Question

I am working on calculating pressure in a tank where the fluid is sitting at its vapor pressure. For example, imagine a 12 in diameter 100 L tank of nitrous oxide at room temperature (745 psi vapor pressure). This tank would be drained at 1 L/s from the liquid side, and some of the nitrous oxide would boil off in order to maintain vapor pressure, but would come at the cost of reducing the temperature and vapor pressure in the fluid.

How do I find what the final fluid temperature at drain would be (assuming no heat being input into the system)?

I was thinking there would be some combination of Antoine's, Clausius-Clapeyron, ideal gas law, and some derivation of an energy balance equation, but I am not too sure.

The experimental situation would literally be a tank (assume perfect insulation) that is filled with nitrous oxide, say a 100 L tank because it is arbitrary. This tank would then be drained through a choked orifice into the atmosphere. The flowrate at the start would be 1 L/s, but as pressure drops, would decrease in flowrate. I want to find out the ending pressure and temperature when the liquid would run out. Experimental data points to the tank draining from liquid before running out, similar to how a propane barbeque runs out of liquid and becomes cold with lower pressures.

Answer 1

To find the final fluid temperature at drain, you can use the ideal gas law and the energy balance equation. Given the initial conditions, you can substitute the values into the equation to calculate the final temperature.

Step-by-step explanation:

In order to find the final fluid temperature at drain, we can use the ideal gas law and the energy balance equation. Let's assume that the fluid in the tank is a perfect gas and behaves ideally. When the fluid is drained at a constant rate, the pressure and temperature in the tank will decrease over time. The decrease in pressure causes some of the fluid to boil off, which leads to a decrease in temperature and vapor pressure. To calculate the final fluid temperature, we can use the ideal gas law equation:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

Since the fluid is draining at a constant rate, we can assume that the volume is also decreasing over time. Therefore, we can express the ideal gas law equation as:

PCV = nRT

Where PC is the initial pressure, CV is the initial volume, and T is the final temperature.

We can rearrange this equation to solve for T:

T = (PCV)/(nR)

Given the initial conditions (PC, CV, and n), we can substitute the values into the equation to calculate the final temperature.