Pipe Flow

[Blobajob88]

Hi,

I'm hoping someone can help me. According to Bernoulli's principle, when water is flowing through a pipe and the pipe restricts in some way, the velocity increases/pressure decreases through the restriction and then ramps back up to the velocity and pressure it was originally at once it gets through the restriction. My question is: Is this only applicable up to a certain point, for example if you're pumping say 20 m3/hr through a 2" pipe and the pipe then restricts to something minute, say 2mm, surely there will be a pressure build up?

 

[handleman]

Pressure in the 2" section will be greater than pressure in the 2mm section, yes.

 

[rb1957]

yes, what you're talking about is choked flow.

if the restriction is small, then the changes in flow properties is small, and everyone is quite happy.

if the restriction is large, and one question would be assuming incompressible fluid (like water) what is the flow rate in the restricted section for conservation of mass/volume ? is it supersonic ? how far does the fluid have to accelerate to this velocity. You will find that there is some restriction (%age of gross area) such that he fluid acannot be expected to pass the obstruction, and so the flow is "choked".

another day in paradise, or is paradise one day closer ?

 

[JStephen]

It "ramps back up to the velocity and pressure it was originally at once it gets through the restriction" for ideal frictionless flow. In real life, you have some flow losses associated with this, which may be large or small depending on the geometry involved. Check fluids textbook for more detail, possibly get info from manufacturers for flow through partially closed valves, etc.

 

[Blobajob88]

Hi,

I'm thinking if I had a pump that was pumping say 20m3/hr through a 4" pipe, i then implement some sort of restriction so that the pipe is now 2" at some point. My thinking is that the flow would remain 20 m3/hr at every point in the line because of the continuity equation and the pressure would reduce/velocity increase in the 2" section . But then say I continue to narrow the pipe, would it just continue to behave like this until there is no access through the pipe at all.

If I had a pump with a pressure gauge on the discharge side followed by an isolation valve, would you expect the pressure to only hike up when the valve was completely shut or would it hike up when it was say 95% shut?

When would choked flow occur. I've never actually heard of this expression

 

[rb1957]

"My thinking is …" not correct. The flow cannot instantaneously accelerate to the restricted flow speed. So what happens ?

assume the pipe flow is stablised in the 4" diameter pipe. Note, the flow is not uniform across the pipe, there is a low flow boundary layer; the "flow rate" we use is the average (as though the flow were uniform). Now somewhere down the pipe the pipe contracts to 2" diameter, so we'd expect the flow to increase 4 times. Let's assume that the fluid can accomplish this (maybe it's 1m/s in the 4" dia and 4m/s in the 2" dia). Now a good design would taper the pipe towards the contraction so the fluid would nicely and calmly accelerate. But say it's a sudden change. Then the fluid does change speed upstream of the obstruction (it cannot accelerate instantly) so that some fluid is flowing faster than the pipe geometry wants. What happens to the rest of the fluid (to maintain change volume flow) ? Turbulent eddies, back flow, etc. The fluid can sense the downstream obstruction (as a change in pressure).

google "choked flow" … it will happen if your 4" pipe closes down to 2mm; as you rightly feel, you can't stuff the (incompressible) fluid from a 4" dia pipe through a 2mm dia hole. As the flow accelerates, a shock (like a super sonic shock in air) will form and greatly restrict the flow (hence, choked). There si simply a step change in the fluid properties.

another day in paradise, or is paradise one day closer ?

 

[LittleInch]

Bernouillis principle ignores friction. Once you enter real life then friction impacts the results.

The losses going into and out of your 20mm to 2mm restriction impact the pressure losses even before you get to choked flow.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[racookpe1978]

The typical hyperdermic needle and syringe illustrate the principle each of the above writers has tried to teach you.

No restrictions, no reductions. Minor (but calculated) friction losses at the walls. Near-zero pressure differences (but again measureable pressure differences down the pipe. Move the push handle, the piston moves, the water moves out the end.

Smaller outlet, but a smooth transition from "big area to small area" like a fire hose nozzle and the small diameter perhaps about 50% of the original diameter. You have to push harder, the water flows out the nozzle much faster, flies through the air much further. But the same volume flows out as flows in, minus losses. The firemen have to work very hard to maintain their position and to keep the nozzle pointed the right direction. That "effort" IS the friction losses, the water pressure energy converted to kinetic energy.

Big hole in the end of the syringe, but a sharp transition. More friction losses at the orifice plate, about the same pressure upstream and downstream of the moving water. We use that pressure difference to (once calibrated) measure flow and velocity. Volume in = volume out.

Very little hole in the outlet. Your piston nearly stops: The outlet is choked off. The water cannot flow out as fast as it needs to, water back pressure against your hand increases substantially. Subsonic and sonic pressure waves go back through the fluid from the ends. Water (the medicine) does flow, but at small volumes and great speeds once it leaves the needle. An engine or pump piston, hitting a solid mass of oil or water or fuel in a confined piston space that cannot flow out fast enough, comes to a stop - which breaks the cylinder walls, the valves, the crankshaft, or the seals.

 

[MJCronin]

Second law of Thermodynamics ....

You cannot change between two forms of fluid energy without losing something !!!

(In this case it will be heat !!)

MJCronin
Sr. Process Engineer