Calculate required valve diameter (Darcy-Weisbach)

[Faustulus]

I am planning to custom build a water tank into which a household washer should discharge it's used water. I have estimated that a tank holding 60 ltrs would be sufficient. This quantity should be released into the building's drainage system within about an hour because the system is old and has difficulty handling surges. My own difficulty is with calculating the required valve diameter. The advice I need is like, "use a 1/4" ball valve (and open it about half)".
Presuming that the draining velocity would be greater with the tank full, my purposes would be served if I could guarantee a maximum discharge rate of near 1 ltr per minute. It doesn't really matter how long the tank takes to drain fully as long as it isn't slower than the washer releases water. According to my research the most water-inefficient washer would use about 50 ltrs per wash which, in my experience, would take about an hour.
Thanks for the help!
Faustulus

 

[SteamKing]

It seems like you are putting the cart before the horse. Most people would first figure out what size the washer's drain line is, and then pipe to suit. Once you know the size of the drain line, you then get the proper valve.

A drain rate of 1 L/min is pretty slow. It's also not clear what type of wash cycle you will typically use. A washing machine will initially fill when washing clothes, drain, and then repeat one or more times for the rinse cycle. Would a 60 L tank be sufficient for the most extended wash cycle?

If your building's drainage system has difficulty handling a washing machine, how does it handle shower/bath water?

 

[Faustulus]

Thank you for this quick response.
Here is more background:-
The building is an old high rise. They have the experience that the sudden surge of washer discharge causes water to back up on the first floor, suds as high as second. So, they bought washers for community use that discharge into a tank which drains more slowly. No calculations were made but the backup stopped.
After a major renovation I have undertaken I want a washer in my apartment. House rules don't allow that. The board has agreed, however, to let me install one if I can guarantee no back up. So, I am working on how to "guarantee".
I figure, if I use the same system they already have experience with (drain into a tank and release at a measured pace) and dazzle them with a scientific calculation they never did on what they have they will not find fault with it easily while I will be able to enjoy reasonable security from future complaints that my washer is causing suds to emerge two floors above ground level.
50 litres is the maximum a 7kg machine might use for all its washes and rinses. More modern machines (of which I am likely to get a sample) use as little as 20 ltrs to do the same job. I need to discharge this quantity (50 ltrs) not faster than the washer is draining it into the tank, I.e. within about an hour or 1 ltr per minute, give or take 20%.
Thank you for the time you take to help me out.
Faustulus

 

[Faustulus]

Bump ...

 

[gmax137]

If you arrange the tank drain to discharge into a sink or a floor drain then you can be sure the discharge pressure is atmospheric. The discharge velocity can then be found from the difference in potential (using (1/2)V^2=gh). Where h is the height of the tank water level above the drain. Using your desired flow rate, you can calculate the area since volumetric flow rate is A*V. The resistance from the pipe and valve will make the actual flow rate lower than what you calculate but that should be OK for what youre trying to achieve. If your drain pipe (from the tank to the sink) is long it might slow you down too much for repeated wash loads) and you would want more accurate predictions --then ask the question in the engineering section, or google (tank discharge rate) to get some more detailed approaches.

 

[Faustulus]

Thank you!
I found a calculator at efunda.com