Flow rate of fluid at a burst leakage in a pipeline due to over pressurization

[Rizkyffq]

TL;DR Summary

Flow rate of fluid at burst leakage in pipeline due over pressured

we have a project to how knowing the flow rate of fluid at the burst leakage due over pressured, probably to make it easier to understand i will attach some pictures of this mechanism.

Picture at above is simply mechanism of pipeline system that installed vertically, with fluid is mud and density of the fluid is approximation 1500 kg/m3. The pipeline system having dead end pipeline and fluids generated by particular pump. If at the end of the pipeline there is a hole/orifice/leak that covered by something and that thing will open by over pressured from fluid inside of pipeline. we intended to make the end of pipeline that having hole/orifice/leak will burst due over pressure in case to make a burst flow rate for our research.

So we design that thing covered hole/orifice/leak will broke with pressure impacted it approximation in 4000 psi, so pump will produced flow rate and makes pressure inside the pipe line until 4000 psi. If thing that covered hole/orifice/leak already broken then we close the valve so there is no flow rate produces by the pump to pipeline, in this state there is no additional fluid that distribute to pipeline.

And automatically fluid inside pipeline will burst out from the pipeline with 4000 psi and because there is no additional pressure cause valve already close and pump stopped to distributing fluid then it is slowly become hydrostatic state.

it is simple if we calculate the flow rate in hydrostatic state because we just need to know height of fluid (head), but what we confusing now is to know how to calculate the initial flow rate when burst fluid started after covered hole/orifice/leak forced opened due over pressured from the inside (4000 psi).

is it right to use this equation to calculate the burst leakage flowrate ?

and additional question :
1. When hole/orifice/leak forced opened due over pressured, is it true the pressure that in intial is 4000 psi will drop drastically in seconds towards zero (hydrostatic pressure) ? assume that outside of pipeline there is empty space so fluid that leakaged will freely flows out.
2. does Q1 = Q2 (continuity) will works in this mechanism when the first second of burst leakage happens ? so let say the Q1 is 5 litre/s from the pump then the Q2 that out from the hole is also 5 litre/s ?

 

[BvU]

2. does Q1 = Q2 (continuity) will works in this mechanism when the first second of burst leakage happens ? so let say the Q1 is 5 litre/s from the pump then the Q2 that out from the hole is also 5 litre/s ?

Definitely not. Compare with your turbulent flow equation.

outside of pipeline there is empty space

Best you can do inside the pipe is empty space too (i.e. vacuum). In other words: once the disk bursts, the pipe will empty itself completely.

 

[Tom.G]

How about a pressure sensor at the top of the pipe that shuts off the pump when the pressure drops? You will probably need a manual switch to start the pump at the start of the pressure cycle.

 

[Rizkyffq]

Best you can do inside the pipe is empty space too (i.e. vacuum). In other words: once the disk bursts, the pipe will empty itself completely.

yes, we also assumed like that too. so after disk burst because there is no fluid distribution because valve already closed and stoping distributing fluid from pump then 4000 psi will drop quickly to hydrostatic pressure.

the problem is i want to know how i can calculate the flow rate that occurs at disk burst before it becomes hydrostatic pressure ? cause isit make sense that the burst leakage will be having supersonic speed in very short time ?

 

[Rizkyffq]

How about a pressure sensor at the top of the pipe that shuts off the pump when the pressure drops? You will probably need a manual switch to start the pump at the start of the pressure cycle.

About that we assume that the valve will adjust in manually, what we concerned is the flow rate that occurs at the time burst leakage happens. how to calculate the flow rate at the time burst ?

 

[jrmichler]

When hole/orifice/leak forced opened due over pressured, is it true the pressure that in intial is 4000 psi will drop drastically in seconds towards zero (hydrostatic pressure) ? assume that outside of pipeline there is empty space so fluid that leakaged will freely flows out.

At the instant of hole opening, the flow rate is calculated from 4000 PSI (minus any back pressure), the hole area, and the orifice coefficient.

When flow begins, the pressure will start to drop. The rate of pressure drop is a function of the amount of fluid, the bulk modulus of the fluid, and the elasticity of the pipe.

The final stage will be an equilibrium where the flow out is equal to the flow in from the pump, and the hydrostatic head will be constant at some height. That height is calculated by solving for the pressure at which the flow out equals the flow in.

Between the start of flow, and the final equilibrium flow, the problem needs a numerical solution.