation ofof linearlinear momentummomentum principleprincipletells us: If a system is isolated, its total linearmomentum does not change
Particles move about in a box: No particles leave orenter, hence the box is a system
Particles can exchange momentum with each other, but that does not affect the total momentum of the system
The only way to change the total momentum is to apply a force to the box
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle5 Dr. Sameer Shadeed
![Page 6: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/6.jpg)
Therefore:
Conservation of Momentum
Notice the similarities and differences betweenconservation of mass and momentum:
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle6 Dr. Sameer Shadeed
(conservation of mass)
(conservation of momentum)
Both equations are applied to the system MassMass is conserved absolutely; MomentumMomentum is conserved
unless a force is applied
![Page 7: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/7.jpg)
Momentum Equation
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle7 Dr. Sameer Shadeed
![Page 8: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/8.jpg)
Momentum Equation
To summarize, we can say , in general in general , that
Rate of change ofmomentum in the givendirection of the fluid passingthrough the control volume
Total force exertedon the fluid in acontrol volume ina given direction
=
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle8 Dr. Sameer Shadeed
through the control volumea given direction=
![Page 9: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/9.jpg)
Pipe Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle9 Dr. Sameer Shadeed
![Page 10: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/10.jpg)
Pipe Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle10 Dr. Sameer Shadeed
![Page 11: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/11.jpg)
Pipe Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle11 Dr. Sameer Shadeed
![Page 12: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/12.jpg)
Pipe Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle12 Dr. Sameer Shadeed
![Page 13: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/13.jpg)
Example 1
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle13 Dr. Sameer Shadeed
![Page 14: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/14.jpg)
Example 1 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle14 Dr. Sameer Shadeed
![Page 15: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/15.jpg)
Example 1 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle15 Dr. Sameer Shadeed
![Page 16: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/16.jpg)
Example 1 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle16 Dr. Sameer Shadeed
![Page 17: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/17.jpg)
Example 1 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle17 Dr. Sameer Shadeed
![Page 18: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/18.jpg)
Example 1 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle18 Dr. Sameer Shadeed
![Page 19: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/19.jpg)
Pipe Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle19 Dr. Sameer Shadeed
![Page 20: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/20.jpg)
Pipe Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle20 Dr. Sameer Shadeed
![Page 21: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/21.jpg)
Pipe Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle21 Dr. Sameer Shadeed
![Page 22: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/22.jpg)
Example 2
Upstream from an axisymmetric abrupt enlargement ina horizontal passage the mean pressure is 140 kPa andthe diameter is 150 mm. Downstream from theenlargement the mean pressure is 210 kPa and thediameter is 300 mm. Estimate the flowrate through thepassage and the force on the enlargement
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle22 Dr. Sameer Shadeed
passage and the force on the enlargement
![Page 23: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/23.jpg)
Example 2 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle23 Dr. Sameer Shadeed
![Page 24: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/24.jpg)
Example 2 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle24 Dr. Sameer Shadeed
![Page 25: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/25.jpg)
Open Channel Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle25 Dr. Sameer Shadeed
![Page 26: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/26.jpg)
Open Channel Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle26 Dr. Sameer Shadeed
![Page 27: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/27.jpg)
Open Channel Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle27 Dr. Sameer Shadeed
![Page 28: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/28.jpg)
Example 3
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle28 Dr. Sameer Shadeed
![Page 29: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/29.jpg)
Example 3 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle29 Dr. Sameer Shadeed
![Page 30: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/30.jpg)
Example 3 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle30 Dr. Sameer Shadeed
![Page 31: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/31.jpg)
Open Channel Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle31 Dr. Sameer Shadeed
![Page 32: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/32.jpg)
Open Channel Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle32 Dr. Sameer Shadeed
![Page 33: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/33.jpg)
Open Channel Flow Application
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle33 Dr. Sameer Shadeed
![Page 34: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/34.jpg)
Example 4
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle34 Dr. Sameer Shadeed
![Page 35: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/35.jpg)
Example 4 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle35 Dr. Sameer Shadeed
![Page 36: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/36.jpg)
Example 4 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle36 Dr. Sameer Shadeed
![Page 37: Fluid Mechanics-61341 - An-Najah Videosvideos.najah.edu/sites/default/files/Chp-6.pdfdirection of the fluid passing through the control volume Total force exerted on the fluid in a](https://reader033.vdocuments.net/reader033/viewer/2022043000/5f74c34ddeb32b540545b013/html5/thumbnails/37.jpg)
Example 4 (Solution)
Fluid Mechanics-2nd Semester 2010- [6] Momentum Principle37 Dr. Sameer Shadeed