[Dr. Raymond AB]

Please help. Consider the case of a system made up of:***

1. A rectangular pipe of area A (breadth B and width W) and length L and open to ambient air (at STP: 101 KPa and 288K) at one end and connected to an on/off valve at the other end,
2. An on/off valve connected the end of the rectangular pipe to instantaneously open or shut off the flow in the pipe when actuated,
3. A Pump/Blower of volumetric Discharge Q (about 7.079211 cubic meters per second rating) and back pressure P (about 4 KPa rating) connected to the on/off valve opposite the side of the on/off valve connected to the pipe.

The blower has already been running while the valve was closed. The valve is then suddenly opened to enable flow through the pipe to the blower. For the purposes of applying Steady Flow Equations, when (a time in seconds measured from the moment the valve is*opened and expressed in terms of the parameters above, e.g. 0.0001L/(Q/A) ) can it be considered that Steady Flow has developed?

Thanks in anticipation of the help.

[mczero57]

Raymond,

Thanks for an interesting problem ! One comment - when you say a blower at one end, it is not blowing air into the pipe but sucking air out of the pipe.

So, if you assume incompressible (density = constant) flow, the time scale is the time taken for a fluid particle to traverse the length of the tube which is L*A/Q and we could guess that steady state is achieved for t > 5L*A/Q (say).

If, however, the air is compressible the physics is different. As soon as the valve is opened, an expansion fan travels from the valve end to the open end and is reflected back. The time scale here is L/a, where a = speed of sound. So, in this case, steady state will be achieved when t > 5 L/a

Hope that helps.

Sam