# Flow between pressure vessels

• fjalla
In summary, the conversation discussed the problem of calculating the flow rate and pressure in two gas pressure vessels connected by a pipe until equilibrium is reached. The suggested approach involved breaking the problem into time steps and using the perfect gas law and compressibility factor to determine the flow rate and new pressures in each vessel. The process is repeated until the two vessel pressures are equal, with the total time being the sum of all the time steps.

#### fjalla

I have two pressure vessels containing gas at different initial pressure and connected by a pipe. I know the initial condition in both vessels and I have to calculate the flow rate and the pressure in the two vessels over time until equilibrium is reached. Do you have any suggestions?

Welcome to PF !

I would break the problem into time steps. Here is the basic procedure:

a) During the time step, assume the pressures in the two vessels are constant and figure out the flow rate.

b) Multiply the flow rate in Step 'a' by the timestep. This will be the quantity of gas that flowed during the time step.

c.1) Subtract the mass determined in Step 'b' from the higher pressure vessel.

c.2) Determine the new (lower) pressure in the higher pressure vessel with the perfect gas law. The pressure is lower since mass has left the vessel. Use the 'Z' compressibility factor if needed.

d.1) Add the mass determined in Step 'b' to the lower pressure vessel.

d.2) Determine the new (higher) pressure in the lower pressure vessel with the perfect gas law. The pressure is higher since mass has entered the vessel. Use the 'Z' compressibility factor if needed.

e) Go To Step 'a'. The difference in pressures is now lower and so will be the flow rate. Repeat until the two vessel pressures are equal. Add up all the time steps and this is the total time.

## 1. What is flow between pressure vessels?

Flow between pressure vessels refers to the movement of fluids or gases from one vessel to another due to a difference in pressure. This flow can occur through pipes, valves, or other connecting mechanisms.

## 2. What factors affect the flow between pressure vessels?

The flow between pressure vessels is influenced by several factors, such as the pressure difference between the vessels, the size and length of the connecting pipes, the viscosity of the fluid, and the presence of any obstacles or restrictions in the flow path.

## 3. How is the flow rate between pressure vessels calculated?

The flow rate between pressure vessels can be calculated using the Bernoulli's equation, which takes into account the fluid's density, velocity, and pressure at different points along the flow path. Other factors, such as the fluid's viscosity and the vessel's geometry, may also affect the flow rate.

## 4. What is the significance of understanding flow between pressure vessels?

Understanding flow between pressure vessels is essential in various industries, such as chemical processing, oil and gas, and manufacturing. It helps engineers and scientists design safe and efficient systems for transporting fluids or gases between vessels while minimizing energy consumption and ensuring the stability of the vessels.

## 5. How can the flow between pressure vessels be controlled?

The flow between pressure vessels can be controlled through various methods, such as adjusting the pressure difference between the vessels, changing the diameter of the connecting pipes, or using valves to regulate the flow rate. Additionally, flow sensors and control systems can be used to monitor and adjust the flow between vessels automatically.