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Alexander Fernandes

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## Homework Statement

I want to design a closed tank with an orifice hole (that can be opened and closed remotely) at the bottom of the tank and model how the mass flow rate of liquid nitrous oxide changes with respect to time, as the liquid nitrous oxide leaves the tank due to a pressure difference across the orifice. I want to also try and stay away from using CFD software as complete accuracy is not really overly important here. I have seen a lot of problems online where they solve discharge problems but all seem to use pressurised gases and the Ideal Gas Law. My problem, however, involves a pressurised liquid or am I missing something.

Known Data:

Initial Tank Pressure (assumed Uniform)

Initial Tank Temperature (assumed Uniform)

External Pressure (let's assume atmospheric)

Orifice Diameter / Area

Tank Diameter / Area

Fluid Density

Tank length

Coefficient of Discharge

## Homework Equations

dm/dt = cd * Ao * rho * sqrt(2 * ((P(t)-Pa)/rho) - gh(t))

where:

dm/dt = mass flow rate

cd = coefficient of discharge

Ao = orifice cross-sectional area

rho = fluid density

P(t) = tank pressure as a function of time

Pa = atmospheric pressure

g = acceleration due to gravity

h(t) = head of fluid as a function of time

## The Attempt at a Solution

I have tried using Bernoulli's equation, shortly after realising that the problem might be unsteady-flow and that the fluid might have to be considered compressible making the aforementioned formula useless. I also used the formula above which I derived from Bernoulli's equation assuming Quasi-steady flow but I'm not sure that is correct either.

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