how can the flow velocity in a sewage vertical stack be calculated ,while the flow dosenot fill the stack?

Question

i wounder if there is a limit for flow speed in a vertical pipe when the condition is not under pressure.

Answer 1

In the simpler case of when the pipe is filled ("fully submerged flow"), the limit would be when the piping loss pressure drop equals the force of gravity. e.g. 100 feet of vertical pipe with a flow rate such that the pressure drop is 100 feet of head (=100/2.31=43.3 psi). Which, eyeballing off a pressure-drop chart would be 1600 gpm in the 4" sewer pipe that leaves my house. That gives a "speed limit" of 40 feet per second in that pipe size.

For comparison, in 1/2" ID schedule 40 pipe, you reach 100 feet of head piping losses (per 100 feet of pipe) at about 11 gpm. A velocity of 12.5 feet per second.

In the other limiting case, you have a falling film on the inside of the pipe in which the frictional losses due to shear equal the gravitional force. And, for a thin film, you could work in x-y-z co-ordinates rather than cylinderical. From memory and experience, I'm going to guestimate a velocity of 5 feet per second for a 0.10 inch film.

In between those two limits, you could draw a line on the graph without an abrupt transition (it is all turbulent flow) Increasing film thickness leads to increasing speed, so it has a flow = (film thickness)^2 shape to it, or something close.

The very lower limit is set by surface tension. If there's not enough fluid going down the pipe to coat all the inside, it will travel in small streams that oscillate back and forth in the paths down the pipe wall.

Hope that helps.