Lecture assignment Classwork Calculate the pressure loss caused by passing 50 m3/s of air with a gallery resistance R = 0.1 Ns2m-8. Suppose that it is possible to parallelize two galleries, each with R = 0.1 Ns2m-8, what is the pressure drop by 50 m3/s? Which is better between series and parallel connections of galleries for efficient air circulation? Why? Solutions 1) Given π = 50π3 /π , π π‘ = 0.1ππ 2 π−8 From πΉππππ‘πππππ ππππ π π’ππ ππππ(π»π ) = π π‘ × π 2 (π»π ) = 0.1ππ 2 π−8 × (50π3 /π )2 π»π = 250ππ 2) Parallelize two galleries, Given π = 50π3 /π , π π‘ = 0.1ππ 2 π−8 , π 1 = π 2 = 0.1ππ 2 π−8 1 1 1 πΌπ ππππππππ, = + … √π ππ √π 1 √π 2 50π3 50π3 100π3 ππ = π1 + π2 = + = π π π 1 1 1 = + = 6.32 √π ππ √0.1 √0.1 π ππ = 0.025ππ 2 π−8 In a combination of two galleries in parallel, flow in the gallery 1 is given by. π 2 π 1 √ π1 = π 1 + √π 2 [ ππ = 50π3 π 1] πππ‘ππ ππ ππππππππ (π»π ) = π ππ × π 2 = 0.025ππ 2 π−8 × (100)2 = 250ππ Pressure drop in parallel by 0.025ππ 2 π−8 × (50)2 = 62.5ππ 50π3 /π , πππ‘ππ ππ ππππππππ (π»π ) = π ππ × π 2 = 3) Which is better between series and parallel connections of galleries for efficient air circulation? Why? In series, π π = π 1 + π 2 = 0.1 + 0.1 = 0.2ππ 2 π−8 πππ‘ππ ππ π πππππ (π»π ) = π ππ × π 2 = 0.2ππ 2 π−8 × (50)2 = 500ππ πππ‘ππ ππ ππππππππ (π»π ) = π ππ × π 2 = 0.025ππ 2 π−8 × (50)2 = 62.5ππ For efficient air circulation, parallel connection is better because it has minimal pressure losses as compared to series connection. For this case the pressure drop in series connection is eight times higher than parallel connection. Question 2 At a coal mine, methane is flowing at the rate of 0.00708 m3/s into the mine opening. The intake air is flowing through airway of 3.96 m wide at the velocity of 0.152 m/s. Determine the layering number and confirm whether the velocity is adequate to prevent layering. Solution Given ππ’ is the velocity of air=0.152 m/s; π is the width of the airway 3.96 m; and ππ is the methane flowrate=0.00708 m3/s and NL is layering number 1 ππ’ π 3 0.152π/π 3.96π 1/3 ππΏ = ( ) = ×( ) = 0.7 1.8 ππ 1.8 0.00708 An NL ≥ 5 is required to control layering in an airway, our NL=0.7<5. The velocity is not adequate to prevent layering.
