Hello,
We have a pipe running a vacuum with a hole. The hole is purposefully placed there for testing purposes, using a ball valve connecting to the pipe with the vacuum. Mass flow rate is known for the air coming through the ball valve. Vacuum is also known inside the pipe. This is a closed system with a pump providing the vacuum. Size of hole and velocity through the hole would therefore be unknown. The purpose of this is to estimate size of a hole in the case a customer had a leak. Could bernoulli’s equation be used to estimate the size of the leak?
Assuming a thin, square-edged orifice, if the upstream pressure is more than 1.893 times the downstream pressure, you’ll have something closely approaching choked flow, in which case the flow rate will be mostly dependent on the upstream pressure/temperature (and orifice size). So if you’re talking about atmospheric pressure upstream and hard vacuum downstream (inside the pipe), then Bernoulli’s equation isn’t going to be useful.
Although your particular situation won’t be true choked flow, I suspect the equations they give for choked flow on that page will probably enable a better estimate of hole size than Bernoulli.
Thank you for the reply, been busy have not had time to look at this. So this would be a closer estimate than bernoulli’s.
The article says this for vacuum cases, “In the case of upstream air pressure at atmospheric pressure and vacuum conditions downstream of an orifice, both the air velocity and the mass flow rate becomes choked or limited when sonic velocity is reached through the orifice.”
I believe you did mention this in your post somewhat though.
In the case of the Cd coefficient, would 1 be a best estimate since we are simulating a hole in a pipe?
Thanks!
There’s a lot of uncertainty here. According to this, Cd for a sharp-edged orifice is around 0.6-0.63, but this makes an assumption about the geometry of the leak in your customer’s piping (is it a clean, round, sharp-edged hole? Is it a gash? was material serendipitously displaced to form a sort of nozzle?).
If all you’re after is a very coarse estimate of the size of a customer’s leak, then 0.6 seems like a reasonable guess. If you keep records of the size of the actual leak, then after a number of service calls investigating multiple leaks, you could develop your own best-fit Cd that would give you better estimates in the future.