[試題] 107-2 葛煥彰 流體力學及操作 期末考
課程名稱︰流體力學及操作
課程性質︰化工系大二必修
課程教師︰葛煥彰教授
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰ 2019/06/18
考試時限（分鐘）： 100分鐘
試題 :
Closed Book(70%)
1.(15%)
At the entrance region of a laminar flow in a straight pipe, the transition
length for the fluid flow (uniform at the entrance) to be fully developed is
roughly proportional to the product of the diameter of the pipe and the
Reynolds number. Pleaase give an explanation (mathematical derivation) based on
the boundary layer theory for flow over a flat plate.
2.(25%)
A packed bed is composed of identical cylinders having a diameter D = 0.030m
and a length l=D. The bulk density of the overall packed bed is 960 kg/m3
and the density of the solid cylinder is 1600 kg/m3
(a) Calculate the sphericity (shape factor) of the cylindrical particles.
(b) Calculate the void fraction of the bed.
(c) Calcualte the specific surface area of the bed.
3.(30%)
Conider the scale-up from a small-scale agitation tank 1 to a full-scale tank 2
in geometric similarity for the same fluid. A scale-up rule n_2 = n_1*R^(-a)
must be selected to determine the rotation speen n_2 to duplicate the small-
scale results using n_1, where R is the scale-up ratio (=D_2 / D_1 , and D is
the impeller diameter). Determine α, respectively, when each of the following
quantities is constant in the scale-up:
(a) the Froude number; (7%)
(b) the impeller tip speed (v_θ at r = D/2) (7%)
(c) the power per unit volume (for the turbulent case, where the power number
N_p = P/(n^3 D^5ρ) = constant); (7%)
(d) the power per unit volume (for the laminar case, where N_p*Re = constant)
Open Books(30%)
4. For the fully developed flow of water at room temperature in a 10 cm ID
smooth pipe at a rate of 6.4x10^-3 m^3/s, determine using the universal
velocity distribution:
(a) thickness of the laminar sublayer,
(b) thickness of the buffer layer,
(c) thickness of the turbulent layer,
(d) the velocity of fluid at the outer rage of the laminar sublayer,
(e) the maximum velocity,
(f) the shear stress at wall, and
(g) the local shear stress at the hypothetical junction of the turbulent core
and the buffer layer.
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