A straight tube, closed at one end and open at the other end, contains a stoichi

Question

A straight tube, closed at one end and open at the other end, contains a stoichiometric CH4-air mixture at 300 K and 1 atm. The mixture is ignited at closed end, causing a planar deflagration to propagate down the tube toward the open end.

Calculate the speed of the unburned gas relative to the tube wall. Assume that the gas density decreases by a factor of 7 as a result of combustion and that viscous effects are negligible. The laminar flame speed is SL = 44 cm/s.

Hint: Apply conservation of mass to an appropriate control volume.estion...

Explanation / Answer

here CH4 gas is used .. CH4 +O2 ----- Co2 +H20

as we can clearly see

.. unburnt gas(containing carbon and hydrogen only ) has less density than the burnt gas(containg oxygen carbon N etc)..

conserving mass

area is same

1 denotes unburnt , where 2 denotes burnt

v1* rho1*a1 =v2 rho2 *a1

hence v1* =v2(rho2/rho1) =44*7 =308 =velocity of unburnt gas

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