# Volumetric flow rate of nitrogen through relieving pressure regulator

• Gnardude
In summary, the conversation discusses how to calculate the upstream flow rate for a relieving pressure regulator on a nitrogen line. The method of using Boyle's law and treating the regulator as isenthalpic and the gas as non-ideal is suggested. The mixture of units used in the problem statement is also noted. The conversation also mentions the need for the spec sheet of the regulator and clarifies that it is a safety relief valve.
Gnardude
TL;DR Summary
Volumetric flow rate of nitrogen through relieving pressure regulator
Hello all,

I'm having trouble figuring out the volumetric flow rate upstream of a relieving pressure regulator used on a 1/4" OD nitrogen line. Upstream of the regulator P=100 PSIG and T=70F, while downstream P=80 PSIG and T=70F with downstream consumption at q=4 L/min or 0.91 SCFM (at std. T=70F, P=14.7 psia). My thoughts are to use boyles law, P1V1=P2V2 (ideal gas law), to calculate the upstream flow rate, which would equal 3.2 LPM not taking into account the flow leaving through the vent, however, I'm not too sure if the pressure regulator would impact the flow in anyway. Does anyone have an idea of how to calculate the upstream flow or if my method is correct? I currently don't have the spec sheet for the regulator, so I'm negating the flow through the vent until I have it tomorrow.

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Hello @Gnardude, !

Gnardude said:
I'm not too sure if the pressure regulator would impact the flow in anyway
That's often what it is used for !

If the vent flow can be neglected you can write a material balance and for isothermal expansion use Boyle.

Usually, though, a pressure regulator is treated as isenthalpic and the gas as non-ideal. Since the flow is small, I expect the correction is reasonably small too (do you agree @Chestermiller ?).

(PS what a horrible mixture of units !)

BvU said:
Hello @Gnardude, !

That's often what it is used for !

If the vent flow can be neglected you can write a material balance and for isothermal expansion use Boyle.

Usually, though, a pressure regulator is treated as isenthalpic and the gas as non-ideal. Since the flow is small, I expect the correction is reasonably small too (do you agree @Chestermiller ?).

(PS what a horrible mixture of units !)
You know the mass flow rate from the problem statement 0.91 SCFM. You also know the upstream pressure and temperature, so, including the non-ideality using the z-factor, you can get the upstream density. The volume flow rate upstream is equal to the mass flow rate divided by the upstream density.

BvU
Gnardude said:
...a relieving pressure regulator...

vent...pressure regulator,,,

I currently don't have the spec sheet for the regulator...
What's a "relieving pressure regulator"? A safety relief valve? If so, it should have a nameplate with its relief pressure and flow rate. Yes, I think we need to know the specs of that device/what exactly it is/is doing.

Lnewqban

## 1. What is the definition of volumetric flow rate?

The volumetric flow rate is the volume of fluid that passes through a given cross-sectional area per unit time. It is typically measured in units of volume per time, such as liters per second or cubic feet per minute.

## 2. How is the volumetric flow rate of nitrogen through a relieving pressure regulator calculated?

The volumetric flow rate of nitrogen through a relieving pressure regulator can be calculated by multiplying the cross-sectional area of the regulator by the velocity of the nitrogen gas. This can be further refined by taking into account factors such as pressure and temperature.

## 3. What is the purpose of a relieving pressure regulator in relation to the volumetric flow rate of nitrogen?

A relieving pressure regulator is designed to maintain a constant pressure in a system by adjusting the flow rate of gas. It ensures that the volumetric flow rate of nitrogen remains within a safe and stable range to prevent any potential hazards or damage to equipment.

## 4. How does the volumetric flow rate of nitrogen through a relieving pressure regulator impact the overall system?

The volumetric flow rate of nitrogen through a relieving pressure regulator is a critical factor in maintaining the stability and efficiency of a system. If the flow rate is too high, it can cause excessive pressure and potentially damage equipment. If it is too low, it can result in inadequate pressure and affect the performance of the system.

## 5. What are some factors that can affect the volumetric flow rate of nitrogen through a relieving pressure regulator?

The volumetric flow rate of nitrogen through a relieving pressure regulator can be affected by factors such as the size and design of the regulator, the pressure and temperature of the nitrogen gas, and any obstructions or restrictions in the system. It can also be influenced by changes in the surrounding environment, such as changes in altitude or weather conditions.

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