Flow through conduits is important to understanding engineering structures, like pipes or culverts, and it is also relevant to flow through pores in rock or soil. Flow through conduits has been investigated extensively and is the topic of entire courses in fluid mechanics. A nice summary of flow through pipes is available here.

http://www.cora.nwra.com/~werne/eos/images/laminar.jpg

Laminar flow from a faucet.

Fracture enlarged by dissolution in limestone, Cumberland Co. , PA. Viewed in the wall of a boring.

http://www.cora.nwra.com/~werne/eos/images/laminar.jpg
http://water.usgs.gov/ogw/karst/img/features/valleyridge/frac287h_small.jpg

Objective: The objective of this exercise is to set up an analysis of laminar flow through a conduit formed from two parallel plates with rough features on the walls, and then conduct numerical experiments to learn about flow through conduits.

Assume the plates are 0.01 m apart and 0.1m long, and that water flows between them at an average velocity of 0.001m/s You want to answer the following questions:

1. Entrance Effects How do the velocity and shear stress profiles develop in a downstream direction from the entrance of the plates? How far from the entrance do the velocity and shear stress profiles stabilize? How do the stabilized profiles compare to the expected profiles? What is the effect of changing the flow velocity on these results?

Video describing analysis of entrance effects

Development of a boundary layer and transition from laminar to turbulent conditions near the entrance of a conduit.

2. Pressure Drop How does the velocity of flow affect the pressure drop or pressure gradient during flow in a conduit form by parallel plates? How does the fluid viscosity affect the pressure drop (at a fixed flow rate)?

Video describing analysis of pressure drop

3. Geometry of wall roughness. What happens if there is a semi-circular protrusion, or bump, on the wall of the conduit? How does the bump affect the relationship between pressure drop and flow velocity?

Video describing analysis of flow past a wall protrusion