Ejection speed and travel distance of a ball in a pressurized water pipe

[Cannonball77]

Diameter of metallic ball : 3.000 inches
SG of ball is : 2
ID of pipe is : 4.05 inches
ID of seat : 2.885 inches
Pressure behind ball when released from seat #1 is 1100 psi
Fluid in pipe is Seawater (above and below the ball)
Fluid flow rate after ball is released is 800 litres pr minute
The pipe is horizontal and made of carbon steel
Distance from Seat 1 to seat 2 in pipe is 110 feet.

 

[Baluncore]

Welcome to PF.

When the ball lands in the seat it will have a moving column of water behind it that is 4” diameter and at least 110 feet long. That will be a critical situation as the ball may be forced through the seat or the pipeline may split. Where will that pressure spike go while the water is decelerating. You effectively have a ram pump, but with nowhere for the water column to go.

 

[anorlunda]

@Baluncore identified the critical problem. Here are some pictures of the possible result; water hammer damage.

 

[Cannonball77]

Some additional information. The pipe system is able to hold significant pressure (10.000 psi), there is an injection point dowstream of seat #2 to allow injection in the first place, then there is a relief valve above seat # 1 that will bleed off pressure in excess of 5000 psi. Seat # 1 will release the ball as soon as there is 1100 psi pressure increase behind it, and the challenge is to understand the speed of the ball as it is released from seat #1 and the speed and impact of it when landing on seat #2 which is 110 feet below.

 

[anorlunda]

So the 110 feet is vertical?

Does the ball free-fall in air or does it follow the front of the water moving behind it at 800 litres pr minute? I guess that is the same as asking what it in the volume between seats before release of the ball from seat 1; water or air?

there is an injection point dowstream of seat #2 to allow injection in the first place

injection of what? Do you fill the pipe with water from that injection point? If so, where does the displaced air go?

Is this a school project?

 

[Baluncore]

If the pipeline is horizontal, how can there be an up and a down ?
Which side of which seat, seats the ball ?
I think we need a diagram of the system before we try to compute anything.
That needs to show the detail of the various pressure relief valves and seats.

 

[hutchphd]

The flow rate (according to you) is 800L/min after release. The pipe holds ~8L/m so the flow speed is 100m/min=1.6m/s. Isn't that then the impact speed of the ball+water column into the second valve seat? So you have a column of at least 250kg of water moving at 1.6m/s

How does one model the closure? I would think the presence of any bubbles in the water column will greatly affect he pressure profile etc etc. Beyond me.`

 

[Cannonball77]

The pipe is horizontal and always fluid filled (no air bubbles). The hydrostatic pressure in the pipe is around 3000 psi. Flow rate is constant @ 800l/m and exits the pipe into the reservoir below Seat #2. Seat #1 is upstream from seat #2 (110 feet distance between them).

When the ball is launched in the pipe it will travel with the flow at about 800 l/m (slight fluid bypass around the ball due to ball OD being 3" and pipe ID being 4") towards seat #1. However, when the ball lands on seat #1 pressure will build as fluid is compressed behind it (we continue pumping at 800 l/m) until we have 1100 psi higher pressure above the ball than below. Seeing the 1100 psi differential pressure Seat #1 will yield and the pressure release (in addition to the 800 l/m flow) will shoot the ball towards Seat # 2. Flowrate in the pumps are always 800 l/m, but trying to understand the effect/speed of the ball releasing from seat #1 with 1100 psi behind it and expected travel time to reach seat #2.

 

[Baluncore]

Flowrate in the pumps are always 800 l/m, but trying to understand the effect/speed of the ball releasing from seat #1 with 1100 psi behind it and expected travel time to reach seat #2.

Water is flowing continuously along the pipeline at 800 litre/min ≈ 1.6 m/s (thanks hutchphd).

At the instant the ball closes flow at seat #1, differential pressure will rise immediately to the 1100 psi pressure that will force the ball through seat #1. Pressure waves will travel both ways from seat #1 as it closes and then yields.

On release the ball will immediately be slowed by the water to match the steady water flow rate. The ball will not overtake the water it is immersed in because the energy of the yield will travel away also as pressure waves in the water. The ball will take the same time as the water to reach seat #2. I'm not going to convert your mixed units. All dimensions should be presented in SI metres and millimetres, not feet and inches.