B. Air at room temperature escapes a house during the winter through a gap benea

Question

B. Air at room temperature escapes a house during the winter through a gap beneath a sliding glass door. The gap is 0.6mm high, 3m long and 50mm through to the great outdoors. The internal over-pressure developed in the house by the furnace/fan is only 0.05 psig. With no more information why would you expect the flow to be laminar? Assume the flow is laminar and use the results from A. above to compute the leakage rate from the house. Confirm whether the flow was laminar/turbulent and fully developed.

Explanation / Answer

0.05 psig = 345 Pa

Since the pressure difference is very less, hence the velocity will be very less. For a internal flow i.e. flow through holes or pipe with this much low pressure . The flow can be assumed to be laminar.

We can confirm this by calculating Reynolds no.

Velocity, v = ((350*2)/1.28)^(0.5) = 23.38 m/s

Now Reynolds No. = ((23.38*0.6*(10^-3)/(1.55*10^(-5))

= 905

Since < 2000, the flow is laminar

Therefore leakage rate is Q = ( 0.6 * 50 * 23.38 * (10^-6))

Q = .701 * 10^(-3) m3/sec

Q = .701 Litres/sec

As it is already confirmed that flow is laminar from the value of Reynolds no.

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