Lecture 03 Flashcards
How do you describe the performance of a pipe?
Head loss
What makes head loss a useful gauge for describing the performance of a pipe versus using something like pressure difference?
Head loss does not change with relation to the fluid flowing through the pipe. The equation does not have a density or a viscosity term.
What are the two regions of flow within a pipe?
Entry region (we won’t deal with much in this class) and the region of fully-developed flow.
What is the “no-slip condition” of fluids?
The velocity of a fluid at the boundary is zero (relative to the boundary), but at some height from the boundary the flow speed must equal the speed of the fluid.
What is the difference between flow in the entry region and flow in the fully-developed region?
In the entry region, the flow at a given point depends on both x and r. In the fully developed region, it depends only on r. The velocity profile will remain the same as you move in the x-direction. (partial u with respect to x equals zero). There is higher shear stress at the boundary within the entrance region which means more losses.
What is the length of the entry region called?
Hydrodynamic entrance length. Most people just call it the entrance length.
What is the equation for shear stress on the boundary of a pipe using viscosity and velocity?
Tau=mu*(partial u with respect to y). Mu is viscosity, u is the velocity of the fluid along the boundary, y is the height above the boundary. The higher the slope of the velocity profile at the wall, the higher the shear stress.
When can you sometimes ignore the entrance region?
If you have a really long pipe. We often see this case.
What is the equation for the entrance length for laminar flow? How about for turbulent flow?
LsubH,LAMINAR is approximately .05(Re)*D.
LsubH,TURBULENT is approximately 1.359(Re^1.4)D.
For which type of flow does the entrance length rely more on the Reynolds number?
Laminar. Turbulent flow only relies on the Reynolds number to the 1/4 power.
What is the maximum entrance length for laminar flow?
The Reynolds number would have to be 2300, which means the entrance length would be 115*D.
In practice, what equation do we use to estimate the entrance length for turbulent flow?
LsubH,TURB=10D
How does the pressure gradient vary in the x direction for laminar flow through a pipe?
The pressure gradient varies constantly, meaning there is a linear relationship. If we know the pressure at two points in the flow, we know the pressure everywhere.
What is the equation for the relationship between velocity profile and pressure gradient for laminar flow through a pipe? How can we use this in the lab to get valuable data?
(mu/r)*d/dr(rdu/dr)=dP/dx.
It’s easy to find the pressure gradient by just finding the pressure at any two points in the flow. Then, you can integrate the left hand side of the equation to get the velocity profile. Once we have that we know the velocity gradient at the wall (du/dy). Then we can get the shear stress and thus the pressure loss.
What is the equation for the velocity profile once the left side of the previous equation is integrated? What type of curve does this create?
u(r)=(r^2)/(4mu)[1-(r^2)/R^2)]
Parabolic curve.
