Hagen–Poiseuille flow from the Navier–Stokes equations

Hagen–Poiseuille Flow From The Navier–Stokes Equations

Hagen–Poiseuille flow from the Navier–Stokes equations

to get instant updates about 'Hagen–Poiseuille Flow From The Navier–Stokes Equations' on your MyPage. Meet other similar minded people. Its Free!


All Updates

In fluid dynamics, the derivation of the Hagen–Poiseuille flow from the Navier–Stokes equations shows how this flow is an exact solution to the Navier–Stokes equations.


The flow of fluid through a pipe of uniform (circular) cross-section is known as Hagen–Poiseuille flow. The equations governing the Hagen–Poiseuille flow can be derived directly from the Navier–Stokes equation in cylindrical coordinates by making the following set of assumptions:

  1. The flow is steady ( <math> partial(...)/partial t = 0 </math> ).
  2. The radial and swirl components of the fluid velocity are zero ( <math> u_r = u_theta = 0 </math> ).
  3. The flow is axisymmetric ( <math> partial(...)/partial theta = 0 </math> ) and fully developed (<math> partial u_z/partial z = 0 </math> ).

Then the second of the three Navier–Stokes momentum equations and the continuity equation are identically satisfied. The first momentum equation reduces to <math> partial p/partial r = 0 </math>, i.e., the pressure <math> p </math> is a function of the axial coordinate <math> z </math> only. The third momentum equation reduces to:

<math> fracfracleft(r fracright)= frac frac</math> where <math>mu</math> is the dynamic viscocity of the fluid.
The solution is
<math> u_z = frac fracr^2 + c_1 ln r + c_2......

Read More

No feeds found

wait Posting your question. Please wait!...

No updates available.
No messages found
Suggested Pages
Tell your friends >
about this page
 Create a new Page
for companies, colleges, celebrities or anything you like.Get updates on MyPage.
Create a new Page
 Find your friends
  Find friends on MyPage from