I have searched the forums for this and while there are lots of postings (especially by Art), I couldn’t find any that would directly help me solve my problem. Hence, the post.
We have a vessel (open to atmosphere) which is used to throw seawater (at 25°C) overboard to the sea via a pipe from vessel bottom. The only driving force available is the static head which is about 10 m (ignoring the change in the level in the vessel which is relatively smaller). The equivalent length of the pipe is 100 m. I need to size the pipe so that the pipe runs full of water. I understand that for the pipe to run water full, or for 'self-venting' flow, the Froude number, v/(gD)0.5 < 0.3, where
v = velocity, m/s;
g = 9.81 m/s2 and
D = pipe ID , m
The way I am trying to do this, is as follows:
- Assume a pipe size
- Calculate the maximum flow possible with static head as the only available driving force (corresponding to 0.1 bar approx.)
- Use the velocity in the pipe obtained in Step 2 and the assumed size to calculate the Froude number. If it is less than 0.3 then the line size is adequate, else increase the line size and repeat the above steps.
The problem with the above is that as I increase the assumed line size, the calculated Froude number also goes up. Hence, there is no solution to the problem.
For example: for a 4” Schedule 40 pipe (102.3 mm ID), maximum flow possible is 99.6 m3/hr. The velocity is 3.37 m/s and the Froude number is 3.36.
For a 8” Schedule 40 pipe (202.7 mm ID) maximum possible flow is 600 m3/hr. The velocity is 5.16 m/s and the Froude number is 3.65.
I have assumed a density of 1,000 kg/m3 and viscosity of 1 cP for the above calculations. Moody friction factor of 0.015 has been used.
So it can be seen that the Froude number is increasing with size and there is no solution using this method.
My questions thus are:
a) Is my method correct? If yes then where is the mistake I am making?
b) If the method is incorrect how can the line be sized?
As a corollary, had this been a vertical pipe, the equivalent length being 10 m (assuming no fittings), the maximum possible flow in an 8" pipe is calculated to be 1,933 m3/hr !! Does this make sense? What would happen in a real life situation?
Thanks and Regards
Sanjay