HW1s - dm dt = m-m sys in inflows out outflows & &...

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Spring 2006 1 ME 201 Thermodynamics Homework #1: Conservation of Mass Solution 1. Describe mass conservation for a real world system such as the human body or a jet aircraft engine. (5 pts) Solution: Various answers possible 2. During an attack, the asthma sufferer actually accumulates air in his/her lungs causing great difficulty in respiration. A critical point comes when the accumulated air fills 75% of the lung capacity at which time medication becomes essential. The volume of lungs may be taken to be 0.006 m 3 and the air intake is 1.26 x 10 -6 kg/s with only 85% of the intake exhausted during an attack. Determine the time it takes from the onset of an attack to the critical point when medication becomes essential. You may take the density of air to be 1.3 kg/m 3 . (10 pts) Solution: Let’s begin by writing our complete conservation of mass equation,
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Unformatted text preview: dm dt = m-m sys in inflows out outflows & & ∑ ∑ We recognize that we have only one inflow (air intake) and just one outflow (exhaust). We can explode the derivative in to a difference and re-write the equation as m ( t) - m (0) t = m- m sys sys in out Δ Δ & & Solving for Δ t Δ Δ t = m ( t) - m (0) m- m sys sys in out & & ME 201 Thermodynamics Spring 2006 2 Now evaluating our masses and mass flows & m = 1.26 x 10 kg / s in-6 ( ) & & m = (0.85)m = (0.85) 1.26 x 10 = 1.07 x 10 kg / s out in-6-6 & m (0) = 0 kg sys (assume no air initially stored in the lungs) & m ( t) = 75% lung capacity = 75% density of air volume capacity of lungs = (0.75)(1.3)(0.006) = 5.85 x 10 kg sys-3 Δ × × Now substituting we find hr 8.6 = s 30,952 = 10 x 1.07-10 x 1.26-10 x .85 5 = t 6-6--3 Δ...
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This note was uploaded on 07/25/2008 for the course ME 201 taught by Professor Somerton during the Spring '06 term at Michigan State University.

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HW1s - dm dt = m-m sys in inflows out outflows & &...

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