The Bernoulli equation is the one to use in this case. It is:
Where P=pressure, p=density, V=velocity, g=gravity and Z=height. We take two points, the top of the reseverior (1) and the front of the water torrent (2), and set them equal to each other:
We assume that P[sub]1[/sub]=P[sub]2[/sub]=Patm becuase both ends are open to air. V[sub]2[/sub] for a large resevoir is negligable and taken to be 0. Z[sub]1[/sub] is taken to be the reference level, and is 0. That gets us:
Solving for V[sub]1[/sub] yields:
Plugging in numbers gets V[sub]1[/sub]=36mph, which mostly agrees with RaftPeople’s number, with the error due to the fact that s/he rounded during the calculation. The Bernoulli equation assumes four things:
[li]Viscous effects are negligible[/li][li]The flow is steady[/li][li]The flow is incompressible[/li][li]The equation is applicale along a streamline[/li][/ol]
2,3 and 4 apply in this situation, but 1 does not. However, all viscous effects due are add in energy losses, and slow the flow. That means 36 mph is theoretically the fastest possible flow in this case. The actual flow will be less due to losses.
For shits and giggles, the two loss modes in this sort of flow are termed “major”, and “minor” losses. The major loss is from viscous effects and the interaction of the flow and the walls of the pipe. The minor loss is due to changes in geometry, in this case from the reseveroir to the pipe. Its important to note that “major”, and “minor” do not necessarily reflect the magnitude of the effect on the flow. In other words, in some cases the “major” loss might be much less than the “minor” loss. The values of the two losses are:
Where f=friction factor, l=length of pipe, d=diameter, V=average velocity and g=gravity. The friction factor depends on the roughness of the pipe, the diameter, and another variable called the Reynolds number. Its values range from roughly .008 to .01.
Where V=velocity at the pipe entrance, g=gravity and a constant K[sub]L[/sub] that depends on how the pipe connects to the resevoir and range from .004 to .8.