Problem 6.19 - Problem 6.19 [Difficulty: 3] Given: Diffuser...

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Problem 6.19 [Difficulty: 3] Given: Diffuser geometry Find: Acceleration of a fluid particle; plot it; plot pressure gradient; find L such that pressure gradient is less than 25 kPa/m Solution: The given data is D i 0.25 m = D o 0.75 m = L1 m = V i 5 m s = ρ 1000 kg m 3 = For a linear increase in diameter Dx () D i D o D i L x + = From continuity QV A = V π 4 D 2 = V i π 4 D i 2 = Q 0.245 m 3 s = Hence Vx π 4 2 Q = 4Q π D i D o D i L x + 2 = or V i 1 D o D i LD i x + 2 = The governing equation for this flow is or, for steady 1D flow, in the notation of the problem a x V x V d d = V i 1 D o D i i x + 2 x V i 1 D o D i i x + 2 d d = Hence a x x 2V i 2 D o D i D i L 1 D o D i D i L x + 5 = This can be plotted in Excel (see below) From Eq. 6.2a, pressure gradient is x p ρ a x = x p 2 ρ
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Problem 6.19 - Problem 6.19 [Difficulty: 3] Given: Diffuser...

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