Kiril

08-03-2008, 12:20 PM

Here are some of the more important fundamental equations and concepts involved in determining flow of fluids.

Most links and all images are from Wiki since their reviews are an acceptable place to start.

No smoke and screens here .... do what you want with the information.

--------------------------

1) Conservation of mass (http://www.grc.nasa.gov/WWW/K-12/airplane/mass.html) with respect to fluid dynamics (derived from Newton's second law of motion (http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newton.27s_second_law:_law_of_resultant_force))

Vol = A * V * t (where A = area, V = velocity, t = time)

2) Bernoulli's principle (http://en.wikipedia.org/wiki/Bernoulli%27s_principle): states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's gravitational potential energy

http://upload.wikimedia.org/math/8/2/c/82cf4ee7e0214e063ea7d24787380f8a.png

3) Navier-Stokes equations (http://en.wikipedia.org/wiki/Navier-Stokes_equations): describe the motion of viscous fluid substances such as liquids and gases.

The following equation is for incompressible flow of Newtonian fluids.

http://upload.wikimedia.org/math/e/e/7/ee73880cc2f0c808e400e1a1b8c7af16.png

4) Hagen-Poiseuille Equation (http://en.wikipedia.org/wiki/Hagen-Poiseuille_equation): describes slow viscous incompressible flow through a constant circular cross-section

http://upload.wikimedia.org/math/d/7/f/d7fc954111a08e3140b5005f6014bd32.png

5) Darcy-Weisbach Equation (http://en.wikipedia.org/wiki/Darcy-Weisbach_equation): relates the head loss or pressure loss due to friction along a given length of pipe to the average velocity of the fluid flow

http://upload.wikimedia.org/math/7/a/f/7af950f7beab571d965664814e631651.png (pressure loss equation)

6) Reynolds Number (http://en.wikipedia.org/wiki/Reynolds_number): ratio of inertial forces to viscous forces

http://upload.wikimedia.org/math/7/8/c/78cb2ea95968e955277b8dc8c7cc3f89.png

secondary reference (http://quest.arc.nasa.gov/aero/teachers/windtunnels.html) given citation note on Wiki

7) Colebrook-White equation (http://en.wikipedia.org/wiki/Colebrook_equation#Colebrook_Equation): used to iteratively solve for the Darcy-Weisbach friction factor f

http://upload.wikimedia.org/math/4/f/0/4f0bd264f60d9c9d040c95349c00e305.png

8) Moody Diagram (http://en.wikipedia.org/wiki/Moody_chart): relates the Friction factor, Reynolds number and relative roughness for fully developed pipe flow in a circular pipe. It can be used for working out pressure drop or flow rate down such a pipe.

http://upload.wikimedia.org/wikipedia/en/thumb/8/80/Moody_diagram.jpg/800px-Moody_diagram.jpg

Most links and all images are from Wiki since their reviews are an acceptable place to start.

No smoke and screens here .... do what you want with the information.

--------------------------

1) Conservation of mass (http://www.grc.nasa.gov/WWW/K-12/airplane/mass.html) with respect to fluid dynamics (derived from Newton's second law of motion (http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newton.27s_second_law:_law_of_resultant_force))

Vol = A * V * t (where A = area, V = velocity, t = time)

2) Bernoulli's principle (http://en.wikipedia.org/wiki/Bernoulli%27s_principle): states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's gravitational potential energy

http://upload.wikimedia.org/math/8/2/c/82cf4ee7e0214e063ea7d24787380f8a.png

3) Navier-Stokes equations (http://en.wikipedia.org/wiki/Navier-Stokes_equations): describe the motion of viscous fluid substances such as liquids and gases.

The following equation is for incompressible flow of Newtonian fluids.

http://upload.wikimedia.org/math/e/e/7/ee73880cc2f0c808e400e1a1b8c7af16.png

4) Hagen-Poiseuille Equation (http://en.wikipedia.org/wiki/Hagen-Poiseuille_equation): describes slow viscous incompressible flow through a constant circular cross-section

http://upload.wikimedia.org/math/d/7/f/d7fc954111a08e3140b5005f6014bd32.png

5) Darcy-Weisbach Equation (http://en.wikipedia.org/wiki/Darcy-Weisbach_equation): relates the head loss or pressure loss due to friction along a given length of pipe to the average velocity of the fluid flow

http://upload.wikimedia.org/math/7/a/f/7af950f7beab571d965664814e631651.png (pressure loss equation)

6) Reynolds Number (http://en.wikipedia.org/wiki/Reynolds_number): ratio of inertial forces to viscous forces

http://upload.wikimedia.org/math/7/8/c/78cb2ea95968e955277b8dc8c7cc3f89.png

secondary reference (http://quest.arc.nasa.gov/aero/teachers/windtunnels.html) given citation note on Wiki

7) Colebrook-White equation (http://en.wikipedia.org/wiki/Colebrook_equation#Colebrook_Equation): used to iteratively solve for the Darcy-Weisbach friction factor f

http://upload.wikimedia.org/math/4/f/0/4f0bd264f60d9c9d040c95349c00e305.png

8) Moody Diagram (http://en.wikipedia.org/wiki/Moody_chart): relates the Friction factor, Reynolds number and relative roughness for fully developed pipe flow in a circular pipe. It can be used for working out pressure drop or flow rate down such a pipe.

http://upload.wikimedia.org/wikipedia/en/thumb/8/80/Moody_diagram.jpg/800px-Moody_diagram.jpg