Pressure drop w.r.to time through a orifice dia(D) in a container of volume (V)

[Jothiram80]

Let initial preasure (P) = 10 bar,volume of container (V)=100000 cubic cm.
At what time period pressure will become 5 bar.

 

[Andrew Mason]

Let initial preasure (P) = 10 bar,volume of container (V)=100000 cubic cm.
At what time period pressure will become 5 bar.

What kind of a substance is in the container? A gas or a liquid? If it is a gas, is it an ideal gas? Is it escaping against atmospheric pressure of 1 bar?

AM

 

[haruspex]

I make no guarantees for the correctness of this, but here's what I got.
Let vol of tank be V, pressure P(t), mass remaining in tank m(t), outlet area A, exit velocity f(t).
In time dt, a volume A*f.dt, mass (Afm/V).dt, exits.
Assuming adiabatic expansion:
P(t+dt)(V+Af.dt)^γ = P(t)V^γ, where γ = 1.4
whence
P' = -P^γAf/V
m' = -fAm/V
By conservation of energy
(P-Pa)Af.dt = Af³m.dt/2V
where Pa is ambient pressure.
I forgot about Pa at first, and obtained
(γ-1)At = ((P₀/P)^(1-γ)/2γ - 1)√(2Vm₀/P₀)
where P₀ = P(0), m₀ = m(0).
I might try to correct that tomorrow.