# How long will it take for compressed air to reach 29 psi?

A large tank filled with air is compressed to 49 PSI. A valve is open and air escapes through the hole (d = 0.04 ft) to the atmosphere. How long will it take for the compressed air to reach 29 PSI.
Assume constant temperature.

Not exactly sure how to approach this problem since the flow rate will change as the pressure changes.
I've been trying to use Bernoulli's Equation to get velocity and therefore flowrate, but that is instantaneous velocity so it doesn't help much. If anyone could point me in the right direction that would be much appreciated.

## Answers and Replies

anorlunda
Staff Emeritus
Is this homework?

No it isnt homework, just something Im working on

JBA
Science Advisor
Gold Member
The volume of the tank is required to calculate the time. What is the volume of the tank?

The volume of the tank is required to calculate the time. What is the volume of the tank?
Volume of tank is 1050 gal or 140.365 cubic ft

JBA
Science Advisor
Gold Member
Based upon the information given plus the tank volume and an assumed or known air temperature this is the way I would approach solving the problem.

It appears that the 29 psi minimum has been carefully selected because it is just above the point that the orifice flow would transition from sonic flow to subsonic flow for an orifice discharging to atmosphere (14.7 psi) . As a result, the orifice sonic flow rate equation can be used to calculate the discharge rate at both pressures; and, since flow rate vs pressure is linear for sonic orifices and constant temperature is to be assumed, then average of the flow rates at 49 to 29 psi can be used for the entire discharge period.
Once that rate is determined, then what remains is to calculate the volume of air in the tank at the two pressures, again assuming constant temperature, to determine the vessel's air volume loss.
With the air volume loss and the average loss rate (average orifice flow) determined, it is simple to calculate the time required.