How Do You Calculate Air Flow Velocity Between Two Tanks?

[supernova1387]

This might be simple but I can't remember how to do it.

problem: we have 2 tanks. One filled with atmospheric air at 1 bar and the other is vacuum. The two tanks are connected by a rigid pipe which has a valve. I open the valve and air flows to the vacuum tank. How do I calculate the air velocity?

P.s: I don't think Bernoulli is valid here because the flow isn't steady I guess. Please state your assumptions clearly.

Thanks in advance

 

[Baluncore]

Flow velocity depends on the thickness and length of the pipe, and on the temperature of the air.

 

[SteamKing]

Instead of 'thickness' of the pipe, the term 'internal diameter' would be more apt.

 

[boneh3ad]

Also pay attention to the pressures. The flow is going to start off choked but will eventually un-choke as the pressures equalize.

 

[PJC01]

To calculate the flow velocity in this scenario, we can use the equation for ideal gas flow through a pipe, which is given by:

v = (2*(P1-P2)/ρ)^0.5

Where:
v = flow velocity
P1 = initial pressure (1 bar for the atmospheric tank)
P2 = final pressure (0 bar for the vacuum tank)
ρ = density of the gas (in this case, air)

Assuming the pipe is horizontal and the flow is adiabatic (no heat transfer), we can also use the ideal gas law to determine the density of the air at both tanks.

Using the ideal gas law (PV = nRT), we can calculate the number of moles of air in each tank, assuming the volume of the tanks and the temperature are constant. Then, we can use the molar mass of air to convert moles to mass, and finally, use the density equation (ρ = m/V) to determine the density of air at each tank.

Once we have the density values, we can plug them into the flow velocity equation and solve for v. It's important to note that this equation assumes steady flow and neglects any frictional losses in the pipe. If these assumptions are not valid, the flow velocity may be slightly different from the calculated value. Additionally, the valve opening time and the length and diameter of the pipe may also affect the flow velocity.